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Log. Methods Comput. Sci.最新文献

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Stream processors and comodels 流处理器和模型
Log. Methods Comput. Sci. Pub Date : 2021-06-10 DOI: 10.46298/lmcs-19(1:2)2023
Richard Garner
{"title":"Stream processors and comodels","authors":"Richard Garner","doi":"10.46298/lmcs-19(1:2)2023","DOIUrl":"https://doi.org/10.46298/lmcs-19(1:2)2023","url":null,"abstract":"In 2009, Hancock, Pattinson and Ghani gave a coalgebraic characterisation of\u0000stream processors $A^mathbb{N} to B^mathbb{N}$ drawing on ideas of\u0000Brouwerian constructivism. Their stream processors have an intensional\u0000character; in this paper, we give a corresponding coalgebraic characterisation\u0000of extensional stream processors, i.e., the set of continuous functions\u0000$A^mathbb{N} to B^mathbb{N}$. Our account sites both our result and that of\u0000op. cit. within the apparatus of comodels for algebraic effects originating\u0000with Power-Shkaravska. Within this apparatus, the distinction between\u0000intensional and extensional equivalence for stream processors arises in the\u0000same way as the the distinction between bisimulation and trace equivalence for\u0000labelled transition systems and probabilistic generative systems.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126577020","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}
引用次数: 4
Instance reducibility and Weihrauch degrees 实例可约性与魏氏度
Log. Methods Comput. Sci. Pub Date : 2021-06-03 DOI: 10.46298/lmcs-18(3:20)2022
Andrej Bauer
{"title":"Instance reducibility and Weihrauch degrees","authors":"Andrej Bauer","doi":"10.46298/lmcs-18(3:20)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:20)2022","url":null,"abstract":"We identify a notion of reducibility between predicates, called instance\u0000reducibility, which commonly appears in reverse constructive mathematics. The\u0000notion can be generally used to compare and classify various principles studied\u0000in reverse constructive mathematics (formal Church's thesis, Brouwer's\u0000Continuity principle and Fan theorem, Excluded middle, Limited principle,\u0000Function choice, Markov's principle, etc.). We show that the instance degrees\u0000form a frame, i.e., a complete lattice in which finite infima distribute over\u0000set-indexed suprema. They turn out to be equivalent to the frame of upper sets\u0000of truth values, ordered by the reverse Smyth partial order. We study the\u0000overall structure of the lattice: the subobject classifier embeds into the\u0000lattice in two different ways, one monotone and the other antimonotone, and the\u0000$lnotlnot$-dense degrees coincide with those that are reducible to the degree\u0000of Excluded middle.\u0000 We give an explicit formulation of instance degrees in a relative\u0000realizability topos, and call these extended Weihrauch degrees, because in\u0000Kleene-Vesley realizability the $lnotlnot$-dense modest instance degrees\u0000correspond precisely to Weihrauch degrees. The extended degrees improve the\u0000structure of Weihrauch degrees by equipping them with computable infima and\u0000suprema, an implication, the ability to control access to parameters and\u0000computation of results, and by generally widening the scope of Weihrauch\u0000reducibility.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127709310","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}
引用次数: 5
A First-Order Complete Temporal Logic for Structured Context-Free Languages 结构化上下文无关语言的一阶完全时间逻辑
Log. Methods Comput. Sci. Pub Date : 2021-05-22 DOI: 10.46298/lmcs-18(3:11)2022
M. Chiari, D. Mandrioli, Matteo Pradella
{"title":"A First-Order Complete Temporal Logic for Structured Context-Free Languages","authors":"M. Chiari, D. Mandrioli, Matteo Pradella","doi":"10.46298/lmcs-18(3:11)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:11)2022","url":null,"abstract":"The problem of model checking procedural programs has fostered much research\u0000towards the definition of temporal logics for reasoning on context-free\u0000structures. The most notable of such results are temporal logics on Nested\u0000Words, such as CaRet and NWTL. Recently, the logic OPTL was introduced, based\u0000on the class of Operator Precedence Languages (OPLs), more powerful than Nested\u0000Words. We define the new OPL-based logic POTL and prove its FO-completeness.\u0000POTL improves on NWTL by enabling the formulation of requirements involving\u0000pre/post-conditions, stack inspection, and others in the presence of\u0000exception-like constructs. It improves on OPTL too, which instead we show not\u0000to be FO-complete; it also allows to express more easily stack inspection and\u0000function-local properties. In a companion paper we report a model checking\u0000procedure for POTL and experimental results based on a prototype tool developed\u0000therefor. For completeness a short summary of this complementary result is\u0000provided in this paper too.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127066303","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}
引用次数: 1
A Separator Theorem for Hypergraphs and a CSP-SAT Algorithm 超图的分隔定理与CSP-SAT算法
Log. Methods Comput. Sci. Pub Date : 2021-05-14 DOI: 10.46298/lmcs-17(4:17)2021
M. Koucký, V. Rödl, N. Talebanfard
{"title":"A Separator Theorem for Hypergraphs and a CSP-SAT Algorithm","authors":"M. Koucký, V. Rödl, N. Talebanfard","doi":"10.46298/lmcs-17(4:17)2021","DOIUrl":"https://doi.org/10.46298/lmcs-17(4:17)2021","url":null,"abstract":"We show that for every $r ge 2$ there exists $epsilon_r > 0$ such that any\u0000$r$-uniform hypergraph with $m$ edges and maximum vertex degree $o(sqrt{m})$\u0000contains a set of at most $(frac{1}{2} - epsilon_r)m$ edges the removal of\u0000which breaks the hypergraph into connected components with at most $m/2$ edges.\u0000We use this to give an algorithm running in time $d^{(1 - epsilon_r)m}$ that\u0000decides satisfiability of $m$-variable $(d, k)$-CSPs in which every variable\u0000appears in at most $r$ constraints, where $epsilon_r$ depends only on $r$ and\u0000$kin o(sqrt{m})$. Furthermore our algorithm solves the corresponding #CSP-SAT\u0000and Max-CSP-SAT of these CSPs. We also show that CNF representations of\u0000unsatisfiable $(2, k)$-CSPs with variable frequency $r$ can be refuted in\u0000tree-like resolution in size $2^{(1 - epsilon_r)m}$. Furthermore for Tseitin\u0000formulas on graphs with degree at most $k$ (which are $(2, k)$-CSPs) we give a\u0000deterministic algorithm finding such a refutation.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130956677","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}
引用次数: 1
Bounded Reachability Problems are Decidable in FIFO Machines FIFO机器的有界可达性问题是可判定的
Log. Methods Comput. Sci. Pub Date : 2021-05-14 DOI: 10.46298/lmcs-18(1:19)2022
B. Bollig, A. Finkel, Amrita Suresh
{"title":"Bounded Reachability Problems are Decidable in FIFO Machines","authors":"B. Bollig, A. Finkel, Amrita Suresh","doi":"10.46298/lmcs-18(1:19)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(1:19)2022","url":null,"abstract":"The undecidability of basic decision problems for general FIFO machines such\u0000as reachability and unboundedness is well-known. In this paper, we provide an\u0000underapproximation for the general model by considering only runs that are\u0000input-bounded (i.e. the sequence of messages sent through a particular channel\u0000belongs to a given bounded language). We prove, by reducing this model to a\u0000counter machine with restricted zero tests, that the rational-reachability\u0000problem (and by extension, control-state reachability, unboundedness, deadlock,\u0000etc.) is decidable. This class of machines subsumes input-letter-bounded\u0000machines, flat machines, linear FIFO nets, and monogeneous machines, for which\u0000some of these problems were already shown to be decidable. These theoretical\u0000results can form the foundations to build a tool to verify general FIFO\u0000machines based on the analysis of input-bounded machines.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128716985","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}
引用次数: 10
Trakhtenbrot's Theorem in Coq: Finite Model Theory through the Constructive Lens Coq中的Trakhtenbrot定理:构造透镜下的有限模型理论
Log. Methods Comput. Sci. Pub Date : 2021-04-29 DOI: 10.46298/lmcs-18(2:17)2022
Dominik Kirst, Dominique Larchey-Wendling
{"title":"Trakhtenbrot's Theorem in Coq: Finite Model Theory through the Constructive Lens","authors":"Dominik Kirst, Dominique Larchey-Wendling","doi":"10.46298/lmcs-18(2:17)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(2:17)2022","url":null,"abstract":"We study finite first-order satisfiability (FSAT) in the constructive setting\u0000of dependent type theory. Employing synthetic accounts of enumerability and\u0000decidability, we give a full classification of FSAT depending on the\u0000first-order signature of non-logical symbols. On the one hand, our development\u0000focuses on Trakhtenbrot's theorem, stating that FSAT is undecidable as soon as\u0000the signature contains an at least binary relation symbol. Our proof proceeds\u0000by a many-one reduction chain starting from the Post correspondence problem. On\u0000the other hand, we establish the decidability of FSAT for monadic first-order\u0000logic, i.e. where the signature only contains at most unary function and\u0000relation symbols, as well as the enumerability of FSAT for arbitrary enumerable\u0000signatures. To showcase an application of Trakhtenbrot's theorem, we continue\u0000our reduction chain with a many-one reduction from FSAT to separation logic.\u0000All our results are mechanised in the framework of a growing Coq library of\u0000synthetic undecidability proofs.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114180691","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}
引用次数: 1
Typability and Type Inference in Atomic Polymorphism 原子多态性中的可类型性和类型推断
Log. Methods Comput. Sci. Pub Date : 2021-04-28 DOI: 10.46298/lmcs-18(3:22)2022
M. Protin, Gilda Ferreira
{"title":"Typability and Type Inference in Atomic Polymorphism","authors":"M. Protin, Gilda Ferreira","doi":"10.46298/lmcs-18(3:22)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:22)2022","url":null,"abstract":"It is well-known that typability, type inhabitation and type inference are\u0000undecidable in the Girard-Reynolds polymorphic system F. It has recently been\u0000proven that type inhabitation remains undecidable even in the predicative\u0000fragment of system F in which all universal instantiations have an atomic\u0000witness (system Fat). In this paper we analyze typability and type inference in\u0000Curry style variants of system Fat and show that typability is decidable and\u0000that there is an algorithm for type inference which is capable of dealing with\u0000non-redundancy constraints.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131972275","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}
引用次数: 0
Why Does Propositional Quantification Make Modal and Temporal Logics on Trees Robustly Hard? 为什么命题量化使树上的模态逻辑和时间逻辑鲁棒性变得困难?
Log. Methods Comput. Sci. Pub Date : 2021-04-27 DOI: 10.46298/lmcs-18(3:5)2022
Bartosz Bednarczyk, Stephane Demri
{"title":"Why Does Propositional Quantification Make Modal and Temporal Logics on Trees Robustly Hard?","authors":"Bartosz Bednarczyk, Stephane Demri","doi":"10.46298/lmcs-18(3:5)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:5)2022","url":null,"abstract":"Adding propositional quantification to the modal logics K, T or S4 is known\u0000to lead to undecidability but CTL with propositional quantification under the\u0000tree semantics (tQCTL) admits a non-elementary Tower-complete satisfiability\u0000problem. We investigate the complexity of strict fragments of tQCTL as well as\u0000of the modal logic K with propositional quantification under the tree\u0000semantics. More specifically, we show that tQCTL restricted to the temporal\u0000operator EX is already Tower-hard, which is unexpected as EX can only enforce\u0000local properties. When tQCTL restricted to EX is interpreted on N-bounded trees\u0000for some N >= 2, we prove that the satisfiability problem is AExpPol-complete;\u0000AExpPol-hardness is established by reduction from a recently introduced tiling\u0000problem, instrumental for studying the model-checking problem for interval\u0000temporal logics. As consequences of our proof method, we prove Tower-hardness\u0000of tQCTL restricted to EF or to EXEF and of the well-known modal logics such as\u0000K, KD, GL, K4 and S4 with propositional quantification under a semantics based\u0000on classes of trees.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127990296","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}
引用次数: 0
Optimal controller synthesis for timed systems 定时系统的最优控制器综合
Log. Methods Comput. Sci. Pub Date : 2021-04-26 DOI: 10.46298/lmcs-19(1:20)2023
Damien Busatto-Gaston, B. Monmege, P. Reynier
{"title":"Optimal controller synthesis for timed systems","authors":"Damien Busatto-Gaston, B. Monmege, P. Reynier","doi":"10.46298/lmcs-19(1:20)2023","DOIUrl":"https://doi.org/10.46298/lmcs-19(1:20)2023","url":null,"abstract":"Weighted timed games are zero-sum games played by two players on a timed\u0000automaton equipped with weights, where one player wants to minimise the\u0000cumulative weight while reaching a target. Used in a reactive synthesis\u0000perspective, this quantitative extension of timed games allows one to measure\u0000the quality of controllers in real-time systems. Weighted timed games are\u0000notoriously difficult and quickly undecidable, even when restricted to\u0000non-negative weights. For non-negative weights, the largest class that can be\u0000analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the\u0000value problem is undecidable, the authors show how to approximate the value by\u0000considering regions with a refined granularity. In this work, we extend this\u0000class to incorporate negative weights, allowing one to model energy for\u0000instance, and prove that the value can still be approximated, with the same\u0000complexity. A small restriction also allows us to obtain a class of decidable\u0000weighted timed games with negative weights and an arbitrary number of clocks.\u0000In addition, we show that a symbolic algorithm, relying on the paradigm of\u0000value iteration, can be used as an approximation/computation schema over these\u0000classes. We also consider the special case of untimed weighted games, where the\u0000same fragments are solvable in polynomial time: this contrasts with the\u0000pseudo-polynomial complexity, known so far, for weighted games without\u0000restrictions.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129689607","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}
引用次数: 0
Lacon-, Shrub- and Parity-Decompositions: Characterizing Transductions of Bounded Expansion Classes Lacon-，灌木-和奇偶分解:表征有界展开类的转导
Log. Methods Comput. Sci. Pub Date : 2021-04-21 DOI: 10.46298/lmcs-19(2:14)2023
Jannik Dreier
{"title":"Lacon-, Shrub- and Parity-Decompositions: Characterizing Transductions of Bounded Expansion Classes","authors":"Jannik Dreier","doi":"10.46298/lmcs-19(2:14)2023","DOIUrl":"https://doi.org/10.46298/lmcs-19(2:14)2023","url":null,"abstract":"The concept of bounded expansion provides a robust way to capture sparse\u0000graph classes with interesting algorithmic properties. Most notably, every\u0000problem definable in first-order logic can be solved in linear time on bounded\u0000expansion graph classes. First-order interpretations and transductions of\u0000sparse graph classes lead to more general, dense graph classes that seem to\u0000inherit many of the nice algorithmic properties of their sparse counterparts.\u0000In this paper, we show that one can encode graphs from a class with\u0000structurally bounded expansion via lacon-, shrub- and parity-decompositions\u0000from a class with bounded expansion. These decompositions are useful for\u0000lifting properties from sparse to structurally sparse graph classes.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127430443","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}
引用次数: 0
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