Date 2124 June 2011
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[Title page i]
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[Title page iii]
Page(s): iii 
[Copyright notice]
Page(s): iv 
Table of contents
Page(s): v  viii 
Foreword
Page(s): ix  x 
Conference organization
Page(s): xi  xii 
List of Additional Reviewers
Page(s): xiii  xiv 
A WhyonEarth Tutorial on Finite Model Theory
Page(s): 3This note advertises the topics that will be covered in the tutorial on finite model theory. View full abstract»

The Meaning of Semantics
Page(s): 4  5I 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 settheoretic 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»

Logic in Software, Dynamical and Biological Systems
Page(s): 9  10Formal 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 discretetime systems, whereas control systems are continuoustime dynamical systems. Systems consisting of interaction between the two are called cyberphysical systems and their dynamics are given using a hybridtime 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»

Qualitative Tree Languages
Page(s): 13  22We 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 nonaccepting 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»

Languages of DotDepth One over Infinite Words
Page(s): 23  32Over finite words, languages of dotdepth one are expressively complete for alternationfree firstorder logic. This fragment is also known as the Boolean closure of existential firstorder logic. Here, the atomic formulas comprise order, successor, minimum, and maximum predicates. Knast (1983) has shown that it is decidable whether a language has dotdepth one. We extend Knast's result to infinite words. In particular, we describe the class of languages definable in alternationfree firstorder 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 dotdepth one over finite words. View full abstract»

Two Views on Multiple MeanPayoff Objectives in Markov Decision Processes
Page(s): 33  42We study Markov decision processes (MDPs) with multiple limitaverage (or meanpayoff) 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 limitaverage value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limitaverage value stays above a given vector. We show that under the expectation objective, in contrast to the singleobjective case, both randomization and memory are necessary for strategies, and that finitememory randomized strategies are sufficient. Under the satisfaction objective, in contrast to the singleobjective case, infinite memory is necessary for strategies, and that randomized memoryless strategies are sufficient for epsilonapproximation, 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 tradeoff curve (Pareto curve) can be epsilonapproximated 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 meanpayoff functions under the expectation objective, correct the flaws and obtain improved results. View full abstract»

Temporal Specifications with Accumulative Values
Page(s): 43  52There 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 quantitativeoriented 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 meanpayoff objectives. We investigate the extension of temporal logics with the prefixaccumulation 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 pathaccumulation 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 prefixaccumulation assertions and extending LTL with pathaccumulation assertions, result in temporal logics whose modelchecking problem is decidable. The extended logics allow to significantly extend the currently known energy and meanpayoff objectives. Moreover, the prefixaccumulation assertions may be refined with "controlledaccumulation", 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 prefixaccumulation assertions permits a decidable modelchecking 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»

First Steps in Synthetic Guarded Domain Theory: StepIndexing in the Topos of Trees
Page(s): 55  64We present the topos S of trees as a model of guarded recursion. We study the internal dependentlytyped higherorder 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 stepindexed models of programming languages and program logics. As an example, we show how to construct a model of a programming language with higherorder store and recursive types entirely inside the internal logic of S. View full abstract»

Imperative Programs as Proofs via Game Semantics
Page(s): 65  74Game semantics extends the CurryHoward isomorphism to a threeway 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 firstorder 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»

Game Semantics for Good General References
Page(s): 75  84We present a new fully abstract and effectively presentable denotational model for RefML, a paradigmatic higherorder programming language combining callbyvalue 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»

The Computational Meaning of Probabilistic Coherence Spaces
Page(s): 87  96We 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 λcalculus: 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 λcalculus. View full abstract»

Continuous Random Variables
Page(s): 97  106We 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 Cartesianclosed category is stable under the latter, we show that the socalled thin (uniform) CRVs define a strong monad on the Cartesianclosed category of bcdomains. We also characterize their inequational theory, as (fair)coin algebras. We apply this to solve a recent problem posed by M. Escardo: testing is semidecidable 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»

Noncomputable Conditional Distributions
Page(s): 107  116We 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[YX] encodes the halting problem. Nevertheless, probabilistic inference has proven remarkably successful in practice, even in infinitedimensional 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»

Propositional Proof Complexity: A Survey on the State of the Art, Including Some Recent Results
Page(s): 119 
A Type System for Complexity Flow Analysis
Page(s): 123  132We 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 securitytyped language and implicit computational complexity. We establish a characterization of the class of polynomial time functions. View full abstract»

Linear Dependent Types and Relative Completeness
Page(s): 133  142A system of linear dependent types for the lambda calculus with full higherorder 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»

CoQMTU: A HigherOrder Type Theory with a Predicative Hierarchy of Universes Parametrized by a Decidable FirstOrder Theory
Page(s): 143  151We study a complex type theory, a Calculus of Inductive Constructions with a predicative hierarchy of universes and a firstorder 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 firstorder structures satisfying the axioms. We first show that CoqMTU enjoys all basic metatheoretical properties of such calculi, confluence, subject reduction and strong normalization when restricted to weakelimination, implying the decidability of typechecking in this case as well as consistency. The case of strong elimination is left open. View full abstract»

Isomorphisms of Types in the Presence of HigherOrder References
Page(s): 152  161We investigate the problem of type isomorphisms in a programming language with higherorder references. We first recall the gametheoretic model of higherorder 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 nontrivial type isomorphism in the extension of L2 with natural numbers. View full abstract»