On the Gap-Complexity of Simple RL-Automata

Analysis by reduction is a method used in linguistics for checking the correctness of sentences of natural languages. This method is modelled by restarting automata. Here we introduce and study a new type of restarting automaton, the so-called t-sRL-automaton, which is an RL-automaton that is rather restricted in that it has a window of size 1 only, and that it works under a minimal acceptance condition. On the other hand, it is allowed to perform up to t rewrite (that is, delete) steps per cycle. Here we study the gap-complexity of these automata. The membership problem for a language that is accepted by a t-sRL-automaton with a bounded number of gaps can be solved in polynomial time. On the other hand, t-sRL-automata with an unbounded number of gaps accept NP-complete languages.