State complexity of some operations on binary regular languages

Jirásková, Galina

doi:10.1016/j.tcs.2004.04.011

Cited by 111 publications

(83 citation statements)

References 12 publications

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“…As in Section 3.1.1, we need to consider three different cases, according to the state and transition complexities of the operands. Although the tight bound for (complete) state complexity can be reached over a binary alphabet [14], all automaton families used in this section have an alphabet Σ = {a, b, c}. − 5 transitions.…”

Section: Worst-case Witnessesmentioning

confidence: 99%

Incomplete operational transition complexity of regular languages

Maia

Moreira

Reis

2015

Information and Computation

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The state complexity of basic operations on regular languages considering complete deterministic finite automata (DFA) has been extensively studied in the literature. But, if incomplete DFAs are considered, transition complexity is also an significant measure. In this paper we study the incomplete (deterministic) state and transition complexity of some operations for regular and finite languages. For regular languages we give a new tight upper bound for the transition complexity of the union, which refutes the conjecture presented by Y. Gao et al.. For finite languages, we correct the published state complexity of concatenation for complete DFAs and provide a tight upper bound for the case when the right operand is larger than the left one. We also present some experimental results to test the behaviour of those operations on the average case, and we conjecture that for many operations and in practical applications the worst-case complexity is seldom reached.

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Section: Worst-case Witnessesmentioning

confidence: 99%

Incomplete operational transition complexity of regular languages

Maia

Moreira

Reis

2015

Information and Computation

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“…2. As shown in [15,Theorem 5], there exists a fooling set We summarize the results given in Lemma 2 and Lemma 3 in the following theorem which provides the tight bound on the nondeterministic state complexity of complementation on prefix-free languages. This solves an open problem from [10].…”

Section: Proposition 1 ([9]) Let N ≥ 2 Andmentioning

confidence: 90%

“…. , n − 1}} be the fooling set for the language K c described in [15,Theorem 5]; notice that x S is a string, by which the initial state 1 of the NFA in Fig. 1 goes to the set S. Let us show that the set …”

Section: Theorem 3 (Complement On Non-returning Languages |σ| ≥ 2) mentioning

confidence: 99%

“…Holzer and Kutrib [12] proved the lower bound 2 n−2 for a binary n-state NFA language. Finally, a binary n-state NFA language meeting the upper bound 2 n was described by Jirásková in [15]. In the unary case, the complexity of complementation is known to be in e Θ( √ n ln n) [12,14].…”

Section: Introductionmentioning

confidence: 99%

“…Finally, a binary n-state NFA language meeting the upper bound 2 n was described by Jirásková in [15]. In the unary case, the complexity of complementation is known to be in e Θ( √ n ln n) [12,14]. In this paper, we investigate the complementation operation on prefix-free, suffix-free, and non-returning languages.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Complement on Prefix-Free, Suffix-Free, and Non-Returning NFA Languages

Jirásková

Mlynárčik

2014

Descriptional Complexity of Formal Systems

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Abstract. We prove that the tight bound on the nondeterministic state complexity of complementation on prefix-free and suffix-free languages is 2 n−1 . To prove tightness, we use a ternary alphabet, and we show that this bound cannot be met by any binary prefix-free language. On nonreturning languages, the upper bound is 2 n−1 + 1, and it is tight already in the binary case. We also study the unary case in all three classes.

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Lower Bounds for Complementation of ω-Automata Via the Full Automata Technique

Yan

2006

Automata, Languages and Programming

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State complexity of some operations on binary regular languages

Cited by 111 publications

References 12 publications

Incomplete operational transition complexity of regular languages

Incomplete operational transition complexity of regular languages

Complement on Prefix-Free, Suffix-Free, and Non-Returning NFA Languages

Lower Bounds for Complementation of ω-Automata Via the Full Automata Technique

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