Checking NFA equivalence with bisimulations up to congruence

Bonchi, Filippo; PousDamien,

doi:10.1145/2480359.2429124

Cited by 63 publications

(85 citation statements)

References 27 publications

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“…In the implementation we use current state-of-the-art algorithms for both: language-equivalence checking via bisimulation up-to techniques due to Bonchi and Pous [1], and NFA minimisation using forward and backwards variants of simulation of Clemente and Mayr [15].…”

Section: Implementation and Resultsmentioning

confidence: 99%

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Compositional Reachability in Petri Nets

Rathke

Sobociński

Stephens

2014

Lecture Notes in Computer Science

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Abstract. We introduce a divide-and-conquer algorithm for a modified version of the reachability/coverability problem in 1-bounded Petri nets that relies on the compositional algebra of nets with boundaries: we consider the algebraic decomposition of the net of interest as part of the input. We formally prove the correctness of the technique and contrast the performance of our implementation with state-of-the-art tools that exploit partial order reduction techniques on the global net.

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Section: Implementation and Resultsmentioning

confidence: 99%

“…The compositional approach was briefly discussed in [22] and in the technical report [23], where further examples are described in detail. Initial efforts were based on determinisation, which was considerably more expensive than our current use of NFA minimisation [15] and language equivalence checking [1].…”

Section: Related Work and Discussionmentioning

confidence: 99%

Compositional Reachability in Petri Nets

Rathke

Sobociński

Stephens

2014

Lecture Notes in Computer Science

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“…This is how we obtained HKC [1], an algorithm that can be exponentially faster than Hopcroft and Karp's algorithm or more recent antichain algorithms [7].…”

Section: The Concrete Case Of Finite Automatamentioning

confidence: 94%

Coalgebraic Up-to Techniques

Pous

2013

Algebra and Coalgebra in Computer Science

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1 The concrete case of finite automata A simple algorithm for checking language equivalence of finite automata consists in trying to compute a bisimulation that relates them. This is possible because language equivalence can be characterised coinductively, as the largest bisimulation.More precisely, consider an automaton S, t, o , where S is a (finite) set of states, t : S → P(S)A is a non-deterministic transition function, and o : S → 2 is the characteristic function of the set of accepting states. Such an automation gives rise to a determinised automaton P(S), t , o , where t : P(S) → P(S) A and o : P(S) → 2 are the natural extensions of t and o to sets. A bisimulation is a relation R between sets of states such that for all sets of states X, Y , X R Y entails:, and 2. for all letter a, t a (X) R t a (Y ).The coinductive characterisation is the following one: two sets of states recognise the same language if and only if they are related by some bisimulation.Taking inspiration from concurrency theory [4,5], one can improve this proof technique by weakening the second item in the definition of bisimulation: given a function f on binary relations, a bisimulation up to f is a relation R between states such that for all sets X, Y , X R Y entails:For well-chosen functions f , bisimulations up to f are contained in a bisimulation, so that the improvement is sound. So is the function mapping each relation to its equivalence closure. In this particular case, one recover the standard algorithm by Hopcroft and Karp [2]: two sets can be skipped whenever they can already be related by a sequence of pairwise related states.One can actually do more, by considering the function c mapping each relation to its congruence closure: the smallest equivalence relation which contains Appeared as an invited talk in Proc.

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“…This algorithm can be easily extended to NFAs as in Almeida et al [1]. A presentation of this algorithm and an improved variant, together with proofs of correctness, can be found in Bonchi and Pous [6].…”

Section: Equivalence Of Ska Expressionsmentioning

confidence: 99%

Deciding Synchronous Kleene Algebra with Derivatives

Broda

Cavadas

Ferreira

et al. 2015

Implementation and Application of Automata

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Abstract. Synchronous Kleene algebra (SKA) is a decidable framework that combines Kleene algebra (KA) with a synchrony model of concurrency. Elements of SKA can be seen as processes taking place within a fixed discrete time frame and that, at each time step, may execute one or more basic actions or then come to a halt. The synchronous Kleene algebra with tests (SKAT) combines SKA with a Boolean algebra. Both algebras were introduced by Prisacariu, who proved the decidability of the equational theory, through a Kleene theorem based on the classical Thompson ε-NFA construction. Using the notion of partial derivatives, we present a new decision procedure for equivalence between SKA terms. The results are extended for SKAT considering automata with transitions labeled by Boolean expressions instead of atoms. This work continous previous research done for KA and KAT, where derivative based methods were used in feasible algorithms for testing terms equivalence.

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Checking NFA equivalence with bisimulations up to congruence

Cited by 63 publications

References 27 publications

Compositional Reachability in Petri Nets

Compositional Reachability in Petri Nets

Coalgebraic Up-to Techniques

Deciding Synchronous Kleene Algebra with Derivatives

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