Prefix-Free Languages: Right Quotient and Reversal

Jirásek, Jozef; Jirásková, Galina; Krausová, Monika; Mlynárčik, Peter; Šebej, Juraj

doi:10.1007/978-3-319-09704-6_19

Cited by 2 publications

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“…Free languages Table 7 summarizes state complexity results of individual operations on prefix-free languages [82,83,112,22,120,116,102,55]. In the case of state complexity, the results are valid for Boolean operations if m, n ≥ 3; for catenation if m, n ≥ 2; for star if k = 1, then m ≥ 3, if k = 2 then m = 3, and else m ≥ 2; and for reversal if m ≥ 4 and the tight bound cannot be reached if k = 2 [112].…”

Section: A Language L Is ¢-Closed (¤-Closed) If and Only Ifmentioning

confidence: 99%

“…In the case of state complexity, the results are valid for Boolean operations if m, n ≥ 3; for catenation if m, n ≥ 2; for star if k = 1, then m ≥ 3, if k = 2 then m = 3, and else m ≥ 2; and for reversal if m ≥ 4 and the tight bound cannot be reached if k = 2 [112]. The state complexty of right quotient is 1, if k = 1 and m = 1 or m > n, and if k = 2 and m = 1 or n = 1; furthermore, if m = 2 then sc(L 1 /L 2 ) = n [102].…”

Section: A Language L Is ¢-Closed (¤-Closed) If and Only Ifmentioning

confidence: 99%

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A Survey on Operational State Complexity

Gao,

Moreira,

Reis

et al. 2015

Preprint

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Descriptional complexity is the study of the conciseness of the various models representing formal languages. The state complexity of a regular language is the size, measured by the number of states of the smallest, either deterministic or nondeterministic, finite automaton that recognises it. Operational state complexity is the study of the state complexity of operations over languages. In this survey, we review the state complexities of individual regularity preserving language operations on regular and some subregular languages. Then we revisit the state complexities of the combination of individual operations. We also review methods of estimation and approximation of state complexity of more complex combined operations.

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