Compressed membership in automata with compressed labels

Abstract. The algorithmic problem of whether a compressed string is accepted by a (nondeterministic) finite state automaton with compressed transition labels is investigated. For string compression, straight-line programs (SLPs), i.e., context-free grammars that generate exactly one string, are used. Two algorithms for this problem are presented. The first one works in polynomial time, if all tran-sition labels are nonperiodic strings (or more generally, the word length divided by the period is bounded polynomially in the input size). This answers a ques-tion of Plandowski and Rytter. The second (nondeterministic) algorithm is an NP-algorithm under the assumption that for each transition label the period is bounded polynomially in the input size. This generalizes the NP upper bound for the case of a unary alphabet, shown by Plandowski and Rytter.