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Abstract

We show that simultaneous rigid $E$-unification, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the A*EA*-fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the EE-fragment, we obtain {\em a complete classification of decidability of the prenex fragment of intuitionistic logic with equality, in terms of the quantifier prefix.} It is also proved that SREU with one variable and a constant bound on the number of rigid equations is P-complete. Moreover, we consider a case of SREU where one allows several variables, but each rigid equation either contains one variable, or has a ground left-hand side and an equality between two variables as a right-hand side. We show that SREU is decidable also in this restricted case.