Shrinking restarting automata

Abstract

Restarting automata are a restricted model of computation that is motivated by the so-called analysis by reduction. A computation of a restarting automaton consists of a sequence of cycles such that in each cycle the automaton performs exactly one rewrite step, which replaces a small part of the tape content by another, even shorter word. Here we consider a natural generalization of this model, called shrinking restarting automaton, where we require that there exists a weight function such that each rewrite step decreases the weight of the tape content with respect to that function. While it is still unknown whether the two most general types of restarting automata, the RWW-automaton and the RRWW-automaton, differ in their expressive power, we will see that the classes of languages accepted by the shrinking RWW-automaton and the shrinking RRWW-automaton coincide. Further, we will relate shrinking RRWW-automata to finite-change automata, which leads to new insights into the relationships between the classes of languages characterized by (shrinking) restarting automata and some well-known time and space complexity classes. © Springer-Verlag Berlin Heidelberg 2005.