Syntactic Complexity of Prefix-, Suffix-, and Bifix-Free Regular Languages
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- Brzozowski J., Li B., Ye Y. (2011) Syntactic Complexity of Prefix-, Suffix-, and Bifix-Free Regular Languages. In: Holzer M., Kutrib M., Pighizzini G. (eds) Descriptional Complexity of Formal Systems. DCFS 2011. Lecture Notes in Computer Science, vol 6808. Springer, Berlin, Heidelberg
The syntactic complexity of a regular language is the cardinality of its syntactic semigroup. The syntactic complexity of a subclass of the class of regular languages is the maximal syntactic complexity of languages in that class, taken as a function of the state complexity n of these languages. We study the syntactic complexity of prefix-, suffix-, and bifix-free regular languages. We prove that nn − 2 is a tight upper bound for prefix-free regular languages. We present properties of the syntactic semigroups of suffix- and bifix-free regular languages, and conjecture tight upper bounds on their size.
Keywordsbifix-free finite automaton monoid prefix-free regular language semigroup suffix-free syntactic complexity
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