On the Complexity of k-Piecewise Testability and the Depth of Automata

Tomáš MasopustTomáš Masopust, Michaël ThomazoMichaël Thomazo

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Tomáš Masopust, Michaël Thomazo
On the Complexity of k-Piecewise Testability and the Depth of Automata
Proc. 19th International Conference on Developments in Language Theory (DLT'15), to appear

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KurzfassungAbstract
For a non-negative integer k, a language is k-piecewise testable (k-PT) if it is a finite boolean combination of languages of the form \Sigma^*a1\Sigma^*...\Sigma^*an for ai in \Sigma and 0 <= n <= k. We study the following problem: Given a DFA recognizing a piecewise testable language, decide whether the language is k-PT. We provide a complexity bound on this problem and a detailed analysis for small k's. The result can be use to find the minimal k for which the language is k-PT. We show that the upper bound on k given by the depth of the minimal DFA can be exponentially bigger than the minimal possible k, and provide a tight upper bound on the depth of the minimal DFA recognizing a k-PT language.
Projekt:Project: DIAMOND
Forschungsgruppe:Research Group: Knowledge SystemsKnowledge-Based Systems

@inproceedings{MT2015,
  author    = {Tom{\'{a}}{\v{s}} Masopust and Micha{\"{e}}l Thomazo},
  title     = {On the Complexity of k-Piecewise Testability and the Depth of
               Automata},
  booktitle = {Proc. 19th International Conference on Developments in Language
               Theory (DLT'15)},
  year      = {2015}
}