Year: 2017
Type: preprint
Abstract: We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an $\exists^*\forall^*$ quantifier prefix (over variables, functions and relations) making EQSMT conducive for modeling synthesis problems. Moreover, EQSMT allows reasoning using a combination of background theories provided that they have a decidable satisfiability problem for the $\exists^*\forall^*$ FO-fragment (e.g., linear arithmetic). Our decision procedure reduces the satisfiability of EQSMT formulae to satisfiability queries of $\exists^*\forall^*$ formulae of each individual background theory, allowing us to use existing efficient SMT solvers supporting $\exists^*\forall^*$ reasoning for these theories; hence our procedure can be seen as effectively quantified SMT (EQSMT) reasoning. Errata: We have modified the transformation step-2 (page 9) to correct for a slight error. Also, the description above Theorem 10 is different from the published version.
Source: arXiv (Cornell University)
Authors: Madhusudan, P., Mathur, Umang, Saha, Shambwaditya, Viswanathan, Mahesh
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Awards: SHF: Small: Automating Software Verification using Natural Proofs, CPS: Breakthrough: Statistical Model Checking of High-Dimensional Cyber-Controlled Systems, Collaborative Research: Expeditions in Computer Augmented Program Engineering (ExCAPE): Harnessing Synthesis for Software Design, CSR: Small: From Simulations to Proofs for Cyberphysical Systems
OpenAlex ID: W2779744813