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  The Word Problem of ACD-Ground theories is Undecidable

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Abstract:

We prove that there exists an ACD-ground theory--- an equational theory defined by a set of ground equations plus the associativity and commutativity of two binary symbols and +, and the distributivity of over +--- for which the word problem is undecidable. 1

Citations

418 Simple word problems in universal algebras – Knuth, Bendix - 1970
68 An Algorithm for Finding a Basis for the Residue Class Ring of a ZeroDimensional Polynomial Ideal – Buchberger - 1965
48 Termination orderings for associativecommutative rewriting systems – Bachmair, Plaisted - 1985
17 Computing a grobner basis of a polynomial ideal over a euclidean domain – Kandri-Rody, Kapur - 1984
14 Unsolvable Problems – Davis - 1977
10 Simulating Buchberger's Algorithm by a Knuth-Bendix Completion Procedure – Bundgen - 1991
1 Constructing Grobner bases for a polynomial ideal. Presented at the workshop Combinatorial algorithms in algebraic structures at Europaische Akademie, Otzenhause – Kapur, Narendran - 1985