2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)最新文献

{"title":"Stochastic mechanics of graph rewriting","authors":"Nicolas Behr, V. Danos, I. Garnier","doi":"10.1145/2933575.2934537","DOIUrl":"https://doi.org/10.1145/2933575.2934537","url":null,"abstract":"We propose an algebraic approach to stochastic graph-rewriting which extends the classical construction of the Heisenberg-Weyl algebra and its canonical representation on the Fock space. Rules are seen as particular elements of an algebra of \"diagrams\": the diagram algebra $mathcal{D}$. Diagrams can be thought of as formal computational traces represented in partial time. They can be evaluated to normal diagrams (each corresponding to a rule) and generate an associative unital non-commutative algebra of rules: the rule algebra ℛ. Evaluation becomes a morphism of unital associative algebras which maps general diagrams in $mathcal{D}$ to normal ones in ℛ. In this algebraic reformulation, usual distinctions between graph observables (real-valued maps on the set of graphs defined by counting subgraphs) and rules disappear. Instead, natural algebraic substructures of ℛ arise: formal observables are seen as rules with equal left and right hand sides and form a commutative subalgebra, the ones counting subgraphs forming a sub-subalgebra of identity rules. Actual graph-rewriting is recovered as a canonical representation of the rule algebra as linear operators over the vector space generated by (isomorphism classes of) finite graphs. The construction of the representation is in close analogy with and subsumes the classical (multi-type bosonic) Fock space representation of the Heisenberg-Weyl algebra.This shift of point of view, away from its canonical representation to the rule algebra itself, has unexpected consequences. We find that natural variants of the evaluation morphism map give rise to concepts of graph transformations hitherto not considered. These will be described in a separate paper [2]. In this extended abstract we limit ourselves to the simplest concept of double-pushout rewriting (DPO). We establish \"jump-closure\", i.e. that the subspace of representations of formal graph observables is closed under the action of any rule set. It follows that for any rule set, one can derive a formal and self-consistent Kolmogorov backward equation for (representations of) formal observables.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114863647","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":"Divide and Congruence II: Delay and Weak Bisimilarity","authors":"W. Fokkink, R. V. Glabbeek","doi":"10.1145/2933575.2933590","DOIUrl":"https://doi.org/10.1145/2933575.2933590","url":null,"abstract":"Earlier we presented a method to decompose modal formulas for processes with the internal action τ; congruence formats for branching and η-bisimilarity were derived on the basis of this decomposition method. The idea is that a congruence format for a semantics must ensure that formulas in the modal characterisation of this semantics are always decomposed into formulas in this modal characterisation. Here the decomposition method is enhanced to deal with modal characterisations that contain a modality 〈ϵ〉〈α〉φ, to derive congruence formats for delay and weak bisimilarity.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124186008","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":"Games with bound guess actions","authors":"Thomas Colcombet, Stefan Göller","doi":"10.1145/2933575.2934502","DOIUrl":"https://doi.org/10.1145/2933575.2934502","url":null,"abstract":"We introduce games with (bound) guess actions. These are games in which the players may be asked along the play to provide numbers that need to satisfy some bounding constraints. These are natural extensions of domination games occurring in the regular cost function theory. In this paper we consider more specifically the case where the constraints to be bounded are regular cost functions, and the long term goal is an ω-regular winning condition. We show that such games are decidable on finite arenas.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132755952","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":"Comparing Chemical Reaction Networks: A Categorical and Algorithmic Perspective","authors":"L. Cardelli, M. Tribastone, Max Tschaikowski, Andrea Vandin","doi":"10.1145/2933575.2935318","DOIUrl":"https://doi.org/10.1145/2933575.2935318","url":null,"abstract":"We study chemical reaction networks (CRNs) as a kernel language for concurrency models with semantics based on ordinary differential equations. We investigate the problem of comparing two CRNs, i.e., to decide whether the trajectories of a source CRN can be matched by a target CRN under an appropriate choice of initial conditions. Using a categorical framework, we extend and relate model-comparison approaches based on structural (syntactic) and on dynamical (semantic) properties of a CRN, proving their equivalence. Then, we provide an algorithm to compare CRNs, running linearly in time with respect to the cardinality of all possible comparisons. Finally, we apply our results to biological models from the literature.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133142949","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":"Effective Brenier Theorem : Applications to Computable Analysis and Algorithmic Randomness","authors":"Alex Galicki","doi":"10.1145/2933575.2933596","DOIUrl":"https://doi.org/10.1145/2933575.2933596","url":null,"abstract":"Brenier’s theorem is a landmark result in Optimal Transport. It postulates existence, monotonicity and uniqueness of an optimal map, with respect to the quadratic cost function, between two given probability measures (under some weak regularity conditions). We prove an effective version of Brenier’s theorem: we show that for any two computable absolutely continuous measures on ℝⁿ, µ and ν, with some restrictions on their support, there exists a computable convex function ϕ, whose gradient ∇ϕ is the optimal transport map between µ and ν.The main insight of the paper is the idea that an effective Brenier’s theorem can be used to construct effective monotone maps on ℝⁿ with desired (non-)differentiability properties. We use it to solve several problems at the interface of algorithmic randomness and computable analysis. In particular, we show that z ∈ ℝⁿ is computably random if and only if every computable monotone function on ℝⁿ is differentiable at z. Furthermore, we prove the converse of the effective Aleksandrov theorem (Galicki 2015): we show that if z ∈ ℝⁿ is not computably random, there exists a computable convex function that is not twice differentiable at z.Finally, we prove several new characterisations of computable randomness in ℝⁿ: in terms of differentiability of computable measures, in terms of a particular Monge-Ampère equation and in terms of critical values of computable Lipschitz functions.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116044286","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":"Plays as Resource Terms via Non-idempotent Intersection Types","authors":"Takeshi Tsukada, C. Ong","doi":"10.1145/2933575.2934553","DOIUrl":"https://doi.org/10.1145/2933575.2934553","url":null,"abstract":"A program is interpreted as a collection of resource terms by the Taylor expansion, as a collection of plays by game semantics, and as a collection of types by a non-idempotent intersection type assignment system. This paper investigates the connection between these models and aims to show that they are essentially the same in a certain sense. Technically we study the relational interpretations of resource terms and of plays, which can be seen as non-idempotent intersection type assignment systems for resource terms and plays, respectively. We show that both relational interpretations are injective, have the same image, and respect composition. This result allows us to study a property of the game model by using the syntax of a resource calculus and vice versa.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130589811","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":"Kolmogorov Extension, Martingale Convergence, and Compositionality of Processes","authors":"D. Kozen","doi":"10.1145/2933575.2933610","DOIUrl":"https://doi.org/10.1145/2933575.2933610","url":null,"abstract":"We show that the Kolmogorov extension theorem and the Doob martingale convergence theorem are two aspects of a common generalization, namely a colimit-like construction in a category of Radon spaces and reversible Markov kernels. The construction provides a compositional denotational semantics for lossless iteration in probabilistic programming languages, even in the absence of a natural partial order.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125244890","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 Generalised Twinning Property for Minimisation of Cost Register Automata*","authors":"Laure Daviaud, P. Reynier, J. Talbot","doi":"10.1145/2933575.2934549","DOIUrl":"https://doi.org/10.1145/2933575.2934549","url":null,"abstract":"Weighted automata (WA) extend finite-state automata by associating with transitions weights from a semiring $mathbb {S}$, defining functions from words to S. Recently, cost register automata (CRA) have been introduced as an alternative model to describe any function realised by a WA by means of a deterministic machine. Unambiguous WA over a monoid $(M,otimes )$ can equivalently be described by cost register automata whose registers take their values in M, and are updated by operations of the form $x :=yotimes c$, with $cin M$. This class is denoted by $mathrm {CRA}_{otimes c}(M)$.We introduce a twinning property and a bounded variation property parametrised by an integer k, such that the corresponding notions introduced originally by Choffrut for finite-state transducers are obtained for k=1. Given an unambiguous weighted automaton W over an infinitary group $(G,otimes )$ realizing some function f, we prove that the three following properties are equivalent: i) W satisfies the twinning property of order k, ii) f satisfies the k-bounded variation property, and iii) f can be described by a $mathrm {CRA}_{otimes c}(G)$ with at most k registers.In the spirit of tranducers, we actually prove this result in a more general setting by considering machines over the semiring of finite sets of elements from $(G,otimes )$ : the three properties are still equivalent for such finite-valued weighted automata, that is the ones associating with words subsets of G of cardinality at most $ell$, for some natural $ell$. Moreover, we show that if the operation $otimes , mathrm {of}, G$ is commutative and computable, then one can decide whether a WA satisfies the twinning property of order k. As a corollary, this allows to decide the register minimisation problem for the class $mathrm {CRA}_{otimes c}(G)$.Last, we prove that a similar result holds for finite-valued finite-state transducers, and that the register minimisation problem for the class CRAc(B*) is PSPACE-complete.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131484829","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":"Quantitative Algebraic Reasoning","authors":"R. Mardare, P. Panangaden, G. Plotkin","doi":"10.1145/2933575.2934518","DOIUrl":"https://doi.org/10.1145/2933575.2934518","url":null,"abstract":"We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We define an equality relation indexed a = ε$b$ which we think of as saying that \"$a$ is approximately equal to $b$ up to an error of $varepsilon $\". We have 4 interesting examples where we have a quantitative equational theory whose free algebras correspond to well known structures. In each case we have finitary and continuous versions. The four cases are: Hausdorff metrics from quantitive semilattices; $p - $Wasserstein metrics (hence also the Kantorovich metric) from barycentric algebras and also from pointed barycentric algebras and the total variation metric from a variant of barycentric algebras.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":" 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113949343","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":"Querying Visible and Invisible Information","authors":"Michael Benedikt, P. Bourhis, B. T. Cate, G. Puppis","doi":"10.1145/2933575.2935306","DOIUrl":"https://doi.org/10.1145/2933575.2935306","url":null,"abstract":"We provide a wide-ranging study of the scenario where a subset of the relations in the schema are visible — that is, their complete contents are known — while the remaining relations are invisible. We also have integrity constraints (invariants given by logical sentences) which may relate the visible relations to the invisible ones. We want to determine which information about a query (a positive existential sentence) can be inferred from the visible instance and the constraints. We consider both positive and negative query information, that is, whether the query or its negation holds. We consider the instance-level version of the problem, where both the query and the visible instance are given, as well as the schema-level version, where we want to know whether truth or falsity of the query can be inferred in some instance of the schema.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120963514","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}