Behavioural Equivalences on Finite-State Systems are PTIME-hard

The paper shows a LOGSPACE-reduction from the Boolean circuit value problem which demonstrates that any relation subsuming bisimilarity and being subsumed by trace preorder (ie, language inclusion) is PTIME-hard, even for finite acyclic labelled transition systems. This reproves and substantially extends the result of Balcazar, Gabarro and Santha (1992) for bisimilarity

Bisimulation equivalence of a BPP and a finite-state system can be decided in polynomial time

AbstractIn this paper we consider the problem of deciding bisimulation equivalence of a BPP and a finite-state system. We show that the problem can be solved in polynomial time and we present an algorithm deciding the problem in time O(n4). The algorithm also constructs for each state of the finite-state system a ‘symbolic’ semilinear representation of the set of all states of the BPP system which are bisimilar with this state

Efficient construction of semilinear representations of languages accepted by unary nondeterministic finite automata

n languages over a unary alphabet, i.e., an alphabet with only one letter, words can be identified with their lengths. It is well known that each regular language over a unary alphabet can be represented as the union of a finite number of arithmetic progressions. Given a nondeterministic finite automaton (NFA) working over a unary alphabet (a unary NFA), the arithmetic progressions representing the language accepted by the automaton can be easily computed by the determinization of the given NFA. However, the number of the arithmetic progressions computed in this way can be exponential with respect to the size of the original automaton. Chrobak (1986) has shown that in fact O(n2) arithmetic progressions are sufficient for the representation of the language accepted by a unary NFA with n states, and Martinez (2002) has shown how these progressions can be computed in polynomial time. Recently, To (2009) has pointed out that Chrobak's construction and Martinez's algorithm, which is based on it, contain a subtle error and has shown how to correct this error. Geffert (2007) presented an alternative proof of Chrobak's result, also improving some of the bounds. In this paper, a new simpler and more efficient algorithm for the same problem is presented, using some ideas from Geffert (2007). The time complexity of the presented algorithm is O(n2(n + m)) and its space complexity is O(n + m), where n is the number of states and m the number of transitions of a given unary NFA.Web of Science12311069

Complexity and decidability of some equivalence-checking problems

Import 20/04/2006Prezenční výpůjčkaVŠB - Technická univerzita Ostrava. Fakulta elektrotechniky a informatiky

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Import 20/04/2006Prezenční výpůjčkaVŠB - Technická univerzita Ostrava. Fakulta elektrotechniky a informatiky. Katedra (456) informatik

Complexity of Equivalence Checking Problems

Abstract. The article summarizes the results of the author in the area of automated verification of systems and concurrency theory. These results are concerning the computational complexity of equivalence checking problems. The main aim of the paper is to present intuitive nonformal overview of these results

Behavioural equivalences on finite-state systems are PTIME-hard

The paper shows a LOGSPACE-reduction from the Boolean circuit value problem which demonstrates that any relation subsuming bisimilarity and being subsumed by trace preorder (ie, language inclusion) is PTIME-hard, even for finite acyclic labelled transition systems. This reproves and substantially extends the result of Balcazar, Gabarro and Santha (1992) for bisimilarity

A note on emptiness for alternating finite automata with a one-letter alphabet

We present a new proof of PSPACE-hardness of the emptiness problem for alternating finite automata with a singleton alphabet. This result was shown by Holzer (1995) who used a proof relying on a series of reductions from several papers. The new proof is simple, direct and self-contained