Undecidability and Complexity for Super-Turing Models of Computation

It seems that intelligent complex systems will require formalisms having richer behavior than Turing machines. Very little is known about the relations (e.g., the expressiveness and/or effectiveness) between new super-Turing models of computation. The objective of this paper is an attempt to establi...

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Bibliographic Details
Published in:Proceedings Vol. 81; no. 1; p. 123
Main Author: Eugene Eberbach
Format: Journal Article
Language:English
Published: MDPI AG 01.03.2022
Subjects:
a-decidability
i-decidability
intractability
super-recursive algorithms
super-Turing computation
undecidability
ISSN:2504-3900
Online Access:Get full text
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Summary:It seems that intelligent complex systems will require formalisms having richer behavior than Turing machines. Very little is known about the relations (e.g., the expressiveness and/or effectiveness) between new super-Turing models of computation. The objective of this paper is an attempt to establish a hierarchy of expressiveness of super-Turing models. Truly, a new theory of undecidability and complexity for super-Turing models has to be developed. Some preliminary steps have been done in this paper by introducing a-decidable and i-decidable algorithms and U-complete, D-complete, and H-complete complexity classes that were inspired by NP-complete and PSPACE-complete classes for intractable problems. This paper should be understood as a preliminary step leading to feasible approximate solutions of Turing machine undecidable problems, in a similar way as approximate, randomized, and parallel algorithms allow for feasible solutions for intractable problems.
ISSN:2504-3900
DOI:10.3390/proceedings2022081123