Membrane system models for super-Turing paradigms
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We extend Calude and Păun’s accelerating P system model of computation, and investigate the computational power of the resulting systems. We show that the resulting systems can solve problems at all levels of the arithmetical hierarchy, and that the higher systems have hyperarithmetical computational power.
KeywordsP system Membrane system Hypercomputation Super-Turing Arithmetical hierarchy Hyperarithmetical hierarchy
A preliminary version of this material was presented at the UC09 Hypercomputation Workshop, Ponta Delgada, The Azores, 7–11 September 2009. The authors would like to thank the anonymous reviewers for their helpful comments. This research was funded in part by the EPSRC (HyperNet, Grant Ref. EP/E064183/1). MG’s research is also partially funded by CNCSIS grant no. 643/2009.
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