When is an extension of a specification consistent? Decidable and undecidable cases†

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The problem of consistency is the following decision problem: Instance: Two finite specifications (∑, E) and (∑1, E1), where the signature ∑ is contained in the signature ∑1.

Question: Is (∑1, E1) a consistent extension of (∑, E)?

For the special case of string-rewriting systems we present decidable and undecidable cases of this problem. As it turns out in order to obtain decidability rather severe restrictions are necessary either on the syntactic form of the equations in E and E1 or on the algebraic structure of the algebras (i.e. monoids) that are presented by (∑, E) and (∑1, E1), respectively.

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†

This work was performed while the author was visiting at Fachbereich Informatik, Universität Kaiserslautern, 6750 Kaiserslautern, Germany. Part of the results were announced at the 3rd International Conference on Rewriting Techniques and Applications, Chapel Hill, NC, U.S.A., April 1989.

Copyright © 1991 Published by Elsevier Ltd.