We show that simultaneous rigid E-uni\fcation, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the 8\u000398\u0003 fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the 99-fragment, we obtain a complete classi\fcation of decidability of the prenex fragment of intuitionistic logic with equality, in terms of the quanti\fer pre\fx. It is also proved that SREU with one variable and a constant bound on the number of rigid equations is Pcomplete.<\/p>\n","protected":false},"excerpt":{"rendered":"
We show that simultaneous rigid E-uni\fcation, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the 8\u000398\u0003 fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the 99-fragment, we obtain a complete classi\fcation of decidability of […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"139","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"UPMAIL Technical Report","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Paliath Narendran, Andrei Voronkov, Anatoli 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