E-unification with Constants vs. General E-unification

Authors:
Jan Otop
Affiliations:
Institute of Computer Science, University of Wrocław, Wrocław, Poland 50-383
Venue:
Journal of Automated Reasoning
Year:
2012

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Abstract

We present a solution to Problem #66 from the RTA open problem list. The question is whether there exists an equational theory E such that E-unification with constants is decidable but general E-unification is undecidable. The answer is positive and we show such a theory. The problem has several equivalent formulations, therefore the solution has many consequences. Our result also shows, that there exist two theories E 1 and E 2 over disjoint signatures, such that E 1-unification with constants and E 2-unification with constants are decidable, but (E 1驴驴驴E 2)-unification with constants is undecidable.