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The first-order theory of linear one-step rewriting is undecidable

✍ Scribed by Ralf Treinen

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
758 KB
Volume
208
Category
Article
ISSN
0304-3975

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✦ Synopsis

The theory of one-step rewriting for a given rewrite system R and signature C is the firstorder theory of the following structure: its universe consists of all C-ground terms, and its only predicate is the relation "x rewrites to y in one step by R". The structure contains no function symbols and no equality. We show that there is no algorithm deciding the 3*V*-fragment of this theory for an arbitrary finite, linear and non-erasing term-rewriting system.

With the same technique we prove that the theory of encompassment plus one-step rewriting by the rule f'(x) + y(x) and the modal theory of one-step rewriting are undecidable.

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