Publication details

Piecewise Testable Languages via Combinatorics on Words

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KLÍMA Ondřej

Year of publication 2011
Type Article in Periodical
Magazine / Source Discrete Mathematics
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Piecewise testable languages; Syntactic congruence
Description A regular language L over an alphabet A is called piecewise testable if it is a finite Boolean combination of languages of the form B a1 B a2 B ... B al B, where a1,... ,al are letters from A and B is the set of all words over A. An effective characterization of piecewise testable languages was given in 1972 by Simon who proved that a language L is piecewise testable if and only if its syntactic monoid is J-trivial. Nowadays, there exist several proofs of this result based on various methods from algebraic theory of regular languages. Our contribution adds a new purely combinatorial proof.
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