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Counter machines. (English) Zbl 0999.68066

Summary: In this paper we study the computational power of counters. Two different notions of a counter occur in the literature. One, which we call a two-way counter, is common in automata theory and is provided with the following operations: increment and decrement by 1 and test for zero. Another notion was used in schematology and logics of programs. The corresponding set of operations comes from the simplest algebraic structure of positive integers with increment by 1, reset to 0 and comparison of two counter values. There is no decrementation, therefore we call it a one-way counter. It is known that two two-way counters are enough to simulate a Turing machine. We present the same result for the one-way model: two one-way counters can simulate each Turing machine. We also discuss some consequences of this result for the hierarchy of program schemes.

MSC:

68Q05 Models of computation (Turing machines, etc.) (MSC2010)
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