# Algebra Seminar talk

2012-09-14

Libor **Polak***On Biautomata*

Abstract:

We initiate the theory and applications of biautomata.
A biautomaton can read a word alternately from the
left and from the right. We assign to each regular
language L its canonical biautomaton.
This structure plays, among all biautomata
recognizing the language L, the same role as the
minimal deterministic automaton has among all
deterministic automata recognizing the language L.
We expect that from the graph structure of this automaton
one could decide the membership of a given language
in certain significant classes of languages.

We present the first two results of this kind: namely, a language L is piecewise testable if and only if the canonical biautomaton of L is acyclic. From this result Simon's famous characterization of piecewise testable languages easily follows.

The second class of languages characterizable by the graph structure of their biautomata are prefix-suffix languages.

In the Development in Language Theory's contribution we improved the result concerning piecewise testable languages in a significant way.

(One can find the corresponding papers on here: Publications (items 20 and 25).