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The word problem distinguishes counter languages

Sean Cleary·Murray Elder·Gretchen Ostheimer
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Abstract

Counter automata are more powerful versions of finite-state automata where addition and subtraction operations are permitted on a set of n integer registers, called counters. We show that the word problem of $\Z^n$ is accepted by a nondeterministic $m$-counter automaton if and only if $m \geq n$.

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Sean Cleary, Murray Elder, Gretchen Ostheimer. 2006-06-17. The word problem distinguishes counter languages. https://arxiv.org/abs/math/0606415

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