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dc.contributor.authorBrzozowski, Janusz
dc.contributor.authorJirásková, Galina
dc.contributor.authorBaiyu, Li
dc.contributor.authorSmith, Joshua 16:58:18 (GMT) 16:58:18 (GMT)
dc.description.abstractA language $L$ is prefix-free if whenever words $u$ and $v$ are in $L$ and $u$ is a prefix of $v$, then $u=v$. Suffix-, factor-, and subword-free languages are defined similarly, where by ``subword" we mean ``subsequence", and a language is bifix-free if it is both prefix- and suffix-free. These languages have important applications in coding theory. The quotient complexity of an operation on regular languages is defined as the number of left quotients of the result of the operation as a function of the numbers of left quotients of the operands. The quotient complexity of a regular language is the same as its state complexity, which is the number of states in the complete minimal deterministic finite automaton accepting the language. The state/quotient complexity of operations in the classes of prefix- and suffix-free languages has been studied before. Here, we study the complexity of operations in the classes of bifix-, factor-, and subword-free languages. We find tight upper bounds on the quotient complexity of intersection, union, difference, symmetric difference, concatenation, star, and reversal in these three classes of languages.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council of Canada [OGP0000871]en
dc.description.sponsorshipSlovak Research and Development Agency [APVV-0035-10]en
dc.description.sponsorshipAlgorithms, Automata, and Discrete Data Structures VEGA, [2/0183/11]en
dc.publisherInstitute of Informatics: University of Szegeden
dc.subjectfinite automatonen
dc.subjectquotient complexityen
dc.subjectregular languageen
dc.subjectstate complexityen
dc.subjecttight upper bounden
dc.titleQuotient Complexity of Bifix-, Factor-, and Subword-Free Regular Languageen
dcterms.bibliographicCitationBrzozowski, J., Jirásková, G., Baiyu, L., & Smith, J. (2014). Quotient Complexity of Bifix-, Factor-, and Subword-Free Regular Language. Acta Cybernetica, 21(4), 507–527.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen

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