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Automata and processes on multisets of communicating objects

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Abstract

Inspired by P systems initiated by Gheorghe Pãun, we study a computation model over a multiset of communicating objects. The objects in our model are instances of finite automata. They interact with each other by firing external transitions between two objects. Our model, called a service automaton, is intended to specify, at a high level, a service provided on top of network devices abstracted as communicating objects. We formalize the concept of processes, running over a multiset of objects, of a service automaton and study the computing power of both single-process and multiprocess service automata. In particular, in the multiprocess case, regular maximal parallelism is defined for inter-process synchronization. It turns out that single-process service automata are equivalent to vector addition systems and hence can define nonregular processes. Among other results, we also show that Presburger reachability problem for single-process service automata is decidable, while it becomes undecidable in the multiprocess case. Hence, multiprocess service automata can not be effectively simulated by vector addition systems.

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Acknowledgments

The authors would like to thank the anonymous referees for their useful comments and suggestions.

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Correspondence to Linmin Yang.

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Yang, L., Wang, Y. & Dang, Z. Automata and processes on multisets of communicating objects. Nat Comput 9, 865–887 (2010). https://doi.org/10.1007/s11047-010-9206-0

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