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ESL0001 - Behavior requirements and constraints

Field Value
Author(s) T.J.L. Schuijbroek, T. Wilschut
Reviewer(s) A.T. Hofkamp
Status Final
Type Standard (S)
Created 29-04-2019
Finalized 12-08-2019

Warning

This LEP's syntax enhancement is written using an EBNF syntax as opposed to the current PEG syntax since it was finalized before the switch.

Abstract

The Elephant Specification Language (ESL) is a language for creating highly structured multi-level system specifications. ESL version 1.0 is particularly suited to describe the static structure of a system. Modern systems, however, are usually dynamic in nature. Therefore, behavior requirements and constraints are introduced in this LEP. Behavior requirements and constraints can be used to describe the dynamic behavior of systems. That is, they describe when (under which conditions) what requirements must be satisfied and what constraints hold. The aim of behavior requirements and constraints is to provide additional detail in the system specifications. Additionally, we aim to enable engineers to automatically derive, visualize and analyze the dynamic dependency structure of systems. The dynamic dependency structure and underling behavior specifications are meant to serve as a structured starting point for modelling and implementing the dynamic behavior of systems.

Motivation

In ESL version 1.0 the static structure of a system can be neatly defined in terms of goal- and transformation-requirements that state the transfer and transformation of flows between and inside components. Those flows can be subject to design-requirements that state the static bounds on the values of flows. Similarly, properties of components, for example length and life-span, can be subject to design-requirements. Together, the goal-, transformation- and design-requirements describe the static structure of a system.

Modern engineering systems, however, are usually dynamic in nature. That is, they change behavior and/or state in response to stimuli such as operator input or changes in their environment. As such, there is a strong need to be able to specify when a system should exhibit what behavior. In other words, there is a strong need to be able to specify dynamic bounds on flows.

By adding behavior requirements and constraints to ESL we aim to provide additional detail and reduce ambiguity in design specifications describing the dynamic behavior of systems. Additionally, we aim to enable engineers to automatically derive, visualize and analyze the dynamic dependency structure of systems. The dependency structure and underlying behavior specifications are meant to serve as a structured starting point for modelling and implementing the dynamic behavior of systems.

Note

The concepts of behavior and state are not limited to the control domain. For example, thermal and mechanical responses of a system as a result of stimuli are considered to be behavior as well.

Rationale

In the literature, system behavior is often modeled in conjunction with system functions and system states. See, for example, the Function-Behavior-State model1, the Structure-Behavior-Function model23 and the requirements engineering book of Hull4. These models all have their own definitions of behavior, function and state.

In light of the literature and the flow based foundation of ESL, function, behavior and state are defined as:

  • Function: everything what a 'thing' must be able to do, i.e., all transfers and transformations of flow which a 'thing' must be able to perform.
  • Behavior: everything what a 'thing' must do in response to stimuli, i.e., when which flows need to be transferred and transformed in what quantity in response to stimuli. Stimuli are changes in (un)controllable flows (state changes).
  • State: description of the behavior of a 'thing' given certain bounded stimuli, i.e., what flows are being transferred and transformed in what quantity given certain bounded stimuli. A state change happens when a stimulus crosses the defined boundaries. For example, a sensor signal (information flow) switches from high to low.

Note

When following the state definition above, a state is a representation of the values of a set of flows within certain bounds. In ESL all flows are represented by variables. Bounds are variables as well. A state in ESL is specified as a variable bounded by other variables.

For example, the specification below contains three variables: door-open and door-closed of type state and door-sensor-voltage of type electrical-energy-flow.

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define type
  state is a boolean
  electrical-energy-flow is a real

world
  variables
    door-open, door-closed is a state
    door-sensor-voltage is an electrical-energy-flow

Here, the variable types enable a reader to easily distinguish the flow variable door-sensor-voltage and the state variables door-open and door-closed. Such a distinction at type level is currently sufficient for the goal of ESL to provide a structured starting point for modelling and implementing the dynamic behavior of systems.

The dynamic behavior itself, however, cannot be described within ESL version 1.0. At best, one can specify a sensor-door-behavior-model relation with variables door-open, door-closed and door-sensor-voltage as arguments, as shown in the example below.

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relation
  door-sensor-behavior: sensor-door-behavior-model with arguments ...
    door-open, door-closed, door-sensor-voltage

Here, relation door-sensor-behavior indicates that there exists a dependency between arguments door-open, door-closed and door-sensor-voltage. The relation contains no information on what behavior should be modeled or implemented. With the addition of behavior requirements and constraints we aim to provide additional structured information on the input-output relation between these arguments.

Syntax rationale

In the literature one can find many boilerplates for behavior requirements, see for example these references256. In general, boilerplates have a "when < A > then < B >" like structure. The when keyword indicates a set of conditional statements A that indicate under which conditions requirement set B must be satisfied.

Furthermore, behavior requirements usually describe a set of alternative cases. Such requirements follow a "when < A1 > then < B1 > or ... or when < An > then < Bn >" structure. The order of the cases in such a requirement is usually meaningless. That is, the order of case specification does not impose any precedence constraints.

Following the literature, the behavior syntax as shown in the example below is proposed. In this example, a behavior requirement named door-state is specified. The requirement comprises the two cases door-is-closed and door-is-open. The case order has no semantics. Each case is composed of when-clauses and then-clauses. The when-clauses state the conditions under which the then-clauses apply. That is, when condition c1 holds then requirements r1 an r2 must be satisfied. When condition c2 holds requirements r3 and r4 must be satisfied.

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behavior-requirement
  door-state:
    case door-is-closed:
      when
        * c1: door-sensor-voltage is greater than 0.9 V
      then
        * r1: door-open must be equal to False
        * r2: door-closed must be equal to True

    case door-is-open:
      when
        * c2: door-sensor-voltage is at most 0.9 V
      then
        * r3: door-open must be equal to True
        * r4: door-closed must be equal to False

In writing behavior requirements one should strive for complete and deterministic requirements. Complete implies that the conditions cover the complete range of stimuli. Deterministic implies that only one case may apply simultaneously. Note that the example above is complete and deterministic as conditions c1 and c2 cover the full range of possible values of door-sensor-voltage and can never hold simultaneously.

Note

In the Completeness and determinism section we briefly explore to possibilities for the compiler to automatically check for completeness and determinism.

Fall-back cases

In striving for completeness, exhaustively specifying all possible cases may become a cumbersome and time consuming task. As such, it is desirable to be able to specify a fall-back case. A fall-back case is similar to the else construct used in many programming languages.

A special when no other case applies clause is used to enable users to specify fall-back cases. The example below specifies behavior requirement output-x which contains cases A, B and C. Case C is the fall-back case that applies when neither A nor B applies. In other words, C applies when y is at least 5 and at most 10.

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behavior-requirement
  output-x:
    case A:
      when
        * c1: y is smaller than 5
      then
        * r1: x must be at most 5
    case B:
      when
        * c2: y is larger than 10
      then
        * r2: x must be at most 10
    case C:
      when no other case applies
      then
        * r3: x must be equal to 0

Note that the when no other case applies when-clause is a short-hand notation for negation of the when-clauses of case A and B.

Behavior, goal and transformation specifications

Behavior specifications are complimentary to goal and transformation specifications. In fact, the addition of behavior requirements allows for more natural transformation specifications. For example, assume we have the following three goal-requirements:

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goal-requirements
  send-control-signal: motor-controller must send motor-control-signal to motor
  provide-power: power-supply must provide power to motor
  provide-torque: motor most provide torque to pump

which are dependent on one another. In ESL version 1.0 one has to define a transformation-requirement convert-power, as shown below, to ensure that goal provide-torque has a functional dependency with goals send-control-signal and provide-power.

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define component ElectricMotor
  parameters
    motor-control-signal is an information-flow
    power is an electrical-energy-flow
    torque is a mechanical-energy-flow

  transformation-requirement
    convert-power: must convert motor-control-signal and power into torque

Physically, however, motor-control-signal is not really transformed into torque by motor. As such, transformation requirement convert-power may seem flawed by readers.

By adding a behavior-requirement, as shown in the listing below, one can separate the physical function of transforming power into torque from the logical behavior that motor must only provide torque when needed.

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define component ElectricMotor
  parameters
    motor-control-signal is an information-flow
    power is an electrical-energy-flow
    torque is a mechanical-energy-flow

  transformation-requirement
    convert-power: must convert power into torque

  behavior-requirement
    motor-behavior:
      case motor-on:
        when
          * c1: motor-control-signal is equal to 'on'
        then
          * r1: torque must be equal to 60 NM
      case motor-off:
        when
          * c2: motor-control-signal is equal to 'off'
        then
          * r2: torque must be equal to 0 NM

That is, variable motor-control-signal is no longer an input argument of convert-power. Instead, it is the subject of conditions c1 and c2. This implies that the desired value of torque, which is an output argument of convert-power, is conditionally dependent on the value of motor-control-signal. Consequently, goal provide-torque torque has a functional dependency on goal provide-power and a behavior dependency on send-control-signal. Since power is needed to provide torque and motor-control-signal denotes when torque must be provided.

Specification

In this section the formal syntax and dependency derivation rules are given and discussed.

Syntax

The Syntax definition below shows the syntax of an ESL behavior section in Extended Backus-Naur Form (EBNF). A behavior section starts with a behavior type keyword, either behavior-requirement or behavior-constraint, followed by a new line. The next line starts with a behavior-NAME, i.e., the identifier of the behavior statement, followed by a colon, a behavior-clause and a new line. Such a pattern is repeated one or more times. A behavior-clause starts with the keyword case followed by a CASE-NAME, a colon and a new line. On the new line one may find a regular-case-clause or a fall-back-case-clause. This pattern may repeat itself one or more times. A behavior-clause may contain at most one fall-back-case-clause.

A regular-case-clause is composed of a when-clause followed by a then-clause. The when-clause states the case conditions and is composed of the keyword when followed by a new line. The new line starts with a CASE-CONDITION-NAME followed by a colon, a design-rule-line and a new line. A when-clause must contain at least one condition.

A then-clause states the case design-rules and starts with the keyword then followed by a new line, a CASE-RULE-NAME, a colon, a design-rule-literal and a new line. Each then-clause must contain at least one design rule. The then-clauses of the cases within the scope of a behavior-requirement must have the same set of subject variables.

A fall-back-case-clause starts with the keyword sequence when no other case applies and a new line where one finds a then-clause.

Syntax definition

Behavior syntax proposal
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behavior-section ::=
    behavior-type \n
    {
        behavior-NAME ":" \n
        behavior-clause
    }+

    behavior-type ::=
    "behavior-requirement" | "behavior-constraint"

    behavior-clause ::=
    {
        "case" CASE-NAME ":" \n
        (
        regular-case-clause
        |
        fall-back-case-clause
        )
    }+ (*At most one fall-back-case-clause per behavior-clause.*)

    regular-case-clause ::=
    when-clause
    then-clause

    when-clause ::=
    "when" \n
        { CASE-CONDITION-NAME ":" design-rule-line \n }+ (*Only 'is' as auxiliary verb.*)

    then-clause ::=
    "then" \n
        { CASE-RULE-NAME ":" design-rule-literal \n }+

    design-rule-line ::=
    design-rule-literal
    {
        "or" design-rule-literal
    }

    fall-back-case-clause ::=
    "when" "no" "other" "case" "applies" \n
    then-clause

Dependency derivations

This section describes the formal derivation rules that are used to derive 'behavior dependencies' between components, goals, transformations, behaviors, variables and combinations thereof. These dependencies are an addition to the function, design and coordination dependencies described in the Dependency derivations section of the ESL reference documentation.

Definitions

Let \(\mathcal{H}\) be the set of all behavior specifications (requirements and constraints) within an instantiated ESL specification. Let a single behavior specification \(h \in \mathcal{H}\) be given by:

\[h = \{ A_1, A_2, \ldots, A_n \}\]

where, \(n\) is the number of cases in \(h\) and \(A_{i}\) is case \(i\). Now note that the when- and then-clauses are syntactically equal to subclauses which are defined in the Dependency derivation section of the ESL reference documentation. As such, a case \(A\) is given by:

\[A = (S, S')\]

where \(S\) and \(S'\) denote the when-clauses and then-clauses, respectively, and are sets of design rule lines \(Q\). A design rule literal \(q \in Q\) is given by:

\[q = (v, b)\]

where \(v\) is the subject variable and bound \(b\) which may be a variable or real, integer, boolean or string value.

Behavior dependencies between variables

In ESL, behavior is expressed in terms of flows which are represented by variables. Therefore, behavior dependencies between variables are the most fundamental behavior dependencies. Behavior dependencies between other ESL elements, such as components and goals, can be derived from the behavior dependencies between variables.

Following the definitions provided in the previous section, the set of behavior dependencies between variables \(E_{\mathrm{v_b}}\) is given by:

\[ \begin{aligned} \begin{array}{rclcl} E_{\mathrm{v_b}} & = & \{ (v, v') & \mid & (S, S') \in h, h \in \mathcal{H}, \\ & & & & (v, b) \in Q, Q \in S, \\ & & & & (v', b') \in Q', Q' \in S'\} \end{array} \end{aligned} \]

That is, \(E_{\mathrm{v_b}}\) consists of all variable pairs \((v, v')\) for which there exist a design-rule \((v, b)\) within design rule line \(Q\) within when-clauses \(S\) and a design-rule \((v', b')\) within design-rule-set \(Q'\) within then-clauses \(S'\). In other words, if there exists a case in which the value of \(v'\) is bound by the the value of \(v\).

Behavior dependencies between components

The set of behavior dependencies between variables \(E_{\mathrm{v_b}}\) can used to derive the set of behavior dependencies between components \(E_{\mathrm{c_b}}\), which is given by:

\[ \begin{aligned} \begin{array}{rclcl} E_{\mathrm{c_b}} & = & \{ (c_i, c_j) & \mid & (c_i, c'_i, V_i, S_i) \in \mathcal{G}, (c_j, c'_j, V_j, S_j) \in \mathcal{G}, \\ & & & & v_i \in V_i, v_j \in V_j , \exists path(v_i, v_j, E_{\mathrm{v_b}}), \\ & & & & \forall v_k \in path(v_i, v_j, E_{\mathrm{v_b}}), v_k \neq v_i, v_k \neq v_j, \\ & & & & (v, t) \notin M, (v, g) \notin M, t \in \mathcal{T}, g \in \mathcal{G} \} \\ & \cup & \{ (c_i, c_j) & \mid & (c_i, V_i, V'_i, S_i) \in \mathcal{T}, (c_j, V_j, V'_j, S_j) \in \mathcal{T}, \\ & & & & v_i \in V'_i, v_j \in V'_j , \exists path(v_i, v_j, E_{\mathrm{v_b}}), \\ & & & & \forall v_k \in path(v_i, v_j, E_{\mathrm{v_b}}), v_k \neq v_i, v_k \neq v_j, \\ & & & & (v, t) \notin M, (v, g) \notin M, t \in \mathcal{T}, g \in \mathcal{G} \} \\ & \cup & \{ (c_i, c_j) & \mid & (c_i, c'_i, V_i, S_i) \in \mathcal{G}, (c_j, V_j, V'_j, S_j) \in \mathcal{T}, \\ & & & & v_i \in V_i, v_j \in V'_j , \exists path(v_i, v_j, E_{\mathrm{v_b}}), \\ & & & & \forall v_k \in path(v_i, v_j, E_{\mathrm{v_b}}), v_k \neq v_i, v_k \neq v_j, \\ & & & & (v, t) \notin M, (v, g) \notin M, t \in \mathcal{T}, g \in \mathcal{G} \} \\ & \cup & \{ (c_i, c_j) & \mid & (c_i, V_i, V'_i, S_i) \in \mathcal{T}, (c_j, c'_j, V_j, S_j) \in \mathcal{G}, \\ & & & & v_i \in V'_i, v_j \in V_j , \exists path(v_i, v_j, E_{\mathrm{v_b}}), \\ & & & & \forall v_k \in path(v_i, v_j, E_{\mathrm{v_b}}), v_k \neq v_i, v_k \neq v_j, \\ & & & & (v, t) \notin M, (v, g) \notin M, t \in \mathcal{T}, g \in \mathcal{G} \} \\ \end{array} \end{aligned} \]

wherein, the first set of component pairs denotes those pairs \(c_i\) and \(c_j\) for which there exist a goal \((c_i, c'_i, V_i, S_i) \in \mathcal{G}\) and a goal \((c_j, c'_j, V_j, S_j) \in \mathcal{G}\) such that there exists a path over the set of behavior dependencies between variables \(E_{\mathrm{v_b}}\) between a variable \(v_i\) in \(V_i\) and a variable \(v_j\) in \(V_j\), such that all intermediate variables \(v_k\) part of this path do not relate to any other transformation \(g\) or transformation \(t\). In other words, the value of a flow to be transferred by component \(c_j\) is bound by the value of a flow to be transferred by component \(c_i\), without any transformations or goals in between.

The second set of component pairs denotes those component pairs \(c_i\) and \(c_j\) for which there exist a transformation \((c_i, V_i, V'_i, S_i) \in \mathcal{T}\) and a transformation \((c_j, V_j, V'_j, S_j) \in \mathcal{T}\), such that there exists a path over the set of behavior dependencies between variables \(E_{\mathrm{v_b}}\) between a variable \(v_i\) in \(V_i\) and a variable \(v_j\) in \(V_j\), such that all intermediate variables \(v_k\) part of this path do not relate to any other transformation \(g\) or transformation \(t\).

The third set of component pairs denotes those pairs \(c_i\) and \(c_j\) for which there exist a goal \((c_i, c'_i, V_i, S_i) \in \mathcal{G}\) and a transformation \((c_j, V_j, V'_j, S_j) \in \mathcal{T}\), such that there exists a path over the set of behavior dependencies between variables \(E_{\mathrm{v_b}}\) between \(v_i\) in \(V_i\) and a variable \(v_j\) in \(V'_j\) , such that all intermediate variables \(v_k\) part of this path do not relate to any other transformation \(g\) or transformation \(t\).

The fourth set is similar to the third set except here a flow in \(V_j\) is bound by an output flow in \(V'_i\).

Behavior dependencies between goals

The set of behavior dependencies between goals \(E_{\mathrm{g_b}}\) is given by:

\[ \begin{aligned} \begin{array}{rclcl} E_{\mathrm{g_b}} & = & \{ (g_i, g_j) & \mid & g_i = (c_i, c'_i, V_i, S_i) \in \mathcal{G}, \\ & & & & g_j = (c_j, c'_j, V_j, S_j) \in \mathcal{G}, \\ & & & & v_i \in V_i, v_j \in V_j, \exists path(v_i, v_j, E_{\mathrm{v_b}}), \\ & & & & \forall v_k \in path(v_i, v_j, E_{\mathrm{v_b}}), v_k \neq v_i, v_k \neq v_j, \\ & & & & (v, t) \notin M, (v, g) \notin M, t \in \mathcal{T}, g \in \mathcal{G} \} \\ \end{array} \end{aligned} \]

That is, \(E_{\mathrm{g_b}}\) contains all pairs of goals \(g_i\) and \(g_j\) for which there exists a path over the set of behavior dependencies between variables \(E_{\mathrm{v_b}}\) between a variable \(v_i\) in \(V_i\) and a variable \(v_j\) in \(V_j\), such that all intermediate variables \(v_k\) part of this path do not relate to any other transformation \(g\) or transformation \(t\). In other words, if at least one variable in \(V_j\) is bound by a variable in \(V_i\).

Behavior dependencies between transformations

Similar to goal behavior dependencies, the set of behavior dependencies between transformations \(E_{\mathrm{t_b}}\) is given by:

\[ \begin{aligned} \begin{array}{rclcl} E_{\mathrm{t_b}} & = & \{ (t_i, t_j) & \mid & t_i = (c_i, V_i, V'_i, S_i) \in \mathcal{T}, t_j = (c_j, V_j, V'_j, S_j) \in \mathcal{T}, \\ & & & & v_i \in V'_i, v_j \in V'_j , \exists path(v_i, v_j, E_{\mathrm{v_b}}), \\ & & & & \forall v_k \in path(v_i, v_j, E_{\mathrm{v_b}}), v_k \neq v_i, v_k \neq v_j, \\ & & & & (v, t) \notin M, (v, g) \notin M, t \in \mathcal{T}, g \in \mathcal{G} \} \\ \end{array} \end{aligned} \]

That is, transformation \(t_i\) has a behavior dependency with transformation \(t_j\) if there exists a path over the set of behavior dependencies between variables \(E_{\mathrm{v_b}}\) between a variable \(v_i\) in \(V'_i\) and a variable \(v_j\) in \(V'_j\), such that all intermediate variables \(v_k\) part of this path do not relate to any other transformation \(g\) or transformation \(t\). In other words, the the output of \(t_j\) is bound by the output of \(t_i\).

Behavior and coordination dependencies between behaviors

Finally, the set of dependencies between behaviors \(E_{\mathrm{h_b}}\) is given by:

\[ \begin{aligned} \begin{array}{rclcl} E_{\mathrm{h_b}} & = & \{ (h_i, h_j) & \mid & (S_i, S'_i) \in h_i, h_i \in \mathcal{H}, \\ & & & & (S_j, S'_j) \in h_j, h_j \in \mathcal{H}, \\ & & & & V'_i = \{ v \mid (v,b) \in Q', Q' \in S'_i \}, \\ & & & & V_j = \{ v \mid (v,b) \in Q, Q \in S_j \}, \\ & & & & V'_i \cap V_j \neq \emptyset, h_i \neq h_j \} \end{array} \end{aligned} \]

That is, two behaviors \(h_i\) and \(h_j\) have a behavior dependency if at least one variable that is used within then-clauses \(S'_i\) of \(h_i\) is used within when-clauses \(S_j\) of \(h_j\). Such a dependency implies that the result of \(h_j\) is bounded by the result of \(h_i\).

Similarly, coordination dependencies \(E_{\mathrm{h_c}}\) are given by:

\[ \begin{aligned} \begin{array}{rclcl} E_{\mathrm{h_c}} & = & \{ (h_i, h_j) & \mid & (S_i, S'_i) \in h_i, h_i \in \mathcal{H}, \\ & & & & (S_j, S'_j) \in h_j, h_j \in \mathcal{H}, \\ & & & & V'_i = \{ v \mid (v,b) \in Q', Q' \in S'_i \}, \\ & & & & V'_j = \{ v \mid (v,b) \in Q', Q' \in S'_j \}, \\ & & & & V'_i \cap V'_j \neq \emptyset, , h_i \neq h_j \} \end{array} \end{aligned} \]

That is, two behaviors \(h_i\) and \(h_j\) have a coordination dependency if at least one variable that is used within a then-clauses \(S'_i\) of \(h_i\) is used within a then-clauses \(S'_j\) of \(h_j\). Such a dependency implies that both behaviors aim to set the values of a least one shared variable.

Mapping relations

The mapping relations between behaviors and other ESL elements can simply be derived based on shared variables. Let \(v_Q\) be a function that collects all variables that are used within a design rule line \(Q\), and be given by:

\[v_Q\colon \mathcal{\mathcal{Q}} \rightarrow \mathcal{V} = \{v\ |\ (v,b)\in Q\}\]

Let \(v_h\) be a function that collects all variables used within a behavior requirement \(h\) and be given by

\[ v_h\colon \mathcal{H} \rightarrow \mathcal{V} = \{v\ |\ (v,b)\in Q, Q\in(S\cup S'), (S, S')\in h\} \]

Now the set of mapping relations of a behaviors is given by:

\[ \begin{aligned} \begin{array}{rcl} M_h & = & \{(c,h)\ |\ c=(V_c, N_c, C_c, G_c, T_c, D_c, R_c, H_c)\in\mathcal{C}, h\in \mathcal{H}, V_c\cap v_h(h) \not=\emptyset\} \\ & \cup & \{(g,h)\ |\ g=(c_g, c'_g, V_g, S_g)\in\mathcal{G}, h\in \mathcal{H}, V_g\cap v_h(h) \not=\emptyset\} \\ & \cup & \{(t,h)\ |\ t=(e_t, V_t, V'_t, S_t)\in\mathcal{T}, h\in \mathcal{H}, (V_t\cup V'_t)\cap v_h(h) \not=\emptyset\} \\ & \cup & \{(d,h)\ |\ d=(Q_d, S_d)\in\mathcal{D}, h\in \mathcal{H}, v_Q(Q_d)\cap v_h(h) \not=\emptyset\} \\ & \cup & \{(r,h)\ |\ r=V_r\in\mathcal{R}, h\in \mathcal{H}, V_r\cap v_h(h) \not=\emptyset\} \end{array} \end{aligned} \]

where \(\mathcal{C}\) is the set of all components, \(\mathcal{G}\) is the set of all goals, \(\mathcal{T}\) is the set of all transformations, \(\mathcal{D}\) is the set of all designs, \(\mathcal{R}\) is the set of all relations, and \(\mathcal{V}\) is the set of all variables over an instantiated ESL specification. \(V_c\) is the set of all variables used by component \(c\), \(V_g\) is the set of all variables used by goal \(g\), \(V_t\) and \(V'_t\) are, respectively, the sets of input and output variables of transformation \(t\), \(V_d\) is the set of all variables used by design specification \(d\), and \(V_r\) is the set of all variables used by relation \(r\).

Backwards Compatibility

Behavior requirements are an addition to ESL. No changes to existing language concepts are required. So backwards compatibility with respect to processing specifications written in ESL version 1.0 is not an issue.

The compiler output, however, contains additional behavior objects and and behavior dependencies. Post processing tools should be adapted to handle these objects and dependencies.

Proof of concept

In this section, four examples are shown which illustrate the usage of behavior-specifications.

The following examples build on some common types, verbs and a torque-curve-model relation. We start with a rudimentary specification without any behavior-requirements. The Example rudiments block shows an illustrative example containing a (wireless) switch and a (electric) motor. The switch must send a motor-control-signal to motor. The motor must internally convert power into torque.

Example rudiments

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define type
  control-signal is a string
  voltage is a real with unit V
  electrical-energy-flow
  mechanical-energy-flow with unit Nm
  state is a string


define verb
  send to
  convert into


world
  variables
    motor-control-signal is a control-signal

  components
    switch is a WirelessSwitch with arguments
      * motor-control-signal
    motor is an ElectricMotor with arguments
      * motor-control-signal

  goal-requirement
    send-control-signal: switch must send motor-control-signal to motor


define component WirelessSwitch
  parameter
    motor-control-signal is a control-signal


define component ElectricMotor
  parameter
    motor-control-signal is a control-signal

  variables
    power is an electrical-energy-flow
    torque is a mechanical-energy-flow

  transformation-requirement
    convert-power-into-torque: must convert power into torque

These lines are assumed to be given for each example and therefore left out of their respective code blocks.

Example 1

In ESL behavior is expressed in terms of (bounded) flows. In the code block below, a behavior-requirement is added for the electric-motor. There, the requirement motor-torque-output denotes that torque must equal to 60 Nm when motor-control-signal is equal to 'on'. When motor-control-signal is equal to 'off', torque must be equal to 0 Nm. Thus, this behavior-requirement denotes a logical dependency between the value of motor-control-signal and torque. Here the values of motor-control-signal and torque are both discrete.

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define component ElectricMotor
  ...
  behavior-requirement
    motor-torque-output:
      case motor-is-on:
        when
          * c1: motor-control-signal is equal to "on"
        then
          * r1: torque must be equal to 60.0 [Nm]
      case motor-is-off:
        when
          * c2: motor-control-signal is equal to "off"
        then
          * r2: torque must be equal to 0.0 [Nm]
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define type
  control-signal is a string
  voltage is a real with unit V
  electrical-energy-flow
  mechanical-energy-flow with unit Nm
  state is a string


define verb
  send to
  convert into


world
  variables
    motor-control-signal is a control-signal

  components
    switch is a WirelessSwitch with arguments
      * motor-control-signal
    motor is an ElectricMotor with arguments
      * motor-control-signal

  goal-requirement
    send-control-signal: switch must send motor-control-signal to motor


define component WirelessSwitch
  parameter
    motor-control-signal is a control-signal

# ---8<--- [start:defname]
define component ElectricMotor
# ---8<--- [end:defname]
  parameter
    motor-control-signal is a control-signal

  variables
    power is an electrical-energy-flow
    torque is a mechanical-energy-flow

  transformation-requirement
    convert-power-into-torque: must convert power into torque

# ---8<--- [start:behavior]
  behavior-requirement
    motor-torque-output:
      case motor-is-on:
        when
          * c1: motor-control-signal is equal to "on"
        then
          * r1: torque must be equal to 60.0 [Nm]
      case motor-is-off:
        when
          * c2: motor-control-signal is equal to "off"
        then
          * r2: torque must be equal to 0.0 [Nm]
# ---8<--- [end:behavior]

The figure below shows a component - function spec - behavior spec - variable multi-domain-matrix. The piecharts within the figure denote the logical dependencies and mapping dependencies that have been derived from the example specification.

Example 1's Component-Function-Behavior-Variable MDM showing logical dependencies.

Example 1's Component-Function-Behavior-Variable MDM showing logical dependencies.

Component motor logically depends on component switch (row 2, col 1) as the amount of torque the motor must produce depends on the control signal sent by the switch. This dependency is seen within the function domain as a logical dependency of transformation specification convert-power-into-torque on goal specification send-control-signal (row 3, col 4). Similarly, within the variable domain (rows, cols 6-8) one can see that variable torque logically depends on variable motor-control-signal.

Example 2

The previous Example 1 contains no information on when the value of motor-control-signal should be equal to 'on' or 'off'. In this example we added transformation-requirement convert-voltage-into-control-signal and behavior-requirement motor-control-signal-value. The transformation requirement denotes that switch must internally convert switch-circuit-voltage into motor-control-signal.

The behavior-requirement denotes that motor-control-signal must be equal to 'on' or 'off' depending on the switch-circuit-voltage value. That is, the moment the switch-circuit-voltage becomes above 1 V, for example by pressing the switch, motor will switch on and produce 60 Nm of torque. The moment the switch-circuit-voltage drops below 1 V, for example by releasing the switch, motor will turn off.

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define component WirelessSwitch
  parameter
    motor-control-signal is a control-signal

  variable
    switch-circuit-voltage is a voltage

  transformation-requirement
    convert-voltage-to-control-signal: must convert switch-circuit-voltage into motor-control-signal

  behavior-requirement
    motor-control-signal-value:
      case switch-motor-on:
        when
          * c1: switch-circuit-voltage is at least 1.0 [V]
        then
          * r1: motor-control-signal must be equal to "on"
      case switch-motor-off:
        when
          * c1: switch-circuit-voltage is smaller than 1.0 [V]
        then
          * r1: motor-control-signal is equal to "off"
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define type
  control-signal is a string
  voltage is a real with unit V
  electrical-energy-flow
  mechanical-energy-flow with unit Nm
  state is a string


define verb
  send to
  convert into


world
  variables
    motor-control-signal is a control-signal

  components
    switch is a WirelessSwitch with arguments
      * motor-control-signal
    motor is an ElectricMotor with arguments
      * motor-control-signal

  goal-requirement
    send-control-signal: switch must send motor-control-signal to motor


define component WirelessSwitch
  parameter
    motor-control-signal is a control-signal

# ---8<--- [start:defname]
define component ElectricMotor
# ---8<--- [end:defname]
  parameter
    motor-control-signal is a control-signal

  variables
    power is an electrical-energy-flow
    torque is a mechanical-energy-flow

  transformation-requirement
    convert-power-into-torque: must convert power into torque

# ---8<--- [start:behavior]
  behavior-requirement
    motor-torque-output:
      case motor-is-on:
        when
          * c1: motor-control-signal is equal to "on"
        then
          * r1: torque must be equal to 60.0 [Nm]
      case motor-is-off:
        when
          * c2: motor-control-signal is equal to "off"
        then
          * r2: torque must be equal to 0.0 [Nm]
# ---8<--- [end:behavior]

The figure below shows the updated MDM showing logical dependencies between components, function specs, behavior specs and variables which are derived from behavior specs motor-control-signal-values and motor-torque-output.

Example 2's Component-Function-Behavior-Variable MDM showing logical dependencies.

Example 2's Component-Function-Behavior-Variable MDM showing logical dependencies.

Note

Transformation-requirement convert-voltage-to-control-signal (row 3), behavior-requirement motor-control-signal-value (row 6), and variable switch-current-voltage are added to the MDM. Within the behavior-domain (rows, cols 6-7) one can see that behavior spec motor-torque-output depends on behavior spec motor-control-signal-value. Within the variable domain (rows, cols 8-11) one can see the logical dependency chain from switch-circuit-voltage to motor-control-signal to torque.

Example 3

In the previous Example 2 the desired of values of torque are discrete and time independent. In certain cases one may want to define continuous time dependent flow values. ESL has no time concept. Hence on cannot directly express time dependent flow values. However, one can make use of relations.

In the next code block the behavior requirement motor-torque-output is modified and behavior requirement motor-state-transitions, relation torque-curves, and variables start-up-curve and shut-down-curve are added to the specification.

Relation torque-curves returns variables start-up-curve and shut-down-curve which represent the continuous time dependent torque values during start-up and shut down of motor.

Behavior-requirement motor-state-transitions defines the different values of motor-state, being 'start-up', 'steady-state', 'shut-down', and 'off', depending on the values of torque and motor-control-signal.

Behavior-requirement motor-torque-output defines the desired (continuous) values of torque depending on the value of motor-state.

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define component ElectricMotor
  parameter
    motor-control-signal is a control-signal

  variables
    power is an electrical-energy-flow
    torque is a mechanical-energy-flow
    start-up-curve, shut-down-curve is a mechanical-energy-flow
    motor-state is a state

  transformation-requirement
    convert-power-into-torque: must convert power into torque

  behavior-requirement
    motor-state-transitions:
      case start-up:
        when
          * c1: motor-control-signal is equal to "on"
          * c2: torque is smaller than  60.0 [Nm]
        then
          * r1: motor-state must be equal to "start-up"
      case steady-state:
        when
          * c1: motor-control-signal is equal to "on"
          * c2: torque is at least  60.0 [Nm]
        then
          * r1: motor-state must be equal to "steady-state"
      case shut-down:
        when
          * c1: motor-control-signal is equal to "off"
          * c2: torque is greater than 0.0 [Nm]
        then
          * r1: motor-state must be equal to "shut-down"
      case off:
        when
          * c1: motor-control-signal is equal to "off"
          * c2: torque is equal to 0.0 [Nm]
        then
          * r2: motor-state must be equal to "off"

    motor-torque-output:
      case motor-start-up:
        when
          * c1: motor-state is equal to "start-up"
        then
          * r1: torque must be equal to start-up-curve
      case motor-is-in-steady-state:
        when
          * c1: motor-state is equal to "steady-state"
        then
          * r1: torque must be equal to 60.0 [Nm]
      case motor-shut-down:
        when
          * c1: motor-state is equal to "shut-down"
        then
          * r2: torque must be equal to shut-down-curve
      case motor-is-off:
        when
          * c2: motor-state is equal to "off"
        then
          * r2: torque must be equal to 0.0 [Nm]

  relation
    torque-curves: torque-curve-model
      returning arguments
        * start-up-curve
        * shut-down-curve


define relation
  torque-curve-model
    returning parameters
      * start-up-curve is a mechanical-energy-flow
      * shut-down-curve is a mechanical-energy-flow
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define type
  control-signal is a string
  voltage is a real with unit V
  electrical-energy-flow
  mechanical-energy-flow with unit Nm
  state is a string


define verb
  send to
  convert into


world
  variables
    motor-control-signal is a control-signal

  components
    switch is a WirelessSwitch with arguments
      * motor-control-signal
    motor is an ElectricMotor with arguments
      * motor-control-signal

  goal-requirement
    send-control-signal: switch must send motor-control-signal to motor


define component WirelessSwitch
  parameter
    motor-control-signal is a control-signal

  variable
    switch-circuit-voltage is a voltage

  transformation-requirement
    convert-voltage-to-control-signal: must convert switch-circuit-voltage into motor-control-signal

  behavior-requirement
    motor-control-signal-value:
      case switch-motor-on:
        when
          * c1: switch-circuit-voltage is at least 1.0 [V]
        then
          * r1: motor-control-signal must be equal to "on"
      case switch-motor-off:
        when
          * c1: switch-circuit-voltage is smaller than 1.0 [V]
        then
          * r1: motor-control-signal is equal to "off"

# ---8<--- [start:motor]
define component ElectricMotor
  parameter
    motor-control-signal is a control-signal

  variables
    power is an electrical-energy-flow
    torque is a mechanical-energy-flow
    start-up-curve, shut-down-curve is a mechanical-energy-flow
    motor-state is a state

  transformation-requirement
    convert-power-into-torque: must convert power into torque

  behavior-requirement
    motor-state-transitions:
      case start-up:
        when
          * c1: motor-control-signal is equal to "on"
          * c2: torque is smaller than  60.0 [Nm]
        then
          * r1: motor-state must be equal to "start-up"
      case steady-state:
        when
          * c1: motor-control-signal is equal to "on"
          * c2: torque is at least  60.0 [Nm]
        then
          * r1: motor-state must be equal to "steady-state"
      case shut-down:
        when
          * c1: motor-control-signal is equal to "off"
          * c2: torque is greater than 0.0 [Nm]
        then
          * r1: motor-state must be equal to "shut-down"
      case off:
        when
          * c1: motor-control-signal is equal to "off"
          * c2: torque is equal to 0.0 [Nm]
        then
          * r2: motor-state must be equal to "off"

    motor-torque-output:
      case motor-start-up:
        when
          * c1: motor-state is equal to "start-up"
        then
          * r1: torque must be equal to start-up-curve
      case motor-is-in-steady-state:
        when
          * c1: motor-state is equal to "steady-state"
        then
          * r1: torque must be equal to 60.0 [Nm]
      case motor-shut-down:
        when
          * c1: motor-state is equal to "shut-down"
        then
          * r2: torque must be equal to shut-down-curve
      case motor-is-off:
        when
          * c2: motor-state is equal to "off"
        then
          * r2: torque must be equal to 0.0 [Nm]

  relation
    torque-curves: torque-curve-model
      returning arguments
        * start-up-curve
        * shut-down-curve


define relation
  torque-curve-model
    returning parameters
      * start-up-curve is a mechanical-energy-flow
      * shut-down-curve is a mechanical-energy-flow
# ---8<--- [end:motor]

The next figure shows the updated component - function spec - behavior spec - variable MDM. Note the additional elements and dependencies within the behavior (rows, cols 6-8) and variable (rows, cols 9-13) domains. Especially, note the bi-directional dependencies between behavior-requirements motor-state-transitions and motor-torque-output and variables motor-state and torque. Hence, we introduced a feedback mechanism.

Example 3's Component-Function-Behavior-Variable MDM showing logical dependencies.

Example 3's Component-Function-Behavior-Variable MDM showing logical dependencies.

Rejected ideas

The following ideas where rejected.

If-clauses

If-clauses attached to goal-, transformation and design requirements and constraints, as shown in the listing below.

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goal-requirement
  provide-foo: blob must provide foo to blab
    if
      < conditions >
    end

In this example, the condition relates to the validity of the goal-requirement and not the the actual value of flow foo. This is not consistent with the definitions of function, behavior and state given in Section Rationale. Additionally, it is preferred to explicitly separate the function specifications from the behavior specifications, as is common in the literature. Hence it has been rejected.

External files

Defining dynamic behavior in external files and linking them via relations. This approach does not support the derivation of the dynamic structure since we have no control over the structure of the external files. Hence it has been rejected.

Extending the relation concept

Extending the relation concept to include behavior. For example, a relation definition:

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define relation xy
  with parameters
    x, y
  is defined as
    when x is equal to 1
      then y must be equal to 1
    when x is equal to 2
      then y must be equal to 2

In the systems engineering domain behavior-requirements and relations have different semantics despite that they are mathematically equivalent. Therefore, we prefer to have behavior and relations as separate concepts within ESL.

For now, relations remain a means to define miscellaneous dependencies between flow and design variables. In a later development stage, we foresee a role for relations equivalent to response functions ( resfunc ) of the Psi language7. Thereby, bridging the gap between requirement engineering, system architecting and MDO applications in an engineering design context.

Nested cases

Nested cases, as shown in the code example below, are rejected. In this example, cases A1 and A2 are subordinate to case A. That is, for case A1 to apply the when-clauses of A and the when-clauses of A1 must hold. For case A2 to apply the when-clauses of A and the when-clauses of A2 must hold.

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behavior-requirement
  case A:
    when
      ...
    then
      case A1:
        when
          ...
        then
          ...
      case A2:
        when
          ...
        then
          ...
  case B:
    ...

Nested cases enable users to create very complex nested requirements of arbitrary depth This is not in line with the general rule of thumb to strive for atomic requirements. As such, for now, we chose to keep it simple and reject nested cases. If the current solution turns out to be insufficient, we may reconsider this idea at a later stage.

Open issues

The following open issues are identified.

Completeness and determinism

Completeness and determinism are important aspects concerning behavior requirements. A complete specification states the desired behavior over the full value range of the stimuli. In a deterministic specification, at most one set of conditions related to the value of a variable evaluates to true at the same time.

Automated checking for completeness and determinism is desirable when a specification matures. However, ESL specifications grow and evolve over the course of a design project. As such, it is unlikely that an ESL specification is (ever) complete and deterministic during the course of a design project. Moreover, the actual value of a variable \(x\) may depend on many other variables and may be given by a relation defined in an external file written in another formalism. As such, evaluating when a condition that includes \(x\) evaluates to true is currently not within the possibilities of ESL.

Events

In defining control logic on often uses the concept of events. That is, state transitions of elements within the system trigger state transition of other components within the system.

In Example 1 for example one has to keep pressing the switch for the motor to produce torque. This may be undesirable since it may quickly drain the battery of the switch. It may be preferred that pressing the button when the motor is off results in the motor turning on. While pressing the button when the motor is on results in the motor shutting down. In this case, the state change of the switch (event) dictates the change in motor control signal rather than the actual state of the switch. Currently it is not possible to define such behavior.

  1. Y. Umeda, M. Ishii, M. Yoshioka, Y. Shimomura, and T. Tomiyama. Supporting conceptual design based on the function-behavior-state modeler. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 10(4):275–288, 1996. ↩

  2. A. K. Goel, S. R. Rugaber, and S. Vattam. Structure, behavior, and function of complex systems: The structure, behavior, and function modeling language. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 23(Special Issue 01):23–35, 2009. ↩↩

  3. H. Komoto and T. Tomiyama. A framework for computer-aided conceptual design and its application to system architecting of mechatronics products. Computer-Aided Design, 44(10):931–946, 2012. ↩

  4. E. Hull, K. Jackson, and J. Dick. Requirements engineering. Springer, London, England, 2nd edition, 2017. ↩

  5. A. Mavin, P. Wilkinson, A. Harwood, and M. Novak. Easy approach to requirements syntax (EARS). In Proceedings of the 17th IEEE International Requirements Engineering Conference, 317–322. Atlanta, Georgia, USA, 2009. ↩

  6. C. Arora, M. Sabetzadeh, L. C. Briand, and F. Zimmer. Requirement boilerplates: transition from manually-enforced to automatically-verifiable natural language patterns. In Proceedings of the 4th IEEE International Workshop on Requirements Patterns, 1–8. Karlskrona, Sweden, 2014. ↩

  7. S. Tosserams, A. T. Hofkamp, L. F. P. Etman, and J. E. Rooda. A specification language for problem partitioning in decomposition-based design optimization. Structural and Multidisciplinary Optimization, 42(5):707–723, 2010. ↩