Supervision equivalence

This paper presents a general framework for modular synthesis of supervisors for discrete event systems. The approach is based on compositional minimisation, using concepts of process equivalence. Its result is a compact representation of a least restrictive supervisor that ensures controllability and nonblocking. The method is demonstrated to reduce the number of states to be constructed for a simple manufacturing example, and the framework is proven to be sound

SYNTHESIS EQUIVALENCE OF TRIPLES

This working paper describes a framework for compositional supervisor synthesis, which is applicable to all discrete event systems modelled as a set of deterministic automata. Compositional synthesis exploits the modular structure of the input model, and therefore works best for models consisting of a large number of small automata. The state-space explosion is mitigated by the use of abstraction to simplify individual components, and the property of synthesis equivalence guarantees that the final synthesis result is the same as it would have been for the non-abstracted model. The working paper describes synthesis equivalent abstractions and shows their use in an algorithm to efficiently compute supervisors. The algorithm has been implemented in the DES software tool Supremica and successfully computes nonblocking modular supervisors, even for systems with more than 1014 reachable states, in less than 30 seconds

A Framework for Compositional Synthesis of Modular Nonblocking Supervisors

This paper describes a framework for compositional supervisor synthesis, which is applicable to all discrete event systems modeled as a set of deterministic automata. Compositional synthesis exploits the modular structure of the input model, and therefore works best for models consisting of a large number of small automata. The state-space explosion is mitigated by the use of abstraction to simplify individual components, and the property of synthesis equivalence guarantees that the final synthesis result is the same as it would have been for the non-abstracted model. The paper describes synthesis equivalent abstractions and shows their use in an algorithm to efficiently compute supervisors. The algorithm has been implemented in the DES software tool Supremica and successfully computes nonblocking modular supervisors, even for systems with more than 1014 reachable states, in less than 30 seconds

Synthesis equivalence of triples

This working paper describes a framework for compositional supervisor synthesis, which is applicable to all discrete event systems modelled as a set of deterministic automata. Compositional synthesis exploits the modular structure of the input model, and therefore works best for models consisting of a large number of small automata. State-space explosion is mitigated by the use of abstraction to simplify individual components, and the property of synthesis equivalence guarantees that the final synthesis result is the same as it would have been for the non-abstracted model. The working paper describes synthesis equivalent abstractions and shows their use in an algorithm to compute supervisors efficiently. The algorithm has been implemented in the DES software tool Supremica and successfully computes modular supervisors, even for systems with more than 1014 reachable states, in less than 30 seconds

Five abstraction rules to remove transitions while preserving compositional synthesis results

This working paper investigates under which conditions transitions can be removed from an automaton while preserving important synthesis properties. The work is part of a framework for compositional synthesis of least restrictive controllable and nonblocking supervisors for modular discrete event systems. The method for transition removal complements previous results, which are largely focused on state merging. Issues concerning transition removal in synthesis are discussed, and redirection maps are introduced to enable a supervisor to process an event, even though the corresponding transition is no longer present in the model. Based on the results, different techniques are proposed to remove controllable and uncontrollable transitions, and an example shows the potential of the method for practical problems

Compositional synthesis of discrete event systems via synthesis equivalence

A two-pass algorithm for compositional synthesis of modular supervisors for largescale systems of composed finite-state automata is proposed. The first pass provides an efficient method to determine whether a supervisory control problem has a solution, without explicitly constructing the synchronous composition of all components. If a solution exists, the second pass yields an over-approximation of the least restrictive solution which, if nonblocking, is a modular representation of the least restrictive supervisor. Using a new type of equivalence of nondeterministic processes, called synthesis equivalence, a wide range of abstractions can be employed to mitigate state-space explosion throughout the algorithm

Transition removal for compositional supervisor synthesis

This paper investigates under which conditions transitions can be removed from an automaton while preserving important synthesis properties. The work is part of a framework for compositional synthesis of least restrictive controllable and nonblocking supervisors for modular discrete event systems. The method for transition removal complements previous results, which are largely focused on state merging. Issues concerning transition removal in synthesis are discussed, and redirection maps are introduced to enable a supervisor to process an event, even though the corresponding transition is no longer present in the model. Based on the results, different techniques are proposed to remove controllable and uncontrollable transitions, and an example shows the potential of the method for practical problems

Three variations of observation equivalence preserving synthesis abstraction

In a previous paper we introduced the notion of synthesis abstraction, which allows efficient compositional synthesis of maximally permissive supervisors for large-scale systems of composed finite-state automata. In the current paper, observation equivalence is studied in relation to synthesis abstraction. It is shown that general observation equivalence is not useful for synthesis abstraction. Instead, we introduce additional conditions strengthening observation equivalence, so that it can be used with the compositional synthesis method. The paper concludes with an example showing the suitability of these relations to achieve substantial state reduction while computing a modular supervisor

On the use of observation equivalence in synthesis abstraction

In a previous paper we introduced the notion of synthesis abstraction, which allows efficient compositional synthesis of maximally permissive supervisors for large-scale systems of composed finite-state automata. In the current paper, observation equivalence is studied in relation to synthesis abstraction. It is shown that general observation equivalence is not useful for synthesis abstraction. Instead, we introduce additional conditions strengthening observation equivalence, so that it can be used with the compositional synthesis method. The paper concludes with an example showing the suitability of these relations to achieve substantial state reduction while computing a modular supervisor

Compositional synthesis of maximally permissive supervisors using supervision equivalence

This paper presents a general framework for efficient synthesis of supervisors for discrete event systems. The approach is based on compositional minimisation, using concepts of process equivalence. In this context, a large number of ways are suggested how a finite-state automaton can be simplified such that the results of supervisor synthesis are preserved. The proposed approach yields a compact representation of a least restrictive supervisor that ensures controllability and nonblocking. The method is demonstrated on a simple manufacturing example to significantly reduce the number of states constructed for supervisor synthesis