Showing papers by "Tomáš Masopust published in 2018"
TL;DR: It is shown that it is not the case by considering DESs represented as deterministic finite automata without non-trivial cycles, which are structurally the simplest deadlock-freeDESs, that even for such very simple DESs, checking weak (periodic) detectability remains intractable.
48 citations
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TL;DR: In this paper, the authors investigated the verification of two detectability properties (strong detectability and weak detectability) for DESs modeled by labeled Petri nets and showed that strong detectability is decidable and weak detection is undecidable.
Abstract: Detectability of discrete event systems (DESs) is a property to determine a priori whether the current and subsequent states can be determined based on observations In this paper, we investigate the verification of two detectability properties -- strong detectability and weak detectability -- for DESs modeled by labeled Petri nets Strong detectability requires that we can always determine, after a finite number of observations, the current and subsequent markings of the system, while weak detectability requires that we can determine, after a finite number of observations, the current and subsequent markings for some trajectories of the system We show that for DESs modeled by labeled Petri nets, checking strong detectability is decidable whereas checking weak detectability is undecidable Our results extend the existing studies on the verification of detectability from finite-state automata to labeled Petri nets As a consequence, we strengthen a result on checking current-state opacity for labeled Petri nets
17 citations
TL;DR: In this article, the authors bring several interesting results from complexity theory and illustrate their relevance to supervisory control by proving new nontrivial results concerning nonblockingness in modular super-visory control of discrete event systems modeled by finite automata.
Abstract: Complexity analysis becomes a common task in supervisory control. However, many results of interest are spread across different topics. The aim of this paper is to bring several interesting results from complexity theory and to illustrate their relevance to supervisory control by proving new nontrivial results concerning nonblockingness in modular supervisory control of discrete event systems modeled by finite automata.
11 citations
TL;DR: The construction shows that such a DFA can be computed in time and shows that the upper bound state complexity on the infimal prefix-closed and observable superlanguage is $2^n + 1$ and that this bound is asymptotically tight.
Abstract: The infimal prefix-closed, controllable, and observable superlanguage plays an essential role in the relationship between controllability, observability, and co-observability—the central notions of supervisory control theory. Existing algorithms for its computation are exponential and it is not known whether a polynomial algorithm exists. We answer the question by studying the state complexity of this language. State complexity of a language is the number of states of its minimal deterministic finite automaton (DFA). For a language with state complexity $n$ , we show that the upper bound state complexity on the infimal prefix-closed and observable superlanguage is $2^n + 1$ and that this bound is asymptotically tight. Hence, there is no algorithm computing a DFA of the infimal prefix-closed and observable superlanguage in polynomial time. Our construction shows that such a DFA can be computed in time $O(2^n)$ . The construction involves nondeterministic finite automata (NFAs) and a computation of the supremal prefix-closed sublanguage. We study the computation of supremal prefix-closed sublanguages and show that there is no polynomial-time algorithm computing an NFA of the supremal prefix-closed sublanguage of a language given as an NFA even if the language is unary.
2 citations
29 Jan 2018
TL;DR: It is shown, using a novel and nontrivial construction, that the universality problem for ptNFAs is PSpace-complete if the alphabet may grow polynomially.
Abstract: An automaton is partially ordered if the only cycles in its transition diagram are self-loops. We study the universality problem for ptNFAs, a class of partially ordered NFAs recognizing piecewise testable languages. The universality problem asks if an automaton accepts all words over its alphabet. Deciding universality for both NFAs and partially ordered NFAs is PSpace-complete. For ptNFAs, the complexity drops to coNP-complete if the alphabet is fixed but is open if the alphabet may grow. We show, using a novel and nontrivial construction, that the problem is PSpace-complete if the alphabet may grow polynomially.
2 citations
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TL;DR: In this paper, the authors study the computational complexity of deciding critical observability for systems modeled as (networks of) finite-state automata and Petri nets, and show that the problem is NP-hard for networks of finite automata.
Abstract: Critical observability is a property of cyber-physical systems to detect whether the current state belongs to a set of critical states. In safety-critical applications, critical states model operations that may be unsafe or of a particular interest. De Santis et al. introduced critical observability for linear switching systems, and Pola et al. adapted it for discrete-event systems, focusing on algorithmic complexity. We study the computational complexity of deciding critical observability for systems modeled as (networks of) finite-state automata and Petri nets. We show that deciding critical observability is (i) NL-complete for finite automata, that is, it is efficiently verifiable on parallel computers, (ii) PSPACE-complete for networks of finite automata, that is, it is very unlikely solvable in polynomial time, and (iii) undecidable for labeled Petri nets, but becoming decidable if the set of critical states (markings) is finite or co-finite, in which case the problem is as hard as the non-reachability problem for Petri nets.