The Church-Turing Thesis over arbitrary domains

Udi Boker*, Nachum Dershowitz

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


The Church-Turing Thesis has been the subject of many variations and interpretations over the years. Specifically, there are versions that refer only to functions over the natural numbers (as Church and Kleene did), while others refer to functions over arbitrary domains (as Turing intended). Our purpose is to formalize and analyze the thesis when referring to functions over arbitrary domains. First, we must handle the issue of domain representation. We show that, prima facie, the thesis is not well defined for arbitrary domains, since the choice of representation of the domain might have a non-trivial influence. We overcome this problem in two steps: (1) phrasing the thesis for entire computational models, rather than for a single function; and (2) proving a "completeness" property of the recursive functions and Turing machines with respect to domain representations. In the second part, we propose an axiomatization of an "effective model of computation" over an arbitrary countable domain. This axiomatization is based on Gurevich's postulates for sequential algorithms. A proof is provided showing that all models satisfying these axioms, regardless of underlying data structure, are of equivalent computational power to, or weaker than, Turing machines.

Original languageEnglish
Title of host publicationPillars of Computer Science - Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday
EditorsArnon Avron, Nachum Dershowitz, Alexander Rabinovich
Number of pages31
StatePublished - 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4800 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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