Abstract
The problem of consistency is the following decision problem: Instance: Two finite specifications (∑, E ) and (∑ 1 , E 1 ), where the signature ∑ is contained in the signature ∑ 1 . Question: Is (∑ 1 , E 1 ) 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 E 1 or on the algebraic structure of the algebras (i.e. monoids) that are presented by (∑, E ) and (∑ 1 , E 1 ), respectively.
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