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Descriptional Complexity of Finite Automata-Selected Highlights
Tekijät: Salomaa, Arto; Salomaa, Kai; Smith, Taylor J.
Kustantaja: IOS Press BV
Julkaisuvuosi: 2024
Journal: Fundamenta Informaticae
Tietokannassa oleva lehden nimi: Fundamenta Informaticae
Vuosikerta: 191
Numero: 3-4
Aloitussivu: 231
Lopetussivu: 237
eISSN: 1875-8681
DOI: https://doi.org/10.3233/FI-242180
Verkko-osoite: https://doi.org/10.3233/FI-242180
Rinnakkaistallenteen osoite: https://arxiv.org/pdf/2301.03708
Preprintin osoite: https://arxiv.org/abs/2301.03708
Tiivistelmä
The state complexity, respectively, nondeterministic state complexity of a regular language L is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for L. Some of the most studied state complexity questions deal with size comparisons of nondeterministic finite automata of differing degree of ambiguity. More generally, if for a regular language we compare the size of description by a finite automaton and by a more powerful language definition mechanism, such as a context-free grammar, we encounter non-recursive trade-offs. Operational state complexity studies the state complexity of the language resulting from a regularity preserving operation as a function of the complexity of the argument languages. Determining the state complexity of combined operations is generally challenging and for general combinations of operations that include intersection and marked concatenation it is uncomputable.
The state complexity, respectively, nondeterministic state complexity of a regular language L is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for L. Some of the most studied state complexity questions deal with size comparisons of nondeterministic finite automata of differing degree of ambiguity. More generally, if for a regular language we compare the size of description by a finite automaton and by a more powerful language definition mechanism, such as a context-free grammar, we encounter non-recursive trade-offs. Operational state complexity studies the state complexity of the language resulting from a regularity preserving operation as a function of the complexity of the argument languages. Determining the state complexity of combined operations is generally challenging and for general combinations of operations that include intersection and marked concatenation it is uncomputable.
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