Pub Date : 2018-05-17DOI: 10.46298/lmcs-17(4:4)2021
A. Lin, R. Majumdar
Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant strings that equate the left and right hand sides of the equation. While the problem of solving word equations is decidable, the decidability of the problem of solving a word equation with a length constraint (i.e., a constraint relating the lengths of words in the word equation) has remained a long-standing open problem. We focus on the subclass of quadratic word equations, i.e., in which each variable occurs at most twice. We first show that the length abstractions of solutions to quadratic word equations are in general not Presburger-definable. We then describe a class of counter systems with Presburger transition relations which capture the length abstraction of a quadratic word equation with regular constraints. We provide an encoding of the effect of a simple loop of the counter systems in the existential theory of Presburger Arithmetic with divisibility (PAD). Since PAD is decidable (NP-hard and is in NEXP), we obtain a decision procedure for quadratic words equations with length constraints for which the associated counter system is flat (i.e., all nodes belong to at most one cycle). In particular, we show a decidability result (in fact, also an NP algorithm with a PAD oracle) for a recently proposed NP-complete fragment of word equations called regular-oriented word equations, when augmented with length constraints. We extend this decidability result (in fact, with a complexity upper bound of PSPACE with a PAD oracle) in the presence of regular constraints.
{"title":"Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility","authors":"A. Lin, R. Majumdar","doi":"10.46298/lmcs-17(4:4)2021","DOIUrl":"https://doi.org/10.46298/lmcs-17(4:4)2021","url":null,"abstract":"Word equations are a crucial element in the theoretical foundation of\u0000constraint solving over strings. A word equation relates two words over string\u0000variables and constants. Its solution amounts to a function mapping variables\u0000to constant strings that equate the left and right hand sides of the equation.\u0000While the problem of solving word equations is decidable, the decidability of\u0000the problem of solving a word equation with a length constraint (i.e., a\u0000constraint relating the lengths of words in the word equation) has remained a\u0000long-standing open problem. We focus on the subclass of quadratic word\u0000equations, i.e., in which each variable occurs at most twice. We first show\u0000that the length abstractions of solutions to quadratic word equations are in\u0000general not Presburger-definable. We then describe a class of counter systems\u0000with Presburger transition relations which capture the length abstraction of a\u0000quadratic word equation with regular constraints. We provide an encoding of the\u0000effect of a simple loop of the counter systems in the existential theory of\u0000Presburger Arithmetic with divisibility (PAD). Since PAD is decidable (NP-hard\u0000and is in NEXP), we obtain a decision procedure for quadratic words equations\u0000with length constraints for which the associated counter system is flat (i.e.,\u0000all nodes belong to at most one cycle). In particular, we show a decidability\u0000result (in fact, also an NP algorithm with a PAD oracle) for a recently\u0000proposed NP-complete fragment of word equations called regular-oriented word\u0000equations, when augmented with length constraints. We extend this decidability\u0000result (in fact, with a complexity upper bound of PSPACE with a PAD oracle) in\u0000the presence of regular constraints.","PeriodicalId":335085,"journal":{"name":"Automated Technology for Verification and Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129170000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-05-15DOI: 10.1007/978-3-030-01090-4_18
Paul Gainer, E. M. Hahn, S. Schewe
{"title":"Accelerated Model Checking of Parametric Markov Chains","authors":"Paul Gainer, E. M. Hahn, S. Schewe","doi":"10.1007/978-3-030-01090-4_18","DOIUrl":"https://doi.org/10.1007/978-3-030-01090-4_18","url":null,"abstract":"","PeriodicalId":335085,"journal":{"name":"Automated Technology for Verification and Analysis","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131781941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-05-10DOI: 10.1007/978-3-030-01090-4_30
E. Albert, Pablo Gordillo, B. Livshits, A. Rubio, Ilya Sergey
{"title":"EthIR: A Framework for High-Level Analysis of Ethereum Bytecode","authors":"E. Albert, Pablo Gordillo, B. Livshits, A. Rubio, Ilya Sergey","doi":"10.1007/978-3-030-01090-4_30","DOIUrl":"https://doi.org/10.1007/978-3-030-01090-4_30","url":null,"abstract":"","PeriodicalId":335085,"journal":{"name":"Automated Technology for Verification and Analysis","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130834497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-04-02DOI: 10.1007/978-3-030-01090-4_27
Rayna Dimitrova, Mahsa Ghasemi, U. Topcu
{"title":"Maximum Realizability for Linear Temporal Logic Specifications","authors":"Rayna Dimitrova, Mahsa Ghasemi, U. Topcu","doi":"10.1007/978-3-030-01090-4_27","DOIUrl":"https://doi.org/10.1007/978-3-030-01090-4_27","url":null,"abstract":"","PeriodicalId":335085,"journal":{"name":"Automated Technology for Verification and Analysis","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134523871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-03-05DOI: 10.1007/978-3-030-01090-4_10
Murat Cubuktepe, N. Jansen, Sebastian Junges, J. Katoen, U. Topcu
{"title":"Synthesis in pMDPs: A Tale of 1001 Parameters","authors":"Murat Cubuktepe, N. Jansen, Sebastian Junges, J. Katoen, U. Topcu","doi":"10.1007/978-3-030-01090-4_10","DOIUrl":"https://doi.org/10.1007/978-3-030-01090-4_10","url":null,"abstract":"","PeriodicalId":335085,"journal":{"name":"Automated Technology for Verification and Analysis","volume":"267 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125056047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-12-16DOI: 10.1007/978-3-030-31784-3_12
Long H. Pham, Quang Loc Le, Quoc-Sang Phan, Jun Sun, S. Qin
{"title":"Enhancing Symbolic Execution of Heap-based Programs with Separation Logic for Test Input Generation","authors":"Long H. Pham, Quang Loc Le, Quoc-Sang Phan, Jun Sun, S. Qin","doi":"10.1007/978-3-030-31784-3_12","DOIUrl":"https://doi.org/10.1007/978-3-030-31784-3_12","url":null,"abstract":"","PeriodicalId":335085,"journal":{"name":"Automated Technology for Verification and Analysis","volume":"208 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115540852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-10-03DOI: 10.1007/978-3-319-68167-2_3
E. Albert, S. Genaim, Pablo Gordillo
{"title":"May-Happen-in-Parallel Analysis with Returned Futures","authors":"E. Albert, S. Genaim, Pablo Gordillo","doi":"10.1007/978-3-319-68167-2_3","DOIUrl":"https://doi.org/10.1007/978-3-319-68167-2_3","url":null,"abstract":"","PeriodicalId":335085,"journal":{"name":"Automated Technology for Verification and Analysis","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125065280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-10-03DOI: 10.1007/978-3-319-68167-2_17
Sumanth Prabhu, P. Schrammel, M. Srivas, Michael Tautschnig, Anand Yeolekar
{"title":"Concurrent Program Verification with Invariant-Guided Underapproximation","authors":"Sumanth Prabhu, P. Schrammel, M. Srivas, Michael Tautschnig, Anand Yeolekar","doi":"10.1007/978-3-319-68167-2_17","DOIUrl":"https://doi.org/10.1007/978-3-319-68167-2_17","url":null,"abstract":"","PeriodicalId":335085,"journal":{"name":"Automated Technology for Verification and Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116013461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-10-03DOI: 10.1007/978-3-319-68167-2_5
G. Gange, P. Ganty, Peter James Stuckey
{"title":"Fixing the State Budget: Approximation of Regular Languages with Small DFAs","authors":"G. Gange, P. Ganty, Peter James Stuckey","doi":"10.1007/978-3-319-68167-2_5","DOIUrl":"https://doi.org/10.1007/978-3-319-68167-2_5","url":null,"abstract":"","PeriodicalId":335085,"journal":{"name":"Automated Technology for Verification and Analysis","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124426219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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