## Simultaneous Rigid E-Unification is not so Simple (1995)

### BibTeX

@MISC{Degtyarev95simultaneousrigid,

author = {Anatoli Degtyarev and Yuri Matiyasevich and Andrei Voronkov},

title = {Simultaneous Rigid E-Unification is not so Simple},

year = {1995}

}

### OpenURL

### Abstract

Simultaneous rigid E-unification has been introduced in the area of theorem proving with equality. It is used in extension procedures, like the tableau method or the connection method. Many articles in this area tacitly assume the existence of an algorithm for simultaneous rigid E-unification. There were several faulty proofs of the decidability of this problem. In this article we prove several results about the simultaneous rigid E-unification. Two results are reductions of known problems to simultaneous rigid E-unification. Both these problems are very hard. The word equation solving (unification under associativity) is reduced to the monadic case of simultaneous rigid E-unification. The variable-bounded semi-unification problem is reduced to the general simultaneous rigid E-unification. The word equation problem used in the first reduction is known to be decidable, but the decidability result is extremely non-trivial. As for the variablebounded semi-unification, its decidability is ...