Some Remarks on Directable Automata

  B. ImrehM. Steinby

Abstract:

  A finite automaton is said to be directable if there exists a word, a directing word, which takes the automaton from every state to the same state. After some general remarks on directable automata and their directing words we present methods for testing the directability of an automaton and for finding the least congruence of an automaton which yields a directable quotient automaton. A well-known conjecture by J. ern claims that any -state directable automaton has a directing word of length , but the best known upper bounds are of the order . However, for special classes of automata lower bounds can be given. We consider a generalized form of ern's conjecture proposed by J.-E. Pin for the classes of commutative, definite, reverse definite, generalized definite and nilpotent automata. We also establish the inclusion relationships between these classes within the class of directable automata.

 Gyenizse Pal 1996. Szeptember 3. Kedd 13:01:45 MET DST