On the Complexity of k-Piecewise Testability and the Depth of Automata
From International Center for Computational Logic
On the Complexity of k-Piecewise Testability and the Depth of Automata
Talk by Tomáš Masopust
- Location: APB 3105
- Start: 31. August 2015 at 2:50 pm
- End: 31. August 2015 at 3:50 pm
- Event series: KBS Seminar
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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.
