Modular Discrete-event Systems Research Articles

Compositional non-blockingness verification of finite automata with prioritised events

This paper addresses the verification of non-blockingness for modular discrete-event systems, i.e., discrete-event systems that are composed from component models. For such systems, the explicit construction of a monolithic representation turns out intractable for relevant applications, since such a construction in general is of exponential cost w.r.t. the number of components. One well established approach to circumvent the need for a monolithic representation for the verification task at hand is to alternate (a) the substitution of individual components by abstractions and (b) the composition of only a small number of strategically chosen components at a time. When successful, one ends up with a single moderately sized automaton which does not represent the overall behaviour in any detail but which does block if and only if the original modular system fails to be non-conflicting. This approach is referred to as compositional verification and originates from the field of process algebra with more recent adaptations to finite automata models. The main contribution of the present study is the development of a number of abstraction rules valid for compositional verification of non-conflictingness in the presence of global event priorities, i.e., where high priority events from one component possibly preempt events with lower priority of all components.

Supervisory Control of Modular Discrete-Event Systems under Partial Observation: Normality

Supervisory Control of Modular Discrete-Event Systems under Partial Observation: Normality

Compositional Verification of Non-Blockingness with Prioritised Events

This paper addresses the verification of non-blockingness for modular discrete-event systems, i.e., discrete-event systems that are composed from component models. For such systems, the explicit construction of a monolithic representation turns out intractable for relevant applications, since such a construction in general is of exponential cost w.r.t. the number of components. One well established approach to circumvent the need for a monolithic representation for the verification task at hand is to alternate (a) the substitution of individual components by abstractions and (b) the composition of only a small number of strategically chosen components at a time. When successful, one ends up with a single moderately sized automaton which does not represent the overall behaviour in any detail but which does block if and only if the original modular system fails to be non-conflicting. This approach is referred to as compositional verification and originates from the field of process algebra with more recent adaptations to finite automata models. The main contribution of the present study is the development of a number of abstraction rules valid for compositional verification of non-conflictingness in the presence of global event priorities, i.e., where high priority events from one component possibly preempt events with lower priority of other components.

Current-state opacity and initial-state opacity of modular discrete event systems

The verifications of current-state opacity (CSO) and initial-state opacity (ISO) in discrete event systems (DESs) both suffer from the curse of dimensionality, as these issues were proved to be PSPACE-complete. Hence, how to reduce the state space is crucial. In this paper, we investigate CSO and ISO in modular DESs, which consist of several individual components. Necessary and sufficient conditions of CSO and ISO for modular DESs are derived under the assumption that all synchronous events are observable by each components of modular DESs. Moreover, we prove that the initial state estimator of modular system is isomorphic to the synchronous composition of initial state estimators for individual components. These results offer us the opportunity to reduce the complexity in verifying the opacity of modular DESs.

Compositional and Abstraction-Based Approach for Synthesis of Edit Functions for Opacity Enforcement

This article develops a novel compositional and abstraction-based approach to synthesize edit functions for opacity enforcement in modular discrete event systems. Edit functions alter the output of the system by erasing or inserting events in order to obfuscate the outside intruder, whose goal is to infer the secrets of the system from its observation. We synthesize edit functions to solve the opacity enforcement problem in a modular setting, which significantly reduces the computational complexity compared with the monolithic approach. Two abstraction methods called opaque observation equivalence and opaque bisimulation are first employed to abstract the individual components of the modular system and their observers. Subsequently, we propose a method to transform the synthesis of edit functions to the calculation of modular supremal nonblocking supervisors. We show that the edit functions synthesized in this manner correctly solve the opacity enforcement problem.

Matrix approach to verification and enforcement of nonblockingness for modular discrete-event systems

Matrix approach to verification and enforcement of nonblockingness for modular discrete-event systems

SCT-based priority-free conditionally-preemptive scheduling of modular real-time systems with exact task execution time

This study presents a novel discrete-event systems (DES) modeling framework to address real-time system (RTS) with sporadic, periodic, and non-repetitive real-time tasks. Our approach is organized in three steps. First, the effect of individual timing parameters of each task, such as job arrival and deadlines, are represented by modular DES. Second, we choose the required modules for the specific RTS at hand to compose an overall model. Third, we utilize supervisory control to find all schedules that are consistent with the timing requirements of all tasks. In contrast to fixed task priorities, we address general preemption relations represented by a preemption matrix and thereby implement priority-free conditionally-preemptive (PFCP) real-time scheduling. As a particular feature of the closed-loop configuration, the schedules obtained refer to the actual job execution time as opposed to upper and lower bounds. We illustrate our approach by a real-world example in the context of an automated manufacturing system.

Complexity of detectability, opacity and A-diagnosability for modular discrete event systems

Modular discrete event systems are modeled as a parallel composition of finite automata. While deciding weak detectability, opacity, and A-diagnosability for monolithic systems is PSPACE-complete, the complexity for modular systems is unknown. We show that for modular systems the problems are EXPSPACE-complete, and hence there is neither a polynomial-time nor a polynomial-space algorithm solving them. While the upper bound is a natural modification of the PSPACE algorithms for monolithic systems, the lower bound requires a novel and nontrivial construction. We further discuss a case where the complexity drops to PSPACE-complete.

Verification complexity of a class of observational properties for modular discrete events systems

A modular discrete event system is modeled by a set of module automata running synchronously. In this paper, we investigate the complexity of the verification problems of three different properties, diagnosability, predictability, and detectability, for partially-observed modular discrete event systems. We first show that deciding diagnosability for modular discrete event systems is PSPACE-complete when the number of modules is unbounded. Then we show that deciding predictability and detectability for modular discrete event systems are both PSPACE-hard problems. These results reveal that in order to verify these properties for the complete system, exploring the state space of the monolithic model may be unavoidable, in the worst case.

Synchronous Codiagnosability of Modular Discrete-Event Systems * *This work was partially supported by the Brazilian Research Council CNPq.

Abstract Automated systems are subject to failures that can alter their expected behavior, leading to a decrease in their performance, and possibly causing equipment damages. In this work, we propose a decentralized synchronized Petri net diagnosis scheme for discrete-event systems modeled as automata. In order to do so, we define the notion of synchronous codiagnosability and propose an algorithm to verify this property. We also discuss the relation between synchronous codiagnosability, synchronous diagnosability and diagnosability of discrete-event systems.

Verification of Modular Diagnosability With Local Specifications for Discrete-Event Systems

In this paper, we study the diagnosability verification for modular discrete-event systems (DESs), i.e., DESs that are composed of multiple components. We focus on a particular modular architecture, where each fault in the system must be uniquely identified by the modular component where it occurs and solely based on event observations of that component. Hence, all diagnostic computations for faults to be detected in this architecture can be performed locally on the respective modular component, and the obtained diagnosis information is only relevant for that component. We define the condition of modular language diagnosability with local specifications (MDLS) in order to capture that each fault can indeed be detected in this modular architecture. Then, we show that MDLS can be formulated as a specific language-diagnosability problem. As the main contribution of this paper, we develop an incremental abstraction-based approach for the verification of MDLS, which is based on projections that fulfill the loop-preserving observer condition. In particular, our approach efficiently avoids the construction of a global system model, which is infeasible for systems of realistic size. Furthermore, we do not rely on the assumption of a live global plant, which is prevalent in previous diagnosability methods for modular DESs. We illustrate our approach and its computational savings by a manufacturing system example.

Efficient Abstractions for the Supervisory Control of Modular Discrete Event Systems

The topic of this technical note is the nonblocking and maximally permissive abstraction-based supervisory control for modular discrete event systems (DES). It is shown, that an efficient abstraction technique, that was developed for the nonconflict verification of modular DES, is also suitable for the nonblocking supervisory control. Moreover, it is proved that this abstraction technique can be extended by the condition of local control consistency, in order to achieve maximally permissive supervision. Different from existing approaches, the presented abstraction does not require to preserve the shared events among the system components in the respective abstraction alphabets, and hence leads to potentially smaller system abstractions. The obtained results are illustrated by a flexible manufacturing system example.

On conditional decomposability

The requirement of a language to be conditionally decomposable is imposed on a specification language in the coordination supervisory control framework of discrete-event systems. In this paper, we present a polynomial-time algorithm for verification whether a language is conditionally decomposable with respect to given alphabets. Moreover, we also present a polynomial-time algorithm to extend the common alphabet so that the language becomes conditionally decomposable. A relationship of conditional decomposability to nonblockingness of modular discrete-event systems in general settings is also discussed in this paper. It is shown that conditional decomposability is a weaker condition than nonblockingness.

Reduced-Complexity Verification for Initial-State Opacity in Modular Discrete Event Systems

In this paper, we propose and analyze reduced-complexity methodologies for verifying initial-state opacity in modular discrete event systems. Initial-state opacity requires that the membership of the system initial state to a given set of secret states S remains opaque (uncertain) to an intruder who has complete knowledge of the system model and observes system activity through some natural projection map. In the modular setting we consider, the given system is modeled as a composition (synchronous product) of M modules [G1, G2, …, GM] where each module Gi is a non-deterministic finite automaton with Ni states with the set of secret states S is of the form S = [(x1, x2, …, xM)|xi Si], where Si is the set of secret states for module Gi. Assuming that the pairwise shared events are pairwise observable and that the intruder observes events that are observable in at least one module, we provide a modular algorithm for verifying initial-state opacity with O(MNM–12N2) state and time complexity, where N = maxi Ni. This is a considerable reduction compared to the O(2(NM)2) state and time complexity of the centralized verification method, which verifies initial-state opacity by considering the composed system as a monolithic system.

PSPACE-completeness of Modular Supervisory Control Problems*

In this paper we investigate computational issues associated with the supervision of concurrent processes modeled as modular discrete-event systems. Here, modular discrete-event systems are sets of deterministic finite-state automata whose interaction is modeled by the parallel composition operation. Even with such a simple model process model, we show that in general many problems related to the supervision of these systems are PSPACE-complete. This shows that although there may be space-efficient methods for avoiding the state-explosion problem inherent to concurrent processes, there are most likely no time-efficient solutions that would aid in the study of such large-scale systems. We show our results using a reduction from a special class of automata intersection problem introduced here where behavior is assumed to be prefix-closed. We find that deciding if there exists a supervisor for a modular system to achieve a global specification is PSPACE-complete. We also show many verification problems for system supervision are PSPACE-complete, even for prefix-closed cases. Supervisor admissibility and online supervision operations are also discussed.

Diagnosis of modular discrete event systems

The diagnosis of unobservable fault events in discrete event systems modeled in a modular manner by means of parallel composition is considered. The notion of modular diagnosability is introduced for these systems. Necessary and sufficient conditions for this new notion of diagnosability are given. A new algorithm for verifying modular diagnosability is presented. The main feature of this algorithm is the exploitation of the modular structure of the system in order to save on computational efforts.

Hierarchical partitioning algorithm for optimistic distributed simulation of DEVS models

Abstract The partitioning problem of models is one of the most important issues which may affect the performance of distributed simulation. This paper presents a novel partitioning algorithm for the optimistic distributed simulation of hierarchical, modular Discrete Event System Specification (DEVS) models. The proposed algorithm pursues the following three goals to achieve the overall objective of the minimum simulation time: (1) to balance the computational loads of partitions, (2) to maximize the parallel execution of independent models, and (3) to minimize inter-processor communication. To maximize parallel execution of independent models, the proposed algorithm utilizes the hierarchical structural information of models available from the hierarchical model design methodology of the DEVS formalism. Through benchmark simulation experiments, we show that the proposed algorithm achieves good performance.