Compressed Membership in Automata with Compressed Labels

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., contextfree grammars that generate exactly one string, are used. Two algorithms for this problem are presented. The first one works in polynomial time, if all transition labels are nonperiodic strings (or more generally, the word length divided by the period is bounded polynomially in the input size). This answers a question 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.