Hashing-based approximate counting of minimal unsatisfiable subsets
In many areas of computer science, we are given an unsatisfiable Boolean formula F in CNF, i.e. a set of clauses, with the goal to analyse the unsatisfiability. Examination of minimal unsatisfiable subsets (MUSes) of F is a kind of such analysis. While researchers in the past two decades focused mai...
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creator | Bendík, Jaroslav Meel, Kuldeep S. |
description | In many areas of computer science, we are given an unsatisfiable Boolean formula
F
in CNF, i.e. a set of clauses, with the goal to analyse the unsatisfiability. Examination of minimal unsatisfiable subsets (MUSes) of
F
is a kind of such analysis. While researchers in the past two decades focused mainly on techniques for explicit identification of MUSes, there have recently emerged various applications that do not require the explicit identification of MUSes. For instance, in the domain of diagnosis, it is often sufficient to count the number of MUSes. While in theory, one can simply count all MUSes by explicitly enumerating them, in practice, the complete explicit enumeration is often not possible for instances with a reasonably large number of MUSes. In this work, we describe our approximate MUS counting procedure called AMUSIC. Our approach avoids exhaustive MUS enumeration by combining the classical technique of universal hashing with advances in QBF solvers along with usage of union and intersection of MUSes to achieve runtime efficiency. Our prototype implementation of AMUSIC is shown to scale to instances that were clearly beyond the realm of enumeration-based approaches. |
doi_str_mv | 10.1007/s10703-023-00419-w |
format | Article |
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F
in CNF, i.e. a set of clauses, with the goal to analyse the unsatisfiability. Examination of minimal unsatisfiable subsets (MUSes) of
F
is a kind of such analysis. While researchers in the past two decades focused mainly on techniques for explicit identification of MUSes, there have recently emerged various applications that do not require the explicit identification of MUSes. For instance, in the domain of diagnosis, it is often sufficient to count the number of MUSes. While in theory, one can simply count all MUSes by explicitly enumerating them, in practice, the complete explicit enumeration is often not possible for instances with a reasonably large number of MUSes. In this work, we describe our approximate MUS counting procedure called AMUSIC. Our approach avoids exhaustive MUS enumeration by combining the classical technique of universal hashing with advances in QBF solvers along with usage of union and intersection of MUSes to achieve runtime efficiency. Our prototype implementation of AMUSIC is shown to scale to instances that were clearly beyond the realm of enumeration-based approaches.</description><identifier>ISSN: 0925-9856</identifier><identifier>EISSN: 1572-8102</identifier><identifier>DOI: 10.1007/s10703-023-00419-w</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>CAE) and Design ; Circuits and Systems ; Computer-Aided Engineering (CAD ; Counting ; Electrical Engineering ; Engineering ; Enumeration ; Software Engineering/Programming and Operating Systems</subject><ispartof>Formal methods in system design, 2024-10, Vol.63 (1-3), p.5-39</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-44b8145f29032860524ed6b60fb93a6f67da5080a8ab744d450da499c97c4c253</cites><orcidid>0000-0001-9784-3028</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10703-023-00419-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10703-023-00419-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Bendík, Jaroslav</creatorcontrib><creatorcontrib>Meel, Kuldeep S.</creatorcontrib><title>Hashing-based approximate counting of minimal unsatisfiable subsets</title><title>Formal methods in system design</title><addtitle>Form Methods Syst Des</addtitle><description>In many areas of computer science, we are given an unsatisfiable Boolean formula
F
in CNF, i.e. a set of clauses, with the goal to analyse the unsatisfiability. Examination of minimal unsatisfiable subsets (MUSes) of
F
is a kind of such analysis. While researchers in the past two decades focused mainly on techniques for explicit identification of MUSes, there have recently emerged various applications that do not require the explicit identification of MUSes. For instance, in the domain of diagnosis, it is often sufficient to count the number of MUSes. While in theory, one can simply count all MUSes by explicitly enumerating them, in practice, the complete explicit enumeration is often not possible for instances with a reasonably large number of MUSes. In this work, we describe our approximate MUS counting procedure called AMUSIC. Our approach avoids exhaustive MUS enumeration by combining the classical technique of universal hashing with advances in QBF solvers along with usage of union and intersection of MUSes to achieve runtime efficiency. Our prototype implementation of AMUSIC is shown to scale to instances that were clearly beyond the realm of enumeration-based approaches.</description><subject>CAE) and Design</subject><subject>Circuits and Systems</subject><subject>Computer-Aided Engineering (CAD</subject><subject>Counting</subject><subject>Electrical Engineering</subject><subject>Engineering</subject><subject>Enumeration</subject><subject>Software Engineering/Programming and Operating Systems</subject><issn>0925-9856</issn><issn>1572-8102</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kE9Lw0AQxRdRsFa_gKeA59XZ_9mjFLVCwYuel91kt6a0Sc0kVL-9ayN48zAMzLw38_gRcs3glgGYO2RgQFDguUAySw8nZMaU4bRkwE_JDCxX1JZKn5MLxA0AlEyLGVksPb437ZoGj7Eu_H7fd5_Nzg-xqLqxHfKq6FKxa9o83BZji35oMDU-bGOBY8A44CU5S36L8eq3z8nb48PrYklXL0_Pi_sVrbiBgUoZSiZV4hYELzUoLmOtg4YUrPA6aVN7BSX40gcjZS0V1F5aW1lTyYorMSc3092c8WOMOLhNN_ZtfukEY5YZqQTPKj6pqr5D7GNy-z5n778cA_cDy02wXIbljrDcIZvEZMIsbtex_zv9j-sb4zVsuA</recordid><startdate>20241001</startdate><enddate>20241001</enddate><creator>Bendík, Jaroslav</creator><creator>Meel, Kuldeep S.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9784-3028</orcidid></search><sort><creationdate>20241001</creationdate><title>Hashing-based approximate counting of minimal unsatisfiable subsets</title><author>Bendík, Jaroslav ; Meel, Kuldeep S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-44b8145f29032860524ed6b60fb93a6f67da5080a8ab744d450da499c97c4c253</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>CAE) and Design</topic><topic>Circuits and Systems</topic><topic>Computer-Aided Engineering (CAD</topic><topic>Counting</topic><topic>Electrical Engineering</topic><topic>Engineering</topic><topic>Enumeration</topic><topic>Software Engineering/Programming and Operating Systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bendík, Jaroslav</creatorcontrib><creatorcontrib>Meel, Kuldeep S.</creatorcontrib><collection>CrossRef</collection><jtitle>Formal methods in system design</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bendík, Jaroslav</au><au>Meel, Kuldeep S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hashing-based approximate counting of minimal unsatisfiable subsets</atitle><jtitle>Formal methods in system design</jtitle><stitle>Form Methods Syst Des</stitle><date>2024-10-01</date><risdate>2024</risdate><volume>63</volume><issue>1-3</issue><spage>5</spage><epage>39</epage><pages>5-39</pages><issn>0925-9856</issn><eissn>1572-8102</eissn><abstract>In many areas of computer science, we are given an unsatisfiable Boolean formula
F
in CNF, i.e. a set of clauses, with the goal to analyse the unsatisfiability. Examination of minimal unsatisfiable subsets (MUSes) of
F
is a kind of such analysis. While researchers in the past two decades focused mainly on techniques for explicit identification of MUSes, there have recently emerged various applications that do not require the explicit identification of MUSes. For instance, in the domain of diagnosis, it is often sufficient to count the number of MUSes. While in theory, one can simply count all MUSes by explicitly enumerating them, in practice, the complete explicit enumeration is often not possible for instances with a reasonably large number of MUSes. In this work, we describe our approximate MUS counting procedure called AMUSIC. Our approach avoids exhaustive MUS enumeration by combining the classical technique of universal hashing with advances in QBF solvers along with usage of union and intersection of MUSes to achieve runtime efficiency. Our prototype implementation of AMUSIC is shown to scale to instances that were clearly beyond the realm of enumeration-based approaches.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10703-023-00419-w</doi><tpages>35</tpages><orcidid>https://orcid.org/0000-0001-9784-3028</orcidid></addata></record> |
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subjects | CAE) and Design Circuits and Systems Computer-Aided Engineering (CAD Counting Electrical Engineering Engineering Enumeration Software Engineering/Programming and Operating Systems |
title | Hashing-based approximate counting of minimal unsatisfiable subsets |
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