Nelson and Oppen provided a methodology for modularly combining decision procedures for individual theories to construct a decision procedure for a combination of theories. In addition to providing a check for satis\ufb01ability, the individual decision procedures need to provide additional functionalities, including equality generation. In this paper, we propose a decision procedure for a conjunction of di\ufb00erence constraints over rationals (where the atomic formulas are of the form x \u2264 y + c or x < y + c). The procedure extends any negative cycle detection algorithm (like the Bellman-Ford algorithm) to generate (1) equalities between all pair of variables, (2) produce proofs and (3) generates models that can be extended by other theories in a Nelson-Oppen framework. All the operations mentioned above can be performed with only a linear overhead to the cycle detection algorithm.<\/p>\n","protected":false},"excerpt":{"rendered":"
Nelson and Oppen provided a methodology for modularly combining decision procedures for individual theories to construct a decision procedure for a combination of theories. In addition to providing a check for satis\ufb01ability, the individual decision procedures need to provide additional functionalities, including equality generation. In this paper, we propose a decision procedure for a conjunction […]<\/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":"Elsevier","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Electr. Notes Theor. Comput. Sci., Pragmatics of Decision Procedures in Automated Reasoning (PDPAR '05)","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Electr. Notes Theor. Comput. 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