Minimization of Non-deterministic Automata with Large Alphabets

Abdulla, Parosh Aziz; Deneux, Johann; Kaati, Lisa; Nilsson, Marcus

doi:10.1007/11605157_3

Cited by 12 publications

(5 citation statements)

References 17 publications

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“…FSA describes the algorithms that we use to perform intersection and determinization. In [2] the authors give an efficient implementation of minimization for NFAs with large alphabets. The representation of NFA is explicit for states, and symbolic (BDD-based) for labels.…”

Section: Related Workmentioning

confidence: 99%

“…AUTLIB is used at the core of an extension of the NUSMV [7] model checker able to deal with the PSL language, and, as explained in [8], it is used to generate the automata necessary for PSL verification. The number of concatenated SEREs is randomly chosen in the range [2,10]. We generated 12 different families of benchmarks, choosing a possible configuration of parameters.…”

Section: Experimental Evaluationmentioning

confidence: 99%

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From Sequential Extended Regular Expressions to NFA with Symbolic Labels

Cimatti

Mover

Roveri

et al. 2011

Implementation and Application of Automata

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Practical property specification languages such as the IEEE standard PSL use at their core Sequential Extended Regular Expressions (SERE). In order to enable the reuse of traditional verification techniques, it is necessary to translate SEREs into automata. SERE are regular expressions built over alphabets resulting from the state variables of the design under analysis. Thus, a traditional approach to generate the automaton would suffer from the fact that the size of the alphabet is exponential in the number of symbols in the design. In this work, we tackle this problem by proposing non-deterministic finite automata with symbolic representation of transitions labels, by way of propositional formulas, while states and transitions are explicitly represented. We provide a symbolic version of the algorithms for all the major operations over nondeterministic finite automata. The approach has been implemented in the AUTLIB library, with Binary Decision Diagrams (BDD) used to represent transition labels. We carried out a thorough experimental evaluation over a set of realistic benchmarks, comparing our library against MONA (which uses deterministic finite automata with BDD-based symbolic transitions), and against GRAZ (which features non-deterministic finite automata with a DNF-based representation of the labels). Experimental results over a realistic set of benchmarks show that both features of AUTLIB (the ability to deal with non-determinism, and a BDD-based treatment of labels) are fundamental to achieve acceptable performance.

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Section: Related Workmentioning

confidence: 99%

Section: Experimental Evaluationmentioning

confidence: 99%

From Sequential Extended Regular Expressions to NFA with Symbolic Labels

Cimatti

Mover

Roveri

et al. 2011

Implementation and Application of Automata

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“…From the Paige-Tarjan algorithm [13] (more precisely, from its generalization allowing multiple labels as in [2]), we know that we can compute…”

Section: Complexity Of Computing Downward Bisimulation Via Lts Translmentioning

confidence: 99%

Composed Bisimulation for Tree Automata

Abdulla

Bouajjani

Holík

et al. 2009

Int. J. Found. Comput. Sci.

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Abstract. We address the problem of reducing the size of (nondeterministic, bottom-up) tree automata (TA) using suitable, languagepreserving equivalences on the states of the automata. In particular, we propose the so-called composed bisimulation equivalence as a new language preserving equivalence. A composed bisimulation equivalence is defined in terms of two different relations, namely the upward and downward bisimulation equivalence. We provide simple and efficient algorithms for computing these relations. The notion of composed bisimulation equivalence is motivated by an attempt to obtain an equivalence that can provide better reductions than what currently known bisimulationbased approaches can offer, but which is not significantly more difficult to compute (and hence stays below the computational requirements of simulation-based reductions). The experimental results we present in the paper show that our composed bisimulation equivalence meets such requirements, and hence provides users of TA with a finer way to resolve the trade-off between the available degree of reduction and its cost.

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“…A rather successful intermediate model is the class of unambiguous finite automata (UFAs). 1 While in general still being exponentially more succinct than an equivalent DFA for the same language, static analysis questions such as inclusion and equivalence can be solved in PTIME for UFAs [17]. However, UFAs do not allow for tractable state minimization [11].…”

Section: Introductionmentioning

confidence: 99%

“…The work of Hromkovic et al [8] about measuring non-determinism in finite automata will be relevant to us in Section 2. Since the minimization problem for NFAs is hard, the bisimulation minimization problem has also been considered; see, e.g., [14,1].…”

Section: Introductionmentioning

confidence: 99%

The tractability frontier for NFA minimization

Björklund

Martens

2012

Journal of Computer and System Sciences

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We essentially show that minimizing finite automata is NP-hard as soon as one deviates from the class of deterministic finite au-tomata. More specifically, we show that minimization is NP-hard for all finite automata classes that subsume the class that is unambiguous, allows at most one state q with a non-deterministic transition for at most one alphabet symbol a, and is allowed to visit state q at most once in a run. Furthermore, this result holds even for automata that only accept finite languages.

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Minimization of Non-deterministic Automata with Large Alphabets

Cited by 12 publications

References 17 publications

From Sequential Extended Regular Expressions to NFA with Symbolic Labels

From Sequential Extended Regular Expressions to NFA with Symbolic Labels

Composed Bisimulation for Tree Automata

The tractability frontier for NFA minimization

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