Opened Access First Steps Towards a Geometry of Computation
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Autor: Muskulus, Michael
Brijder, Robert
Fecha: 2005
Publicado en: Proceedings of the Third Brainstorming Week on Membrane Computing, 197-218. Sevilla, E.T.S. de Ingeniería Informática, 31 de Enero-4 de Febrero, 2005,
ISBN/ISSN: 84-609-6771-9
Tipo de documento: Ponencia
Resumen: We introduce a geometrical setting which seems promising for the study of computation in multiset rewriting systems, but could also be applied to register machines and other models of computation. This approach will be applied here to membrane systems (also known as P systems) without dynamical membrane creation. We discuss the role of maximum parallelism and further simplify our model by considering only one membrane and sequential application of rules, thereby arriving at asynchronous multiset rewriting systems (AMR systems). Considering only one membrane is no restriction, as each static membrane system has an equivalent AMR system. It is further shown that AMR systems without a priority relation on the rules are equivalent to Petri Nets. For these systems we introduce the notion of asymptotically exact computation, which allows for stochastic appearance checking in a priori bounded (for some complexity measure) computations. The geometrical analogy in the lattice Nd0 ; ...
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