Is There a Nonrecursive Decidable Equational Theory?
- Benjamin WellsAffiliated withDepartments of Mathematics and Computer Science, University of San Francisco
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The Church-Turing Thesis (CTT) is often paraphrased as ``every computable function is computable by means of a Turing machine.'' The author has constructed a family of equational theories that are not Turing-decidable, that is, given one of the theories, no Turing machine can recognize whether an arbitrary equation is in the theory or not. But the theory is called pseudorecursive because it has the additional property that when attention is limited to equations with a bounded number of variables, one obtains, for each number of variables, a fragment of the theory that is indeed Turing-decidable. In a 1982 conversation, Alfred Tarski announced that he believed the theory to be decidable, despite this contradicting CTT. The article gives the background for this proclamation, considers alternate interpretations, and sets the stage for further research.
- Is There a Nonrecursive Decidable Equational Theory?
Minds and Machines
Volume 12, Issue 2 , pp 301-324
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
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- Church-Turing Thesis
- effective procedure
- pseudorecursive theory
- quotidian procedure
- Turing decidability
- Industry Sectors
- Benjamin Wells (1)
- Author Affiliations
- 1. Departments of Mathematics and Computer Science, University of San Francisco, San Francisco, CA, USA