Deterministic and nondeterministic computation, and horn programs, on abstract data types

doi:10.1016/0743-1066(92)90020-4

The Journal of Logic Programming

Volume 13, Issue 1, May 1992, Pages 23-55

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Abstract

We investigate the notion of “semicomputability,” intended to generalize the notion of recursive enumerability of relations to abstract structures. Two characterizations are considered and shown to be equivalent: one in terms of “partial computable functions” (for a suitable notion of computability over abstract structures) and one in terms of definability by means of Horn programs over such structures. This leads to the formulation of a “Generalized Church-Turing Thesis” for definability of relations on abstract structures.

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^∗: Department of Mathematics and Computer Science, University College of Swansea SA2 8PP, Wales. The research of J.V.T. was partially supported by SERC Research Grants GR/F 10606 (under the Alvey Programme) and GR/F 59070.

^†: Department of Computer Science and Systems, McMaster University, Hamilton, Ontario L8S 4K1, Canada. The research of J.I.Z. was supported by the National Science Foundation under grant no. DCR-8504296, by SERC Research Grant GR/F 10606 (under the Alvey Programme), by a grant from the Science and Engineering Research Board of McMaster University, by a grant from the Natural Sciences and Engineering Research Council of Canada, and by an academic travel grant from the British Council.