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One-counter nets are nondeterministic one-counter automata without zero-testing (Petri Nets with at most one unbounded place). A one-counter circuit of length ∆ is a strongly connected one-counter net, such that ∆ is a greatest common divisor of effects of all its cycles. A circuit has simple periodic behaviour: for any control state the set of corresponding reachable counter values is an arithmetic progression with difference ∆ (with an exception of a bounded subset). Properties of circuits and general one-counter nets are studied. It is shown that the infinite behaviour of a one-counter net can be represented by a composition of a finite set of circuits

Year: 2014

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