Ordering regular languages and automata: Complexity
نویسندگان
چکیده
Given an order of the underlying alphabet, we can lift it to states a finite deterministic automaton: compare use strings reaching them. When on is co-lexicographic one and this turns out be total, DFA called Wheeler. This recently introduced class automata—the Wheeler automata—constitute important data-structure for languages, since allows design implementation very efficient tool-set storage mechanisms transition function, supporting large variety substring queries. In context natural consider regular languages accepted by automata, i.e. languages. An inspiring result in area following: has been shown that, as opposed general case, classic determinization powerset construction polynomial automata. As consequence, most classical problems, when considered turn “easy”—that is, solvable time. paper computational problems related Wheelerness, but starting from non-deterministic We also case reduced ones—a NFAs where recognizing Wheelerness still polynomial, DFAs. Our collection results shows that moving towards non-determinism cases, dangerous path leading quickly intractability. Moreover, start study “state complexity” DFAs proving intersection computationally simpler than case. provide minimum given language.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2023
ISSN: ['1879-2294', '0304-3975']
DOI: https://doi.org/10.1016/j.tcs.2023.113709