{"title":"An Efficient Cyclic Entailment Procedure in a Fragment of Separation Logic","authors":"Quang Loc Le, X. Le","doi":"10.48550/arXiv.2210.00616","DOIUrl":"https://doi.org/10.48550/arXiv.2210.00616","url":null,"abstract":"An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but only works with hardwired lists and trees. Other procedures that can support general inductive predicates run exponentially in time as their proof search requires back-tracking to deal with a disjunction in the consequent. This paper presents a decision procedure to derive cyclic entailment proofs for general inductive predicates in polynomial time. Our procedure is efficient and does not require back-tracking; it uses normalisation rules that help avoid the introduction of disjunction in the consequent. Moreover, our decidable fragment is sufficiently expressive: It is based on compositional predicates and can capture a wide range of data structures, including sorted and nested list segments, skip lists with fast forward pointers, and binary search trees. We have implemented the proposal in a prototype tool and evaluated it over challenging problems taken from a recent separation logic competition. The experimental results confirm the efficiency of the proposed system.","PeriodicalId":330721,"journal":{"name":"Foundations of Software Science and Computation Structure","volume":"100 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114002773","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}
{"title":"Fixed Points and Noetherian Topologies","authors":"Aliaume Lopez","doi":"10.48550/arXiv.2207.07614","DOIUrl":"https://doi.org/10.48550/arXiv.2207.07614","url":null,"abstract":"This paper provides a canonical construction of a Noetherian least fixed point topology. While such least fixed point are not Noetherian in general, we prove that under a mild assumption, one can use a topological minimal bad sequence argument to prove that they are. We then apply this fixed point theorem to rebuild known Noetherian topologies with a uniform proof. In the case of spaces that are defined inductively (such as finite words and finite trees), we provide a uniform definition of a divisibility topology using our fixed point theorem. We then prove that the divisibility topology is a generalisation of the divisibility preorder introduced by Hasegawa in the case of well-quasi-orders.","PeriodicalId":330721,"journal":{"name":"Foundations of Software Science and Computation Structure","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125499448","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}
S. Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder, P. Wild
{"title":"Kantorovich Functors and Characteristic Logics for Behavioural Distances","authors":"S. Goncharov, Dirk Hofmann, Pedro Nora, Lutz Schröder, P. Wild","doi":"10.1007/978-3-031-30829-1_3","DOIUrl":"https://doi.org/10.1007/978-3-031-30829-1_3","url":null,"abstract":"","PeriodicalId":330721,"journal":{"name":"Foundations of Software Science and Computation Structure","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131066132","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}
{"title":"A Higher-Order Language for Markov Kernels and Linear Operators","authors":"P. Amorim","doi":"10.1007/978-3-031-30829-1_5","DOIUrl":"https://doi.org/10.1007/978-3-031-30829-1_5","url":null,"abstract":"","PeriodicalId":330721,"journal":{"name":"Foundations of Software Science and Computation Structure","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129936591","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}
{"title":"On the Translation of Automata to Linear Temporal Logic","authors":"Udi Boker, K. Lehtinen, Salomon Sickert","doi":"10.1007/978-3-030-99253-8_8","DOIUrl":"https://doi.org/10.1007/978-3-030-99253-8_8","url":null,"abstract":"","PeriodicalId":330721,"journal":{"name":"Foundations of Software Science and Computation Structure","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114556166","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}
C. Baier, Florian Funke, Jakob Piribauer, Robin Ziemek
{"title":"On probability-raising causality in Markov decision processes","authors":"C. Baier, Florian Funke, Jakob Piribauer, Robin Ziemek","doi":"10.1007/978-3-030-99253-8_3","DOIUrl":"https://doi.org/10.1007/978-3-030-99253-8_3","url":null,"abstract":"","PeriodicalId":330721,"journal":{"name":"Foundations of Software Science and Computation Structure","volume":"11 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116794249","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}
{"title":"A Faithful and Quantitative Notion of Distant Reduction for Generalized Applications (Long Version)","authors":"J. E. Santo, D. Kesner, Loïc Peyrot","doi":"10.1007/978-3-030-99253-8_15","DOIUrl":"https://doi.org/10.1007/978-3-030-99253-8_15","url":null,"abstract":"","PeriodicalId":330721,"journal":{"name":"Foundations of Software Science and Computation Structure","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130889658","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}
{"title":"First-order separation over countable ordinals","authors":"Thomas Colcombet, S. V. Gool, Rémi Morvan","doi":"10.1007/978-3-030-99253-8_14","DOIUrl":"https://doi.org/10.1007/978-3-030-99253-8_14","url":null,"abstract":"","PeriodicalId":330721,"journal":{"name":"Foundations of Software Science and Computation Structure","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129673954","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}
{"title":"Token Games and History-Deterministic Quantitative-Automata","authors":"Udi Boker, K. Lehtinen","doi":"10.1007/978-3-030-99253-8_7","DOIUrl":"https://doi.org/10.1007/978-3-030-99253-8_7","url":null,"abstract":"","PeriodicalId":330721,"journal":{"name":"Foundations of Software Science and Computation Structure","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122312617","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}