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Decidability and Complexity of Simultaneous Rigid E-unification with One Variable and Related Results

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons45106

Narendran,  Paliath
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45662

Veanes,  Margus
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45678

Voronkov,  Andrei
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Degtyarev, A., Gurevich, Y., Narendran, P., Veanes, M., & Voronkov, A. (2000). Decidability and Complexity of Simultaneous Rigid E-unification with One Variable and Related Results. Theoretical Computer Science, 243(1/2), 167-184.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-341B-9
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.