Theoretical Aspects of Symbolic Automata

Symbolic finite automata extend classical automata by allowing infinite alphabets given by Boolean algebras and having transitions labeled by predicates over such algebras. Symbolic automata have been intensively studied recently and they have proven useful in several applications. We study some theoretical aspects of symbolic automata. Especially, we study minterms of symbolic automata, that is, the set of maximal satisfiable Boolean combinations of predicates of automata. We define canonical minterms of a language accepted by a symbolic automaton and show that these minterms can be used to define symbolic versions of some known classical automata. Also we show that canonical minterms have an important role in finding minimal nondeterministic symbolic automata. We show that Brzozowski's double-reversal method for minimizing classical deterministic automata as well as its generalization is applicable for symbolic automata.