Finite-change automata

Abstract

Beside the question of nondeterminism the connection between time and space is the most urgent problem in automata theory. In this paper we introduce a new storage medium with properties between space and time: the finite-change tape (FC-tape), a Turing tape, on which every cell can be changed only a bounded number of times. This is an extension of both the measures considered by Hibbard (1967) and Wechsung (1976). In common with the medium time it has the limited possibility of re-using. We consider automata with one bounded FC-tape also used as input tape and automata with additional Turing tape. In the first chapter we summarize some simple properties which already implies the close relationship to computation time. In the second chapter we give more arguments for the position between time and space: even nondeterministic automata with linear FC-tape and ~-bounded Turing tape can be simulated by deterministic linear bounded automata; on the other hand any multitape Turing machine operating in linear time is simulated by some singletape machine which exclusively changes symbols of the original input (i.e. only once) with determinism preserved. From this follows that the class of languages accepted by automata with f(n)-bounded FC-tape is located between the classes of languages accepted by multitape Turing machines in time f(n) and singletape Turing machines in time (f(n)) 2. For the nondeterministic automata with linear FC-tape and log n-bounded Turing tape (equivalent to multihead FC-automata) there is a lot of relations to the questions concerning P, NP, DSPACE(Iog n) and NSPACE(log n): these automata recognize any language in the least AFL containing NSPACE(Iog n); their running time is polynomial, and they can be simulated by deterministic linear bounded automata.