Computation as an unbounded process

Authors:
Jan van Leeuwen;Jií Wiedermann
Affiliations:
Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands;Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou ví 2, 182 07 Prague 8, Czech Republic
Venue:
Theoretical Computer Science
Year:
2012

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Abstract

We develop a model of computation as an unbounded process, measuring complexity by the number of observed behavioural changes during the computation. In a natural way, the model brings effective unbounded computation up to the second level of the Arithmetical Hierarchy, unifying several earlier concepts like trial-and-error predicates and relativistic computing. The roots of the model can be traced back to the circular a-machines already distinguished by Turing in 1936. The model allows one to introduce nondeterministic unbounded computations and to formulate an analogue of the P-versus-NP question. We show that under reasonable assumptions, the resource-bounded versions of deterministic and nondeterministic unbounded computation have equal computational power but that in general, the corresponding complexity classes are different (P^m^i^n^d@?NP^m^i^n^d).