Computability
Comparing the Church and Turing approaches: two prophetical messages
A half-century survey on The Universal Turing Machine
Recursion theory
Computability and complexity: from a programming perspective
Computability and complexity: from a programming perspective
Sequential abstract-state machines capture sequential algorithms
ACM Transactions on Computational Logic (TOCL)
Computable analysis: an introduction
Computable analysis: an introduction
Computation: finite and infinite machines
Computation: finite and infinite machines
How to compare the power of computational models
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
On the completeness of quantum computation models
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Persistent queries in the behavioral theory of algorithms
ACM Transactions on Computational Logic (TOCL)
Exact exploration and hanging algorithms
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Fields of logic and computation
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Towards an axiomatization of simple analog algorithms
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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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.