Piecewise Testable Languages via Combinatorics on Words
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Discrete Mathematics |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.disc.2011.06.013 |
| 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. |
| Related projects: |