{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T07:00:48Z","timestamp":1762326048281,"version":"build-2065373602"},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:p>Satisfiability Modulo Theory (SMT) has recently emerged as a powerful tool for solving various automated reasoning problems across diverse domains. Unlike traditional satisfiability methods confined to Boolean variables, SMT can reason on real-life variables like bitvectors, integers, and reals. A natural extension in this context is to ask quantitative questions. One such query in the SMT theory of Linear Real Arithmetic (LRA) is computing the volume of the entire satisfiable region defined by SMT formulas. This problem is important in solving different quantitative verification queries in software verification, cyber-physical systems, and neural networks, to mention a few.\n\n\n\n\n\nWe introduce ttc, an efficient algorithm that extends the capabilities of SMT solvers to volume computation. Our method decomposes the solution space of SMT Linear Real Arithmetic formulas into a union of overlapping convex polytopes, then computes their volumes and calculates their union. Our algorithm builds on recent developments in streaming-mode set unions, volume computation algorithms, and AllSAT techniques. Experimental evaluations demonstrate significant performance improvements over existing\n\nstate-of-the-art approaches.<\/jats:p>","DOI":"10.24963\/kr.2025\/53","type":"proceedings-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:10:44Z","timestamp":1762323044000},"page":"544-554","source":"Crossref","is-referenced-by-count":0,"title":["Efficient Volume Computation for SMT Formulas"],"prefix":"10.24963","author":[{"given":"Arijit","family":"Shaw","sequence":"first","affiliation":[{"name":"Chennai Mathematical Institute"},{"name":"IAI, TCG CREST, Kolkata"}]},{"given":"Uddalok","family":"Sarkar","sequence":"additional","affiliation":[{"name":"Indian Statistical Institute, Kolkata"}]},{"given":"Kuldeep S.","family":"Meel","sequence":"additional","affiliation":[{"name":"Georgia Institute of Technology"},{"name":"University of Toronto"}]}],"member":"10584","event":{"name":"22nd International Conference on Principles of Knowledge Representation and Reasoning {KR-2025}","theme":"Artificial Intelligence","location":"Melbourne, Australia","acronym":"KR-2025","number":"22","sponsor":["Artificial Intelligence Journal","Principles of Knowledge Representation and Reasoning Inc.","Academic College of Tel-Aviv","European Association for Artificial Intelligence","National Science Foundation"],"start":{"date-parts":[[2025,11,11]]},"end":{"date-parts":[[2025,11,17]]}},"container-title":["Proceedings of the TwentySecond International Conference on Principles of Knowledge Representation and Reasoning"],"original-title":[],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:11:14Z","timestamp":1762323074000},"score":1,"resource":{"primary":{"URL":"https:\/\/proceedings.kr.org\/2025\/53"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2025,11]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/kr.2025\/53","relation":{},"subject":[],"published":{"date-parts":[[2025,11]]}}}