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Checking NFA equivalence with bisimulations up to congruence
"... Abstract—We introduce bisimulation up to congruence as a technique for proving language equivalence of nondeterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp [12] that, instead of computing the whole determinised automa ..."
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Abstract—We introduce bisimulation up to congruence as a technique for proving language equivalence of nondeterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp [12] that, instead of computing the whole determinised automata, explores only a small portion of it. Although the optimised algorithm remains exponential in worst case (the problem is PSPACEcomplete), experimental results show improvements of several orders of magnitude over the standard algorithm. I.
Brzozowski’s algorithm (co)algebraically
"... Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctn ..."
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Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. 1
A AlgebraCoalgebra Duality in Brzozowski’s Minimization Algorithm
"... We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simpl ..."
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We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. Notably, we derive algorithms to obtain minimal, language equivalent automata from Moore, nondeterministic and weighted automata.
ContextFree Languages, Coalgebraically
"... Abstract. We give a coalgebraic account of contextfree languages using the functor D(X) =2 × X A for deterministic automata over an alphabet A, in three different but equivalent ways: (i) by viewing contextfree grammars as Dcoalgebras; (ii) by defining a format for behavioural differential equati ..."
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Abstract. We give a coalgebraic account of contextfree languages using the functor D(X) =2 × X A for deterministic automata over an alphabet A, in three different but equivalent ways: (i) by viewing contextfree grammars as Dcoalgebras; (ii) by defining a format for behavioural differential equations (w.r.t. D) for which the unique solutions are precisely the contextfree languages; and (iii) as the Dcoalgebra of generalized regular expressions in which the Kleene star is replaced by a unique fixed point operator. In all cases, semantics is defined by the unique homomorphism into the final coalgebra of all languages, paving the way for coinductive proofs of contextfree language equivalence. Furthermore, the three characterizations can serve as the basis for the definition of a general coalgebraic notion of contextfreeness, which we see as the ultimate longterm goal of the present study. 1
CNRS,ENSLyon,Université de Lyon LIP (UMR 5668)
"... Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctn ..."
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Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. This paper is dedicated to Dexter Kozen on the occasion of his 60th birthday. Dexter always seeks simplicity and crystalclear proofs in his research: “a beautiful result deserves a beautiful proof ” could be the motto of his work. This paper is a tribute to that ⋆. 1
www.elsevier.com/locate/entcs Final Semantics for Decorated Traces
"... In concurrency theory, various semantic equivalences on labelled transition systems are based on traces enriched or decorated with some additional observations. They are generally referred to as decorated traces, and examples include ready, failure, trace and complete trace equivalence. Using the ge ..."
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In concurrency theory, various semantic equivalences on labelled transition systems are based on traces enriched or decorated with some additional observations. They are generally referred to as decorated traces, and examples include ready, failure, trace and complete trace equivalence. Using the generalized powerset construction, recently introduced by a subset of the authors [13], we give a coalgebraic presentation of decorated trace semantics. This yields a uniform notion of canonical, minimal representatives for the various decorated trace equivalences, in terms of final Moore automata. As a consequence, proofs of decorated trace equivalence can be given by coinduction, using different types of (Moore) bisimulation (upto), which is helpful for automation.
DOI: 10.1145/2429069.2429124 Checking NFA equivalence with bisimulations up to congruence
, 2012
"... We introduce bisimulation up to congruence as a technique for proving language equivalence of nondeterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp [16]. We compare our approach to the recently introduced antichain alg ..."
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We introduce bisimulation up to congruence as a technique for proving language equivalence of nondeterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp [16]. We compare our approach to the recently introduced antichain algorithms, by analysing and relating the two underlying coinductive proof methods. We give concrete examples where we exponentially improve over antichains; experimental results moreover show non negligible improvements.