Log. Methods Comput. Sci.最新文献

A Finite Axiomatisation of Finite-State Automata Using String Diagrams 利用弦图的有限状态自动机的有限公理化

Log. Methods Comput. Sci. Pub Date : 2022-11-29 DOI: 10.46298/lmcs-19(1:13)2023

R. Piedeleu, F. Zanasi

引用次数: 1

Flexible Correct-by-Construction Programming 灵活的按结构校正编程

Log. Methods Comput. Sci. Pub Date : 2022-11-28 DOI: 10.48550/arXiv.2211.15261

Tobias Runge, Tabea Bordis, A. Potanin, Thomas Thüm, Ina Schaefer

{"title":"Flexible Correct-by-Construction Programming","authors":"Tobias Runge, Tabea Bordis, A. Potanin, Thomas Thüm, Ina Schaefer","doi":"10.48550/arXiv.2211.15261","DOIUrl":"https://doi.org/10.48550/arXiv.2211.15261","url":null,"abstract":"Correctness-by-Construction (CbC) is an incremental program construction\u0000process to construct functionally correct programs. The programs are\u0000constructed stepwise along with a specification that is inherently guaranteed\u0000to be satisfied. CbC is complex to use without specialized tool support, since\u0000it needs a set of predefined refinement rules of fixed granularity which are\u0000additional rules on top of the programming language. Each refinement rule\u0000introduces a specific programming statement and developers cannot depart from\u0000these rules to construct programs. CbC allows to develop software in a\u0000structured and incremental way to ensure correctness, but the limited\u0000flexibility is a disadvantage of CbC. In this work, we compare classic CbC with\u0000CbC-Block and TraitCbC. Both approaches CbC-Block and TraitCbC, are related to\u0000CbC, but they have new language constructs that enable a more flexible software\u0000construction approach. We provide for both approaches a programming guideline,\u0000which similar to CbC, leads to well-structured programs. CbC-Block extends CbC\u0000by adding a refinement rule to insert any block of statements. Therefore, we\u0000introduce CbC-Block as an extension of CbC. TraitCbC implements\u0000correctness-by-construction on the basis of traits with specified methods. We\u0000formally introduce TraitCbC and prove soundness of the construction strategy.\u0000All three development approaches are qualitatively compared regarding their\u0000programming constructs, tool support, and usability to assess which is best\u0000suited for certain tasks and developers.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134565694","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 first-order logic characterization of safety and co-safety languages 安全和共安全语言的一阶逻辑表征

Log. Methods Comput. Sci. Pub Date : 2022-09-06 DOI: 10.48550/arXiv.2209.02307

A. Cimatti, Luca Geatti, N. Gigante, A. Montanari, Stefano Tonetta

{"title":"A first-order logic characterization of safety and co-safety languages","authors":"A. Cimatti, Luca Geatti, N. Gigante, A. Montanari, Stefano Tonetta","doi":"10.48550/arXiv.2209.02307","DOIUrl":"https://doi.org/10.48550/arXiv.2209.02307","url":null,"abstract":"Linear Temporal Logic (LTL) is one of the most popular temporal logics, that\u0000comes into play in a variety of branches of computer science. Among the various\u0000reasons of its widespread use there are its strong foundational properties: LTL\u0000is equivalent to counter-free omega-automata, to star-free omega-regular\u0000expressions, and (by Kamp's theorem) to the First-Order Theory of Linear Orders\u0000(FO-TLO). Safety and co-safety languages, where a finite prefix suffices to\u0000establish whether a word does not belong or belongs to the language,\u0000respectively, play a crucial role in lowering the complexity of problems like\u0000model checking and reactive synthesis for LTL. SafetyLTL (resp., coSafetyLTL)\u0000is a fragment of LTL where only universal (resp., existential) temporal\u0000modalities are allowed, that recognises safety (resp., co-safety) languages\u0000only. The main contribution of this paper is the introduction of a fragment of\u0000FO-TLO, called SafetyFO, and of its dual coSafetyFO, which are expressively\u0000complete with respect to the LTL-definable safety and co-safety languages. We\u0000prove that they exactly characterize SafetyLTL and coSafetyLTL, respectively, a\u0000result that joins Kamp's theorem, and provides a clearer view of the\u0000characterization of (fragments of) LTL in terms of first-order languages. In\u0000addition, it gives a direct, compact, and self-contained proof that any safety\u0000language definable in LTL is definable in SafetyLTL as well. As a by-product,\u0000we obtain some interesting results on the expressive power of the weak tomorrow\u0000operator of SafetyLTL, interpreted over finite and infinite words. Moreover, we\u0000prove that, when interpreted over finite words, SafetyLTL (resp. coSafetyLTL)\u0000devoid of the tomorrow (resp., weak tomorrow) operator captures the safety\u0000(resp., co-safety) fragment of LTL over finite words.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133308529","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

SAT-Inspired Higher-Order Eliminations sat启发的高阶消去

Log. Methods Comput. Sci. Pub Date : 2022-08-16 DOI: 10.48550/arXiv.2208.07775

J. Blanchette, Petar Vukmirovi'c

引用次数: 1

Bridging Causal Reversibility and Time Reversibility: A Stochastic Process Algebraic Approach 桥接因果可逆性和时间可逆性:一个随机过程代数方法

Log. Methods Comput. Sci. Pub Date : 2022-05-03 DOI: 10.46298/lmcs-19(2:6)2023

M. Bernardo, C. A. Mezzina

引用次数: 0

On Presburger arithmetic extended with non-unary counting quantifiers 非一元计数量词扩展的Presburger算术

Log. Methods Comput. Sci. Pub Date : 2022-04-08 DOI: 10.48550/arXiv.2204.03903

P. Habermehl, D. Kuske

{"title":"On Presburger arithmetic extended with non-unary counting quantifiers","authors":"P. Habermehl, D. Kuske","doi":"10.48550/arXiv.2204.03903","DOIUrl":"https://doi.org/10.48550/arXiv.2204.03903","url":null,"abstract":"We consider a first-order logic for the integers with addition. This logic\u0000extends classical first-order logic by modulo-counting, threshold-counting and\u0000exact-counting quantifiers, all applied to tuples of variables (here, residues\u0000are given as terms while moduli and thresholds are given explicitly). Our main\u0000result shows that satisfaction for this logic is decidable in two-fold\u0000exponential space. If only threshold- and exact-counting quantifiers are\u0000allowed, we prove an upper bound of alternating two-fold exponential time with\u0000linearly many alternations. This latter result almost matches Berman's exact\u0000complexity of first-order logic without counting quantifiers.\u0000 To obtain these results, we first translate threshold- and exact-counting\u0000quantifiers into classical first-order logic in polynomial time (which already\u0000proves the second result). To handle the remaining modulo-counting quantifiers\u0000for tuples, we first reduce them in doubly exponential time to modulo-counting\u0000quantifiers for single elements. For these quantifiers, we provide a quantifier\u0000elimination procedure similar to Reddy and Loveland's procedure for first-order\u0000logic and analyse the growth of coefficients, constants, and moduli appearing\u0000in this process. The bounds obtained this way allow to restrict quantification\u0000in the original formula to integers of bounded size which then implies the\u0000first result mentioned above.\u0000 Our logic is incomparable with the logic considered by Chistikov et al. in\u00002022. They allow more general counting operations in quantifiers, but only\u0000unary quantifiers. The move from unary to non-unary quantifiers is non-trivial,\u0000since, e.g., the non-unary version of the H\"artig quantifier results in an\u0000undecidable theory.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121376175","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

Quasilinear-time Computation of Generic Modal Witnesses for Behavioural Inequivalence 行为不等价的一般模态见证的拟线性时间计算

Log. Methods Comput. Sci. Pub Date : 2022-03-21 DOI: 10.46298/lmcs-18(4:6)2022

Thorsten Wißmann, Stefan Milius, Lutz Schröder

{"title":"Quasilinear-time Computation of Generic Modal Witnesses for Behavioural Inequivalence","authors":"Thorsten Wißmann, Stefan Milius, Lutz Schröder","doi":"10.46298/lmcs-18(4:6)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(4:6)2022","url":null,"abstract":"We provide a generic algorithm for constructing formulae that distinguish\u0000behaviourally inequivalent states in systems of various transition types such\u0000as nondeterministic, probabilistic or weighted; genericity over the transition\u0000type is achieved by working with coalgebras for a set functor in the paradigm\u0000of universal coalgebra. For every behavioural equivalence class in a given\u0000system, we construct a formula which holds precisely at the states in that\u0000class. The algorithm instantiates to deterministic finite automata, transition\u0000systems, labelled Markov chains, and systems of many other types. The ambient\u0000logic is a modal logic featuring modalities that are generically extracted from\u0000the functor; these modalities can be systematically translated into custom sets\u0000of modalities in a postprocessing step. The new algorithm builds on an existing\u0000coalgebraic partition refinement algorithm. It runs in time $mathcal{O}((m+n)\u0000log n)$ on systems with $n$ states and $m$ transitions, and the same\u0000asymptotic bound applies to the dag size of the formulae it constructs. This\u0000improves the bounds on run time and formula size compared to previous\u0000algorithms even for previously known specific instances, viz. transition\u0000systems and Markov chains; in particular, the best previous bound for\u0000transition systems was $mathcal{O}(m n)$.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"505 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114137846","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: 2

A Coinductive Reformulation of Milner's Proof System for Regular Expressions Modulo Bisimilarity 正则表达式模双相似的Milner证明系统的一个共归纳重表述

Log. Methods Comput. Sci. Pub Date : 2022-03-17 DOI: 10.48550/arXiv.2203.09501

C. Grabmayer

{"title":"A Coinductive Reformulation of Milner's Proof System for Regular Expressions Modulo Bisimilarity","authors":"C. Grabmayer","doi":"10.48550/arXiv.2203.09501","DOIUrl":"https://doi.org/10.48550/arXiv.2203.09501","url":null,"abstract":"Milner (1984) defined an operational semantics for regular expressions as\u0000finite-state processes. In order to axiomatize bisimilarity of regular\u0000expressions under this process semantics, he adapted Salomaa's proof system\u0000that is complete for equality of regular expressions under the language\u0000semantics. Apart from most equational axioms, Milner's system Mil inherits from\u0000Salomaa's system a non-algebraic rule for solving single fixed-point equations.\u0000Recognizing distinctive properties of the process semantics that render\u0000Salomaa's proof strategy inapplicable, Milner posed completeness of the system\u0000Mil as an open question.\u0000 As a proof-theoretic approach to this problem we characterize the\u0000derivational power that the fixed-point rule adds to the purely equational part\u0000Mil$^-$ of Mil. We do so by means of a coinductive rule that permits cyclic\u0000derivations that consist of a finite process graph with empty steps that\u0000satisfies the layered loop existence and elimination property LLEE, and two of\u0000its Mil$^{-}$-provable solutions. With this rule as replacement for the\u0000fixed-point rule in Mil, we define the coinductive reformulation cMil as an\u0000extension of Mil$^{-}$. In order to show that cMil and Mil are theorem\u0000equivalent we develop effective proof transformations from Mil to cMil, and\u0000vice versa. Since it is located half-way in between bisimulations and proofs in\u0000Milner's system Mil, cMil may become a beachhead for a completeness proof of\u0000Mil.\u0000 This article extends our contribution to the CALCO 2022 proceedings. Here we\u0000refine the proof transformations by framing them as eliminations of derivable\u0000and admissible rules, and we link coinductive proofs to a coalgebraic\u0000formulation of solutions of process graphs.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122329086","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

HyperATL*: A Logic for Hyperproperties in Multi-Agent Systems HyperATL*:多智能体系统中的超属性逻辑

Log. Methods Comput. Sci. Pub Date : 2022-03-14 DOI: 10.46298/lmcs-19(2:13)2023

Raven Beutner, B. Finkbeiner

{"title":"HyperATL*: A Logic for Hyperproperties in Multi-Agent Systems","authors":"Raven Beutner, B. Finkbeiner","doi":"10.46298/lmcs-19(2:13)2023","DOIUrl":"https://doi.org/10.46298/lmcs-19(2:13)2023","url":null,"abstract":"Hyperproperties are system properties that relate multiple computation paths\u0000in a system and are commonly used to, e.g., define information-flow policies.\u0000In this paper, we study a novel class of hyperproperties that allow reasoning\u0000about strategic abilities in multi-agent systems. We introduce HyperATL*, an\u0000extension of computation tree logic with path variables and strategy\u0000quantifiers. Our logic supports quantification over paths in a system - as is\u0000possible in hyperlogics such as HyperCTL* - but resolves the paths based on the\u0000strategic choices of a coalition of agents. This allows us to capture many\u0000previously studied (strategic) security notions in a unifying hyperlogic.\u0000Moreover, we show that HyperATL* is particularly useful for specifying\u0000asynchronous hyperproperties, i.e., hyperproperties where the execution speed\u0000on the different computation paths depends on the choices of a scheduler. We\u0000show that finite-state model checking of HyperATL* is decidable and present a\u0000model checking algorithm based on alternating automata. We establish that our\u0000algorithm is asymptotically optimal by proving matching lower bounds. We have\u0000implemented a prototype model checker for a fragment of HyperATL* that can\u0000check various security properties in small finite-state systems.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125444768","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: 3

Lowerbounds for Bisimulation by Partition Refinement 分区细化双仿真的下限

Log. Methods Comput. Sci. Pub Date : 2022-03-14 DOI: 10.48550/arXiv.2203.07158

J. F. Groote, Jan Martens, E. Vink

引用次数: 2