Computational processes, observers and Turing incompleteness

We propose a formal definition of Wolfram’s notion of computational process based on iterated transducers together with a weak observer, a model of computation that captures some aspects of physics-like computation. These processes admit a natural classification into decidable, intermediate and complete, where intermediate processes correspond to recursively enumerable sets of intermediate degree in the classical setting. It is shown that a standard finite injury priority argument will not suffice to establish the existence of an intermediate computational process. Key words: Computational process, degrees of unsolvability, intermediate degrees PACS:

• Type: Journal
• Year: 2011
• Where: TCS
• Authors: Klaus Sutner
• Keywords: Computational Process, Intermediate Computational Process, Intermediate Degrees, TCS 2011, Theoretical Computer Science