# zbMATH — the first resource for mathematics

Simulation is decidable for one-counter nets (extended abstract). (English) Zbl 0940.68055
Sangiorgi, Davide (ed.) et al., CONCUR ’98. Concurrency theory. 9th international conference, Nice, France, September 8-11, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1466, 253-268 (1998).
Summary: We prove that the simulation preorder is decidable for the class of one-counter nets. A one-counter net consists of a finite-state machine operating on a variable (counter) which ranges over the natural numbers. Each transition can increase or decrease the value of the counter. A transition may not be performed if this implies that the value of the counter becomes negative. The class of one-counter nets is computationally equivalent to the class of Petri nets with one unbounded place, and to the class of pushdown automata where the stack alphabet is restricted to one symbol. To our knowledge, this is the first result in the literature which gives a positive answer to the decidability of simulation preorder between pairs of processes in a class whose elements are neither finite-state nor allow finite partitioning of their state spaces.
For the entire collection see [Zbl 0895.00051].

##### MSC:
 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
##### Keywords:
simulation preorder; Petri nets; pushdown automata