Biautomata for k-Piecewise Testable Languages

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F12%3A00057569" target="_blank" >RIV/00216224:14310/12:00057569 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-642-31653-1_31" target="_blank" >http://dx.doi.org/10.1007/978-3-642-31653-1_31</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-642-31653-1_31" target="_blank" >10.1007/978-3-642-31653-1_31</a>

Result language
angličtina
Original language name
Biautomata for k-Piecewise Testable Languages
Original language description
An effective characterization of piecewise testable languages was given by Simon in 1972. A difficult part of the proof is to show that if L has a J -trivial syntactic monoid M(L) then L is k-piecewise testable for a suitable k. By Simon?s original proof, an appropriate k could be taken as two times the maximal length of a chain of ideals in M(L) . In this paper we improve this estimate of k using the concept of biautomaton: a kind of finite automaton which arbitrarily alternates between reading the input word from the left and from the right. We prove that an appropriate k could be taken as the length of the longest simple path in the canonical biautomaton of L. We also show that this bound is better than the known bounds which use the syntactic monoid of L.
Czech name
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Czech description
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Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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