Experimental Evaluation of Classical Automata Constructions

Tabakov, Deian; Vardi, Moshe Y.

doi:10.1007/11591191_28

Cited by 85 publications

(75 citation statements)

References 33 publications

(44 reference statements)

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“…But its performance is good in practice, often better than Hopcroft's algorithm [17,18]. Furthermore, this algorithm applied to an NFA still yields an equivalent minimal DFA; see [18], for example.…”

Section: Extension Of Brzozowski's Theorem On Dfa Minimizationmentioning

confidence: 99%

Theory of átomata

Brzozowski

Tamm

2014

Theoretical Computer Science

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We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call "átomaton", whose states are the "atoms" of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of the language. We describe methods of constructing theátomaton, and prove that it is isomorphic to the reverse automaton of the minimal deterministic finite automaton (DFA) of the reverse language. We study "atomic" NFAs in which the right language of every state is a union of atoms. We generalize Brzozowski's double-reversal method for minimizing a deterministic finite automaton (DFA), showing that the result of applying the subset construction to an NFA is a minimal DFA if and only if the reverse of the NFA is atomic. We prove that Sengoku's claim that his method always finds a minimal NFA is false.

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Section: Extension Of Brzozowski's Theorem On Dfa Minimizationmentioning

confidence: 99%

Theory of átomata

Brzozowski

Tamm

2014

Theoretical Computer Science

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“…d'Amorim and Roşu describe such a construction in terms of nondeterministic multi-transitions and binary transition trees [14]. Instead of introducing these formalisms, here we use instead the approach in [2,43], which presents the same concept in automatatheoretic terms. The idea in both papers is to perform the subset construction on the fly, as we read the inputs from the trace.…”

Section: Theorem 1 [14]mentioning

confidence: 99%

Optimized Temporal Monitors for SystemC

Tabakov

Vardi

2010

Runtime Verification

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SystemC is a modeling language built as an extension of C++. Its growing popularity and the increasing complexity of designs have motivated research efforts aimed at the verification of SystemC models using assertionbased verification (ABV), where the designer asserts properties that capture the design intent in a formal language such as PSL or SVA. The model then can be verified against the properties using runtime or formal verification techniques. In this paper we focus on automated generation of runtime monitors from temporal properties. Our focus is on minimizing runtime overhead, rather than monitor size or monitor-generation time. We identify four issues in monitor generation: state minimization, alphabet representation, alphabet minimization, and monitor encoding. We conduct extensive experimentation and identify a combination of settings that offers the best performance in terms of runtime overhead.

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“…for A n , and this algorithm can be a good solution (see [17] for an experimental comparison of Brzozowski algorithm versus determinization combined with Hopcroft algorithm). However, if the input is a deterministic automaton, Brzozowski algorithm still has exponential worst-case complexity, which is easily seen by taking the reverse of A n as input.…”

Section: Introductionmentioning

confidence: 99%

Brzozowski Algorithm Is Generically Super-Polynomial for Deterministic Automata

Felice¹,

Nicaud²

2013

Developments in Language Theory

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Abstract. We study the number of states of the minimal automaton of the mirror of a rational language recognized by a random deterministic automaton with n states. We prove that, for any d > 0, the probability that this number of states is greater than n d tends to 1 as n tends to infinity. As a consequence, the generic and average complexities of Brzozowski minimization algorithm are super-polynomial for the uniform distribution on deterministic automata.

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Experimental Evaluation of Classical Automata Constructions

Cited by 85 publications

References 33 publications

Theory of átomata

Theory of átomata

Optimized Temporal Monitors for SystemC

Brzozowski Algorithm Is Generically Super-Polynomial for Deterministic Automata

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