Austinat, Diekert, Hertrampf, and Petersen [2] proved that every language L that is (m,n)-recognizable by a deterministic frequency automaton such that m > n/2 can be recognized by a deterministic finite automaton as well. First, the size of deterministic frequency automata and of deterministic finite automata recognizing the same language is compared. Then approximations of a language are considered, where a language L′ is called an approximation of a language L if L′ differs from L in only a finite number of strings. We prove that if a deterministic frequency automaton has k states and (m,n)-recognizes a language L, where m > n/2, then there is a language L′ approximating L such that L′ can be recognized by a deterministic finite automaton with no more than k states. Austinat et al. [2] also proved that every language L over a single-letter alphabet that is (1,n)-recognizable by a deterministic frequency automaton can be recognized by a deterministic finite automaton. For languages over a single-letter alphabet we show that if a deterministic frequency automaton has k states and (1,n)-recognizes a language L then there is a language L′ approximating L such that L′ can be recognized by a deterministic finite automaton with no more that k states. However, there are approximations such that our bound is much higher, i.e., k!. © 2013 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Freivalds, R., Zeugmann, T., & Pogosyan, G. R. (2013). On the size complexity of deterministic frequency automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7810 LNCS, pp. 287–298). Springer Verlag. https://doi.org/10.1007/978-3-642-37064-9_26
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