{"title":"A limitation on the KPT interpolation","authors":"J. Krajícek","doi":"10.23638/LMCS-16(3:9)2020","DOIUrl":"https://doi.org/10.23638/LMCS-16(3:9)2020","url":null,"abstract":"We prove a limitation on a variant of the KPT theorem proposed for propositional proof systems by Pich and Santhanam (2020), for all proof systems that prove the disjointness of two NP sets that are hard to distinguish.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133746716","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}
B. Mannaa, Rasmus Ejlers Møgelberg, Niccolò Veltri
{"title":"Ticking clocks as dependent right adjoints: Denotational semantics for clocked type theory","authors":"B. Mannaa, Rasmus Ejlers Møgelberg, Niccolò Veltri","doi":"10.23638/LMCS-16(4:17)2020","DOIUrl":"https://doi.org/10.23638/LMCS-16(4:17)2020","url":null,"abstract":"Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract form of step-indexing. CloTT has previously been shown to enjoy a number of syntactic properties including strong normalisation, canonicity and decidability of the equational theory. In this paper we present a denotational semantics for CloTT useful, e.g., for studying future extensions of CloTT with constructions such as path types. \u0000The main challenge for constructing this model is to model the notion of ticks on a clock used in CloTT for coinductive reasoning about coinductive types. We build on a category previously used to model guarded recursion with multiple clocks. In this category there is an object of clocks but no object of ticks, and so tick-assumptions in a context can not be modelled using standard tools. Instead we model ticks using dependent right adjoint functors, a generalisation of the category theoretic notion of adjunction to the setting of categories with families. Dependent right adjoints are known to model Fitch-style modal types, but in the case of CloTT, the modal operators constitute a family indexed internally in the type theory by clocks. We model this family using a dependent right adjoint on the slice category over the object of clocks. Finally we show how to model the tick constant of CloTT using a semantic substitution. \u0000This work improves on a previous model by the first two named authors which not only had a flaw but was also considerably more complicated.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131092599","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":"Axiomatizing Hybrid XPath with Data","authors":"C. Areces, Raul Fervari","doi":"10.46298/lmcs-17(3:5)2021","DOIUrl":"https://doi.org/10.46298/lmcs-17(3:5)2021","url":null,"abstract":"In this paper we introduce sound and strongly complete axiomatizations for\u0000XPath with data constraints extended with hybrid operators. First, we present\u0000HXPath=, a multi-modal version of XPath with data, extended with nominals and\u0000the hybrid operator @. Then, we introduce an axiomatic system for HXPath=, and\u0000we prove it is strongly complete with respect to the class of abstract data\u0000models, i.e., data models in which data values are abstracted as equivalence\u0000relations. We prove a general completeness result similar to the one presented\u0000in, e.g., [BtC06], that ensures that certain extensions of the axiomatic system\u0000we introduce are also complete. The axiomatic systems that can be obtained in\u0000this way cover a large family of hybrid XPath languages over different classes\u0000of frames, for which we present concrete examples. In addition, we investigate\u0000axiomatizations over the class of tree models, structures widely used in\u0000practice. We show that a strongly complete, finitary, first-order\u0000axiomatization of hybrid XPath over trees does not exist, and we propose two\u0000alternatives to deal with this issue. We finally introduce filtrations to\u0000investigate the status of decidability of the satisfiability problem for these\u0000languages.\u0000","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129927047","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":"Hilbert's Tenth Problem in Coq (Extended Version)","authors":"Dominique Larchey-Wendling, Y. Forster","doi":"10.46298/lmcs-18(1:35)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(1:35)2022","url":null,"abstract":"We formalise the undecidability of solvability of Diophantine equations, i.e.\u0000polynomial equations over natural numbers, in Coq's constructive type theory.\u0000To do so, we give the first full mechanisation of the\u0000Davis-Putnam-Robinson-Matiyasevich theorem, stating that every recursively\u0000enumerable problem -- in our case by a Minsky machine -- is Diophantine. We\u0000obtain an elegant and comprehensible proof by using a synthetic approach to\u0000computability and by introducing Conway's FRACTRAN language as intermediate\u0000layer. Additionally, we prove the reverse direction and show that every\u0000Diophantine relation is recognisable by $mu$-recursive functions and give a\u0000certified compiler from $mu$-recursive functions to Minsky machines.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131864921","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":"Uniform Interpolants in EUF: Algorithms using DAG-representations","authors":"S. Ghilardi, Alessandro Gianola, D. Kapur","doi":"10.46298/lmcs-18(2:2)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(2:2)2022","url":null,"abstract":"The concept of uniform interpolant for a quantifier-free formula from a given\u0000formula with a list of symbols, while well-known in the logic literature, has\u0000been unknown to the formal methods and automated reasoning community for a long\u0000time. This concept is precisely defined. Two algorithms for computing\u0000quantifier-free uniform interpolants in the theory of equality over\u0000uninterpreted symbols (EUF) endowed with a list of symbols to be eliminated are\u0000proposed. The first algorithm is non-deterministic and generates a uniform\u0000interpolant expressed as a disjunction of conjunctions of literals, whereas the\u0000second algorithm gives a compact representation of a uniform interpolant as a\u0000conjunction of Horn clauses. Both algorithms exploit efficient dedicated DAG\u0000representations of terms. Correctness and completeness proofs are supplied,\u0000using arguments combining rewrite techniques with model theory.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"185 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131481861","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}
M. Hendriks, M. Geilen, K. Goossens, R. D. Jong, T. Basten
{"title":"Interface Modeling for Quality and Resource Management","authors":"M. Hendriks, M. Geilen, K. Goossens, R. D. Jong, T. Basten","doi":"10.23638/LMCS-17(2:19)2021","DOIUrl":"https://doi.org/10.23638/LMCS-17(2:19)2021","url":null,"abstract":"We develop an interface-modeling framework for quality and resource management that captures configurable working points of hardware and software components in terms of functionality, resource usage and provision, and quality indicators such as performance and energy consumption. We base these aspects on partially-ordered sets to capture quality levels, budget sizes, and functional compatibility. This makes the framework widely applicable and domain independent (although we aim for embedded and cyber-physical systems). The framework paves the way for dynamic (re-)configuration and multi-objective optimization of component-based systems for quality- and resource-management purposes.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122819570","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":"Discovering ePassport Vulnerabilities using Bisimilarity","authors":"Ross Horne, S. Mauw","doi":"10.23638/LMCS-17(2:24)2021","DOIUrl":"https://doi.org/10.23638/LMCS-17(2:24)2021","url":null,"abstract":"We uncover privacy vulnerabilities in the ICAO 9303 standard implemented by ePassports worldwide. These vulnerabilities, confirmed by ICAO, enable an ePassport holder who recently passed through a checkpoint to be reidentified without opening their ePassport. This paper explains how bisimilarity was used to discover these vulnerabilities, which exploit the BAC protocol -- the original ICAO 9303 standard ePassport authentication protocol -- and remains valid for the PACE protocol, which improves on the security of BAC in the latest ICAO 9303 standards. In order to tackle such bisimilarity problems, we develop here a chain of methods for the applied $pi$-calculus including a symbolic under-approximation of bisimilarity, called open bisimilarity, and a modal logic, called classical FM, for describing and certifying attacks. Evidence is provided to argue for a new scheme for specifying such unlinkability problems that more accurately reflects the capabilities of an attacker.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130722351","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":"Theories of real addition with and without a predicate for integers","authors":"A. Bès, C. Choffrut","doi":"10.23638/LMCS-17(2:18)2021","DOIUrl":"https://doi.org/10.23638/LMCS-17(2:18)2021","url":null,"abstract":"We show that it is decidable whether or not a relation on the reals definable in the structure $langle mathbb{R}, +,<, mathbb{Z} rangle$ can be defined in the structure $langle mathbb{R}, +,<, 1 rangle$. This result is achieved by obtaining a topological characterization of $langle mathbb{R}, +,<, 1 rangle$-definable relations in the family of $langle mathbb{R}, +,<, mathbb{Z} rangle$-definable relations and then by following Muchnik's approach of showing that the characterization of the relation $X$ can be expressed in the logic of $langle mathbb{R}, +,<,1, X rangle$. The above characterization allows us to prove that there is no intermediate structure between $langle mathbb{R}, +,<, mathbb{Z} rangle$ and $langle mathbb{R}, +,<, 1 rangle$. We also show that a $langle mathbb{R}, +,<, mathbb{Z} rangle$-definable relation is $langle mathbb{R}, +,<, 1 rangle$-definable if and only if its intersection with every $langle mathbb{R}, +,<, 1 rangle$-definable line is $langle mathbb{R}, +,<, 1 rangle$-definable. This gives a noneffective but simple characterization of $langle mathbb{R}, +,<, 1 rangle$-definable relations.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134379717","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":"Relating Apartness and Bisimulation","authors":"H. Geuvers, B. Jacobs","doi":"10.46298/lmcs-17(3:15)2021","DOIUrl":"https://doi.org/10.46298/lmcs-17(3:15)2021","url":null,"abstract":"A bisimulation for a coalgebra of a functor on the category of sets can be\u0000described via a coalgebra in the category of relations, of a lifted functor. A\u0000final coalgebra then gives rise to the coinduction principle, which states that\u0000two bisimilar elements are equal. For polynomial functors, this leads to\u0000well-known descriptions. In the present paper we look at the dual notion of\u0000\"apartness\". Intuitively, two elements are apart if there is a positive way to\u0000distinguish them. Phrased differently: two elements are apart if and only if\u0000they are not bisimilar. Since apartness is an inductive notion, described by a\u0000least fixed point, we can give a proof system, to derive that two elements are\u0000apart. This proof system has derivation rules and two elements are apart if and\u0000only if there is a finite derivation (using the rules) of this fact.\u0000 We study apartness versus bisimulation in two separate ways. First, for weak\u0000forms of bisimulation on labelled transition systems, where silent (tau) steps\u0000are included, we define an apartness notion that corresponds to weak\u0000bisimulation and another apartness that corresponds to branching bisimulation.\u0000The rules for apartness can be used to show that two states of a labelled\u0000transition system are not branching bismilar. To support the apartness view on\u0000labelled transition systems, we cast a number of well-known properties of\u0000branching bisimulation in terms of branching apartness and prove them. Next, we\u0000also study the more general categorical situation and show that indeed,\u0000apartness is the dual of bisimilarity in a precise categorical sense: apartness\u0000is an initial algebra and gives rise to an induction principle. In this\u0000analogy, we include the powerset functor, which gives a semantics to\u0000non-deterministic choice in process-theory.\u0000","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"12 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123308003","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 open well-filtered spaces","authors":"Chong Shen, Xiaoyong Xi, Xiaoquan Xu, Dongsheng Zhao","doi":"10.23638/LMCS-16(4:18)2020","DOIUrl":"https://doi.org/10.23638/LMCS-16(4:18)2020","url":null,"abstract":"We introduce and study a new class of $T_0$ spaces, called open well-filtered spaces. The main results we proved include (1) every well-filtered space is an open well-filtered space; (2) every core-compact open well-filtered space is sober. As an immediate corollary, we deduce that every core-compact well-filtered space is sober. This provides another different and relatively more straight forward method to answer the open problem posed by Jia and Jung: Is every core-compact well-filtered space sober?","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117037940","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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