Operations on Self-Verifying Finite Automata

Jirásek, Jozef; Jirásková, Galina; Szabari, Alexander

doi:10.1007/978-3-319-20297-6_16

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…While investigating operational state complexity on self-verifying or unambiguous automata, which are nondeterministic, the NFA-to-DFA trade-off provides an upper bound on the complexity of the corresponding operation since every DFA is self-verifying as well as unambiguous. As shown in [8,9], these upper bounds are tight for several operations.…”

Section: Introductionmentioning

confidence: 80%

“…Table 2 shows the operational state complexity on languages represented by self-verifying and unambiguous finite automata from [8,9]. The NFA-to-DFA trade-off for concatenation, shuffle, left and right quotient is up to one state almost the same as the complexity of these operations on unambiguous automata.…”

Section: Discussionmentioning

confidence: 99%

“…Holzer and Kutrib [6] considered the representation of regular languages by nondeterministic finite automata (NFAs) and defined and studied the nondeterministic state complexity of regular languages and operations in an analogous way. Jirásek Jr. et al [8,9] investigated operational state complexity using representation of regular languages by self-verifying and unambiguous finite automata. Notice that in all of the above mentioned cases, the arguments and the results of regular operations are represented by the same computational model.…”

Section: Introductionmentioning

confidence: 99%

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NFA-to-DFA Trade-Off for Regular Operations

Jirásková

Krajňáková

2019

Descriptional Complexity of Formal Systems

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We examine the operational state complexity assuming that the operands of a regular operation are represented by nondeterministic finite automata, while the language resulting from the operation is required to be represented by a deterministic finite automaton. We get tight upper bounds 2 n for complementation, reversal, and star, 2 m for left and right quotient, 2 m+n for union and symmetric difference, 2 m+n − 2 m − 2 n + 2 for intersection, 2 m+n − 2 n + 1 for difference, 3 4 2 m+n for concatenation, and 2 mn for shuffle. We use a binary alphabet to describe witnesses for complementation, reversal, star, and left and right quotient, and a quaternary alphabet otherwise. Whenever we use a binary alphabet, it is always optimal.

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Section: Introductionmentioning

confidence: 80%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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NFA-to-DFA Trade-Off for Regular Operations

Jirásková

Krajňáková

2019

Descriptional Complexity of Formal Systems

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“…The investigation of self-verifying automata was further deepened by Jirásek et al [9]. Using the tight bound g(n) from [11], it was shown that a minimal SVFA for a regular language may not be unique.…”

Section: Introductionmentioning

confidence: 99%