On Stateless Multicounter Machines

Authors:
Ömer Eğecioğlu;Oscar H. Ibarra
Affiliations:
Department of Computer Science, University of California, Santa Barbara, USA 93106;Department of Computer Science, University of California, Santa Barbara, USA 93106
Venue:
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Year:
2009

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Abstract

We investigate the computing power of stateless multi-counter machines with reversal-bounded counters. Such a machine has m -counters and it operates on a one-way input delimited by left and right end markers. The move of the machine depends only on the symbol under the input head and the signs of the counters (zero or positive). At each step, every counter can be incremented by 1, decremented by 1 (if it is positive), or left unchanged. An input string is accepted if, when the input head is started on the left end marker with all counters zero, the machine eventually reaches the configuration where the input head is on the right end marker with all the counters again zero. Moreover, for a specified k , no counter makes more than k -reversals (i.e., alternations between increasing mode and decreasing mode) on any computation, accepting or not. We mainly focus our attention on deterministic realtime (the input head moves right at every step) machines. We show hierarchies of computing power with respect to the number of counters and reversals. It turns out that the analysis of these machines gives rise to rather interesting combinatorial questions.