2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)最新文献

{"title":"Efficient Local Computation of Differential Bisimulations via Coupling and Up-to Methods","authors":"G. Bacci, Giovanni Bacci, K. Larsen, M. Tribastone, Max Tschaikowski, Andrea Vandin","doi":"10.1109/LICS52264.2021.9470555","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470555","url":null,"abstract":"We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial differential equations, a ubiquitous model of dynamical systems across science and engineering. The algorithm enjoys polynomial time complexity and complements classical partition-refinement approaches because: (a) it implements a local exploration of the system, possibly yielding equivalences that do not necessarily involve the inspection of the whole system of differential equations; (b) it can be enhanced by up-to techniques; and (c) it allows the specification of pairs which ought not be included in the output. Using a prototype, these advantages are demonstrated on case studies from systems biology for applications to model reduction and comparison. Notably, we report four orders of magnitude smaller runtimes than partition-refinement approaches when disproving equivalences between Markov chains.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"143 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":"116906959","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":"Asynchronous Extensions of HyperLTL","authors":"L. Bozzelli, A. Peron, César Sánchez","doi":"10.1109/LICS52264.2021.9470583","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470583","url":null,"abstract":"Hyperproperties are a modern specification paradigm that extends trace properties to express properties of sets of traces. Temporal logics for hyperproperties studied in the literature, including HyperLTL, assume a synchronous semantics and enjoy a decidable model checking problem. In this paper, we introduce two asynchronous and orthogonal extensions of HyperLTL, namely Stuttering HyperLTL (HyperLTLS) and Context HyperLTL (HyperLTLC). Both of these extensions are useful, for instance, to formulate asynchronous variants of information-flow security properties. We show that for these logics, model checking is in general undecidable. On the positive side, for each of them, we identify a fragment with a decidable model checking that subsumes HyperLTL and that can express meaningful asynchronous requirements. Moreover, we provide the exact computational complexity of model checking for these two fragments which, for the HyperLTLS fragment, coincides with that of the strictly less expressive logic HyperLTL.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"32 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":"130563342","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 Logics and Homomorphism Closure","authors":"M. Bodirsky, Thomas Feller, Simon Knäuer, S. Rudolph","doi":"10.1109/LICS52264.2021.9470511","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470511","url":null,"abstract":"Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of characterizing (classes of) structures are of fundamental interest and can be highly non-trivial to answer. We investigate several problems regarding the homomorphism closure (homclosure) of the class of all (finite or arbitrary) models of logical sentences: membership of structures in a sentence’s homclosure; sentence homclosedness; homclosure characterizability in a logic; normal forms for homclosed sentences in certain logics. For a wide variety of fragments of first- and second-order predicate logic, we clarify these problems’ computational properties.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116267598","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":"Parikh’s theorem for infinite alphabets","authors":"Piotr Hofman, Marta Juzepczuk, S. Lasota, Mohnish Pattathurajan","doi":"10.1109/LICS52264.2021.9470626","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470626","url":null,"abstract":"We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this setting by allowing for orbit-finite unions instead of only finite ones. We prove that commutative images of languages of one-register automata are not always semi-linear, but they are always rational. We also lift the latter result to grammars: commutative images of one- register context-free languages are rational, and in consequence commutatively equivalent to register automata. We conjecture analogous results for automata and grammars with arbitrarily many registers.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129937948","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 sequentiality and well-bracketing in the π-calculus","authors":"D. Hirschkoff, Enguerrand Prebet, D. Sangiorgi","doi":"10.1109/LICS52264.2021.9470559","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470559","url":null,"abstract":"The π-calculus is used as a model for programming languages. Its contexts exhibit arbitrary concurrency, making them very discriminating. This may prevent validating desirable behavioural equivalences in cases when more disciplined contexts are expected.In this paper we focus on two such common disciplines: sequentiality, meaning that at any time there is a single thread of computation, and well-bracketing, meaning that calls to external services obey a stack-like discipline. We formalise the disciplines by means of type systems. The main focus of the paper is on studying the consequence of the disciplines on behavioural equivalence. We define and study labelled bisimilarities for sequentiality and well-bracketing. These relations are coarser than ordinary bisimilarity. We prove that they are sound for the respective (contextual) barbed equivalence, and also complete under a certain technical condition.We show the usefulness of our techniques on a number of examples, that have mainly to do with the representation of functions and store.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"340 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134263430","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":"Towards a more efficient approach for the satisfiability of two-variable logic","authors":"Ting-wei Lin, Chia-hsuan Lu, Tony Tan","doi":"10.1109/LICS52264.2021.9470502","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470502","url":null,"abstract":"We revisit the satisfiability problem for two-variable logic, denoted by SAT(FO2), which is known to be NEXP-complete. The upper bound is usually derived from its well known exponential size model property. Whether it can be determinized/randomized efficiently is still an open question.In this paper we present a different approach by reducing it to a novel graph-theoretic problem that we call Conditional Independent Set (CIS). We show that CIS is NP-complete and present three simple algorithms for it: Deterministic, randomized with zero error and randomized with small one-sided error, with run time O(1.4423n), O(1.6181n) and O(1.3661n), respectively.We then show that without the equality predicate SAT(FO2) is in fact equivalent to CIS in succinct representation. This yields the same three simple algorithms as above for SAT(FO2) without the the equality predicate with run time $O({1.4423^{({2^n})}})$, $O({1.6181^{({2^n})}})$ and $O({1.3661^{({2^n})}})$, respectively, where n is the number of predicates in the input formula. To the best of our knowledge, these are the first deterministic/randomized algorithms for an NEXP-complete decidable logic with time complexity significantly lower than $O({2^{({2^n})}})$. We also identify a few lower complexity fragments of FO2 which correspond to the tractable fragments of CIS.For the fragment with the equality predicate, we present a linear time many-one reduction to the fragment without the equality predicate. The reduction yields equi-satisfiable formulas and incurs a small constant blow-up in the number of predicates.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"32 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":"126395927","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":"Decidability and Complexity in Weakening and Contraction Hypersequent Substructural Logics","authors":"A. Balasubramanian, Timo Lang, Revantha Ramanayake","doi":"10.1109/LICS52264.2021.9470733","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470733","url":null,"abstract":"We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a cut-free hypersequent proof calculus. Specifically: every analytic structural rule extension of HFLew. Decidability for the corresponding extensions of its contraction counterpart FLec was established recently but their computational complexity was left unanswered. In the second part of this paper, we introduce just enough on length functions for well-quasi-orderings and the fast-growing complexity classes to obtain complexity upper bounds for both the weakening and contraction extensions. A specific instance of this result yields the first complexity bound for the prominent fuzzy logic MTL (monoidal t-norm based logic) providing an answer to a longstanding open problem.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114296479","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":"Symbolic Time and Space Tradeoffs for Probabilistic Verification","authors":"K. Chatterjee, W. Dvořák, M. Henzinger, A. Svozil","doi":"10.1109/LICS52264.2021.9470739","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470739","url":null,"abstract":"We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with n vertices and m edges, the classical symbolic algorithm from the 1990s for the MEC decomposition requires O(n2) symbolic operations and O(1) symbolic space. The only other symbolic algorithm for the MEC decomposition requires $O(nsqrt m )$ symbolic operations and $O(sqrt m )$ symbolic space. The main open question has been whether the worst-case O(n2) bound for symbolic operations can be beaten for MEC decomposition computation. In this work, we answer the open question in the affirmative. We present a symbolic algorithm that requires $widetilde Oleft( {{n^{1.5}}} right)$ symbolic operations and $widetilde Oleft( {sqrt n } right)$ symbolic space. Moreover, the parametrization of our algorithm provides a trade-off between symbolic operations and esymbolic space: for all 0 < ϵ ≤ 1/2 the symbolic algorithm requires $widetilde Oleft( {{n^{2 - in }}} right)$ symbolic operations and $widetilde Oleft( {{n^ in }} right)$ symbolic space ($widetilde O(cdot)$ hides poly-logarithmic factors).Using our techniques we also present faster algorithms for computing the almost-sure winning regions of ω-regular objectives for MDPs. We consider the canonical parity objectives for ω-regular objectives, and for parity objectives with d-priorities we present an algorithm that computes the almost-sure winning region with $widetilde Oleft( {{n^{2 - in }}} right)$ symbolic operations and $widetilde Oleft( {{n^ in }} right)$ symbolic space, for all 0 < ϵ ≤ 1/2. In contrast, previous approaches require either (a) O(n2•d) symbolic operations and O(log n) symbolic space; or (b) $O(nsqrt m cdot d)$ symbolic operations and $widetilde Oleft( {sqrt m } right)$ symbolic space. Thus we improve the time-space product from $widetilde Oleft( {{n^2}cdot d} right)$ to $widetilde Oleft( {{n^2}} right)$.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"64 839 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123070976","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":"Stochastic Processes with Expected Stopping Time","authors":"K. Chatterjee, L. Doyen","doi":"10.1109/LICS52264.2021.9470595","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470595","url":null,"abstract":"Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129562501","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 Constructive Logic with Classical Proofs and Refutations","authors":"Pablo Barenbaum, Teodoro Freund","doi":"10.1109/LICS52264.2021.9470649","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470649","url":null,"abstract":"We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be constructive in some sense, whereas proofs of classical propositions proceed by contradiction. The system, in natural deduction style, is shown to be sound and complete with respect to a Kripke semantics. We develop the system from the perspective of the propositions-as-types correspondence by deriving a term assignment system with confluent reduction. The proof of strong normalization relies on a translation to System F with Mendler-style recursion.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128187835","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}