# On the complexity of (off-line) 1-tape ATM's running in constant reversals

Theory Of Computing, Algorithms And Programming

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## Abstract

Yamamoto and Noguchi [YN87] raised the question of whether every recursively enumberable set can be accepted by a 1-tape or off-line 1-tape alternating Turing machine (ATM) whose (work)tape head makes only a constant number of reversals. In this paper, we answer the open question in the negative. We show that (1) constant-reversal 1-tape ATM's accept only regular languages and (2) there exists a recursive function h(k,r,n) such that for every k-state off-line 1-tape ATM M running in r reversals, the language accepted by M is in ASPACE(h(k,r,n)).

## Key words

computational complexity alternating Turing machine 1-tape off-line 1-tape head reversal## Preview

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© Springer-Verlag Berlin Heidelberg 1991