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Logic in Computer Science (LICS), 2011 26th Annual IEEE Symposium on

Date 21-24 June 2011

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Displaying Results 1 - 25 of 52
  • [Title page i]

    Page(s): i
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  • [Title page iii]

    Page(s): iii
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  • [Copyright notice]

    Page(s): iv
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  • Table of contents

    Page(s): v - viii
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  • Foreword

    Page(s): ix - x
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  • Conference organization

    Page(s): xi - xii
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  • List of Additional Reviewers

    Page(s): xiii - xiv
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  • A Why-on-Earth Tutorial on Finite Model Theory

    Page(s): 3
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    This note advertises the topics that will be covered in the tutorial on finite model theory. View full abstract»

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  • The Meaning of Semantics

    Page(s): 4 - 5
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    I will present three main themes in current research in semantics: (a) models of programming languages, (b) concurrency and (c) approximation. The first theme covers denotational semantics and operational semantics and the search for tight connections between them. This led to the full abstraction problem and ultimately to game semantics. The second theme began with the attempt to understand processes and the realization that there were brand new issues to deal with. In particular it was hard to even find compositional models at first. Finally, domain theory originally invented to provide set-theoretic models of the lambda calculus, turned into a general theory of approximation and has had an impact on the theory of probabilistic processes. View full abstract»

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  • Logic in Software, Dynamical and Biological Systems

    Page(s): 9 - 10
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (170 KB) |  | HTML iconHTML  

    Formal methods is a key area within the Computer Science discipline. Formal methods is concerned with analyzing systems formally. Here, we focus on three different systems: software systems, dynamical control systems, and biological systems. Software systems are discrete-time systems, whereas control systems are continuous-time dynamical systems. Systems consisting of interaction between the two are called cyber-physical systems and their dynamics are given using a hybrid-time model. Biological systems are complex systems that have been modeled and analyzed as discrete, continuous, and hybrid dynamical systems. The analysis questions can be broadly classified into verification and synthesis questions. We focus on both these aspects here. Logic and logical methods play a key role in the tools and techniques across this whole range of systems and analyses. View full abstract»

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  • Qualitative Tree Languages

    Page(s): 13 - 22
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    We study finite automata running over infinite binary trees and we relax the notion of accepting run by allowing a negligible set (in the sense of measure theory) of non-accepting branches. In this qualitative setting, a tree is accepted by the automaton if there exists a run over this tree in which almost every branch is accepting. This leads to a new class of tree languages, called the qualitative tree languages that enjoys many properties. Then, we replace the existential quantification - a tree is accepted if there exists some accepting run over the input tree - by a probabilistic quantification - a tree is accepted if almost every run over the input tree is accepting. Together with the qualitative acceptance and the Büchi condition, we obtain a class of probabilistic tree automata with a decidable emptiness problem. To our knowledge, this is the first positive result for a class of probabilistic automaton over infinite trees. View full abstract»

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  • Languages of Dot-Depth One over Infinite Words

    Page(s): 23 - 32
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    Over finite words, languages of dot-depth one are expressively complete for alternation-free first-order logic. This fragment is also known as the Boolean closure of existential first-order logic. Here, the atomic formulas comprise order, successor, minimum, and maximum predicates. Knast (1983) has shown that it is decidable whether a language has dot-depth one. We extend Knast's result to infinite words. In particular, we describe the class of languages definable in alternation-free first-order logic over infinite words, and we give an effective characterization of this fragment. This characterization has two components. The first component is identical to Knast's algebraic property for finite words and the second component is a topological property, namely being a Boolean combination of Cantor sets. As an intermediate step we consider finite and infinite words simultaneously. We then obtain the results for infinite words as well as for finite words as special cases. In particular, we give a new proof of Knast's Theorem on languages of dot-depth one over finite words. View full abstract»

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  • Two Views on Multiple Mean-Payoff Objectives in Markov Decision Processes

    Page(s): 33 - 42
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (494 KB) |  | HTML iconHTML  

    We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with k reward functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the single-objective case, both randomization and memory are necessary for strategies, and that finite-memory randomized strategies are sufficient. Under the satisfaction objective, in contrast to the single-objective case, infinite memory is necessary for strategies, and that randomized memoryless strategies are sufficient for epsilon-approximation, for all epsilon>;0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be epsilon-approximated in time polynomial in the size of the MDP and 1/epsilon, and exponential in the number of reward functions, for all epsilon>;0. Our results also reveal flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, correct the flaws and obtain improved results. View full abstract»

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  • Temporal Specifications with Accumulative Values

    Page(s): 43 - 52
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (330 KB) |  | HTML iconHTML  

    There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(ν) ≥ c and Avg(ν) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(ν) and Avg(ν) denote the accumulated sum and average of the values of ν from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimlnfAvg(ν) ≥ c and LimSupAvg(ν) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with "controlled-accumulation", allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modaliti- - es, and in particular CTL and LTL, makes the problem undecidable. View full abstract»

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  • First Steps in Synthetic Guarded Domain Theory: Step-Indexing in the Topos of Trees

    Page(s): 55 - 64
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (314 KB) |  | HTML iconHTML  

    We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms, predicates, and types. In particular, we show how to solve recursive type equations involving dependent types. We propose that the internal logic of S provides the right setting for the synthetic construction of abstract versions of step-indexed models of programming languages and program logics. As an example, we show how to construct a model of a programming language with higher-order store and recursive types entirely inside the internal logic of S. View full abstract»

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  • Imperative Programs as Proofs via Game Semantics

    Page(s): 65 - 74
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (299 KB) |  | HTML iconHTML  

    Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this paper we describe a logical counterpart to this extension, in which proofs denote such strategies. We can embed intuitionistic first-order linear logic into this system, as well as an imperative total programming language. The logic makes explicit use of the fact that in the game semantics the exponential can be expressed as a final co algebra. We establish a full completeness theorem for our logic, showing that every bounded strategy is the denotation of a proof. View full abstract»

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  • Game Semantics for Good General References

    Page(s): 75 - 84
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    We present a new fully abstract and effectively presentable denotational model for RefML, a paradigmatic higher-order programming language combining call-by-value evaluation and general references in the style of ML. Our model is built using game semantics. In contrast to the previous model by Abramsky, Honda and McCusker, it provides a faithful account of reference types, and the full abstraction result does not rely on the availability of spurious constructs of reference type (bad variables). This is the first denotational model of this kind, preceded only by the trace model recently proposed by Laird. View full abstract»

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  • The Computational Meaning of Probabilistic Coherence Spaces

    Page(s): 87 - 96
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    We study the probabilistic coherent spaces - a denotational semantics interpreting programs by power series with non negative real coefficients. We prove that this semantics is adequate for a probabilistic extension of the untyped λ-calculus: the probability that a term reduces to ahead normal form is equal to its denotation computed on a suitable set of values. The result gives, in a probabilistic setting, a quantitative refinement to the adequacy of Scott's model for untyped λ-calculus. View full abstract»

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  • Continuous Random Variables

    Page(s): 97 - 106
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (342 KB) |  | HTML iconHTML  

    We introduce the domain of continuous random variables (CRV) over a domain, as an alternative to Jones and Plotkin's probabilistic power domain. While no known Cartesian-closed category is stable under the latter, we show that the so-called thin (uniform) CRVs define a strong monad on the Cartesian-closed category of bc-domains. We also characterize their inequational theory, as (fair-)coin algebras. We apply this to solve a recent problem posed by M. Escardo: testing is semi-decidable for EPCF terms. CRVs arose from the study of the second author's (layered) Hoare indexed valuations, and we also make the connection apparent. View full abstract»

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  • Noncomputable Conditional Distributions

    Page(s): 107 - 116
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (287 KB) |  | HTML iconHTML  

    We study the computability of conditional probability, a fundamental notion in probability theory and Bayesian statistics. In the elementary discrete setting, a ratio of probabilities defines conditional probability. In more general settings, conditional probability is defined axiomatically, and the search for more constructive definitions is the subject of a rich literature in probability theory and statistics. However, we show that in general one cannot compute conditional probabilities. Specifically, we construct a pair of computable random variables (X, Y) in the unit interval whose conditional distribution P[Y|X] encodes the halting problem. Nevertheless, probabilistic inference has proven remarkably successful in practice, even in infinite-dimensional continuous settings. We prove several results giving general conditions under which conditional distributions are computable. In the discrete or dominated setting, under suitable computability hypotheses, conditional distributions are computable. Likewise, conditioning is a computable operation in the presence of certain additional structure, such as independent absolutely continuous noise. View full abstract»

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  • A Type System for Complexity Flow Analysis

    Page(s): 123 - 132
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    We propose a type system for an imperative programming language, which certifies program time bounds. This type system is based on secure flow information analysis. Each program variable has a level and we prevent information from flowing from low level to higher level variables. We also introduce a downgrading mechanism in order to delineate a broader class of programs. Thus, we propose a relation between security-typed language and implicit computational complexity. We establish a characterization of the class of polynomial time functions. View full abstract»

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  • Linear Dependent Types and Relative Completeness

    Page(s): 133 - 142
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (468 KB) |  | HTML iconHTML  

    A system of linear dependent types for the lambda calculus with full higher-order recursion, called dℓPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dℓPCF is not only able to precisely capture the functional behaviour of PCF programs (i.e. how the output relates to the input) but also some of their intensional properties, namely the complexity of evaluating them with Krivine's Machine. dℓPCF is designed around dependent types and linear logic and is parametrized on the underlying language of index terms, which can be tuned so as to sacrifice completeness for tractability. View full abstract»

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  • CoQMTU: A Higher-Order Type Theory with a Predicative Hierarchy of Universes Parametrized by a Decidable First-Order Theory

    Page(s): 143 - 151
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (422 KB) |  | HTML iconHTML  

    We study a complex type theory, a Calculus of Inductive Constructions with a predicative hierarchy of universes and a first-order theory T built in its conversion relation. The theory T is specified abstractly, by a set of constructors, a set of defined symbols, axioms expressing that constructors are free and defined symbols completely defined, and a generic elimination principle relying on crucial properties of first-order structures satisfying the axioms. We first show that CoqMTU enjoys all basic meta-theoretical properties of such calculi, confluence, subject reduction and strong normalization when restricted to weak-elimination, implying the decidability of type-checking in this case as well as consistency. The case of strong elimination is left open. View full abstract»

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  • Isomorphisms of Types in the Presence of Higher-Order References

    Page(s): 152 - 161
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (559 KB) |  | HTML iconHTML  

    We investigate the problem of type isomorphisms in a programming language with higher-order references. We first recall the game-theoretic model of higher-order references by Abramsky, Honda and McCusker. Solving an open problem by Laurent, we show that two finitely branching arenas are isomorphic if and only if they are geometrically the same, up to renaming of moves (Laurent's forest isomorphism). We deduce from this an equational theory characterizing isomorphisms of types in a finitary language L2 with higher order references. We show however that Laurent's conjecture does not hold on infinitely branching arenas, yielding a non-trivial type isomorphism in the extension of L2 with natural numbers. View full abstract»

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