Results 1  10
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39
Finiteness spaces
 Mathematical Structures in Computer Science
, 1987
"... We investigate a new denotational model of linear logic based on the purely relational model. In this semantics, webs are equipped with a notion of “finitary ” subsets satisfying a closure condition and proofs are interpreted as finitary sets. In spite of a formal similarity, this model is quite dif ..."
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Cited by 72 (13 self)
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We investigate a new denotational model of linear logic based on the purely relational model. In this semantics, webs are equipped with a notion of “finitary ” subsets satisfying a closure condition and proofs are interpreted as finitary sets. In spite of a formal similarity, this model is quite different from the usual models of linear logic (coherence semantics, hypercoherence semantics, the various existing game semantics...). In particular, the standard fixpoint operators used for defining the general recursive functions are not finitary, although the primitive recursion operators are. This model can be considered as a discrete version of the Köthe space semantics introduced in a previous paper: we show how, given a field, each finiteness space gives rise to a vector space endowed with a linear topology, a notion introduced by Lefschetz in 1942, and we study the corresponding model where morphisms are linear continuous maps (a version of Girard’s quantitative semantics with coefficients in the field). We obtain in that way a new model of the recently introduced differential lambdacalculus. Notations. If S is a set, we denote by M(S) = N S the set of all multisets over S. If µ ∈ M(S), µ denotes the support of µ which is the set of all a ∈ S such that µ(a) ̸ = 0. A multiset is finite if it has a finite support. If a1,..., an are elements of some given set S, we denote by [a1,..., an] the corresponding multiset over S. The usual operations on natural numbers are extended to multisets pointwise. If (Si)i∈I are sets, we denote by πi the ith projection πi: ∏ j∈I Sj → Si.
On Köthe sequence spaces and linear logic
 Mathematical Structures in Computer Science
, 2001
"... We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Kothe sequence spaces. In this setting, the spaces interpreting the exponential have a quite simple structure of commutative Hopf algebra. The ..."
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Cited by 39 (10 self)
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We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Kothe sequence spaces. In this setting, the spaces interpreting the exponential have a quite simple structure of commutative Hopf algebra. The coKleisli category of this linear category is a cartesian closed category of entire mappings. This work provides a simple setting where typed calculus and dierential calculus can be combined; we give a few examples of computations. 1
Definability and full abstraction
 GDP FESTSCHRIFT
"... Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown sin ..."
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Cited by 24 (1 self)
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Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown since the early nineties. In this note, we review the relation between definability and full abstraction, and we put a few old and recent results of this kind in perspective.
On Automated Verification of Probabilistic Programs
, 2007
"... We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over nite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, whic ..."
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Cited by 14 (7 self)
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We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over nite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, which we call apex, for this language, based on game semantics. We illustrate our approach with three nontrivial case studies: (i) Herman's selfstabilisation algorithm; (ii) an analysis of the average shape of binary search trees obtained by certain sequences of random insertions and deletions; and (iii) the problem of anonymity in the Dining Cryptographers protocol. In particular, we record an exponential speedup in the latter over stateoftheart competing approaches.
Language equivalence for probabilistic automata
 In Proceedings of the 23rd international conference on Computer aided verification, CAV’11
, 2011
"... Abstract. In this paper, we propose a new randomised algorithm for deciding language equivalence for probabilistic automata. This algorithm is based on polynomial identity testing and thus returns an answer with an error probability that can be made arbitrarily small. We implemented our algorithm, a ..."
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Abstract. In this paper, we propose a new randomised algorithm for deciding language equivalence for probabilistic automata. This algorithm is based on polynomial identity testing and thus returns an answer with an error probability that can be made arbitrarily small. We implemented our algorithm, as well as deterministic algorithms of Tzeng and Doyen et al., optimised for running time whilst adequately handling issues of numerical stability. We conducted extensive benchmarking experiments, including the verification of randomised anonymity protocols, the outcome of which establishes that the randomised algorithm significantly outperforms the deterministic ones in a majority of our test cases. Finally, we also provide finegrained analytical bounds on the complexity of these algorithms, accounting for the differences in performance. 1
Algorithmic Game Semantics  A tutorial introduction
 IN SCHICHTENBERG AND STEINBRUGGEN [16
, 2001
"... ..."
On probabilistic program equivalence and refinement
 In Proceedings of CONCUR, volume 3653 of LNCS
, 2005
"... Abstract. We study notions of equivalence and refinement for probabilistic programs formalized in the secondorder fragment of Probabilistic Idealized Algol. Probabilistic programs implement randomized algorithms: a given input yields a probability distribution on the set of possible outputs. Intuit ..."
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Abstract. We study notions of equivalence and refinement for probabilistic programs formalized in the secondorder fragment of Probabilistic Idealized Algol. Probabilistic programs implement randomized algorithms: a given input yields a probability distribution on the set of possible outputs. Intuitively, two programs are equivalent if they give rise to identical distributions for all inputs. We show that equivalence is decidable by studying the fully abstract game semantics of probabilistic programs and relating it to probabilistic finite automata. For terms in βnormal form our decision procedure runs in time exponential in the syntactic size of programs; it is moreover fully compositional in that it can handle open programs (probabilistic modules with unspecified components). In contrast, we show that the natural notion of program refinement, in which the inputoutput distributions of one program uniformly dominate those of the other program, is undecidable. 1
Distributed probabilistic and quantum strategies
 Submitted LICS
"... Abstract—Building on a new definition and characterization of probabilistic event structures, a general definition of distributed probabilistic strategies is proposed. Probabilistic strategies are shown to compose, with probabilistic copycat strategies as identities. A higherorder probabilistic pr ..."
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Cited by 6 (4 self)
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Abstract—Building on a new definition and characterization of probabilistic event structures, a general definition of distributed probabilistic strategies is proposed. Probabilistic strategies are shown to compose, with probabilistic copycat strategies as identities. A higherorder probabilistic process language reminiscent of Milner’s CCS is interpreted within probabilistic strategies. Probabilistic games extend to games with payoff and games of imperfect information. W.r.t. new definitions of quantum event structures, it is shown how consistent parts of a quantum event structure are automatically probabilistic event structures, and so possess a probability measure. This gives a nontraditional take on the consistenthistories approach to quantum theory. The paper concludes with an extension to quantum strategies. I.
Apex: An analyzer for open probabilistic programs
 In Madhusudan Parathasarathy and Sanjit
, 2012
"... Abstract. We present APEX, a tool for analysing probabilistic programs that are open, i.e. where variables or even functions can be left unspecified. APEX transforms a program into an automaton that captures the program’s probabilistic behaviour under all instantiations of the unspecified components ..."
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Abstract. We present APEX, a tool for analysing probabilistic programs that are open, i.e. where variables or even functions can be left unspecified. APEX transforms a program into an automaton that captures the program’s probabilistic behaviour under all instantiations of the unspecified components. The translation is compositional and effectively leverages state reduction techniques. APEX can then further analyse the produced automata; in particular, it can check two automata for equivalence which translates to equivalence of the corresponding programs under all environments. In this way, APEX can verify a broad range of anonymity and termination properties of randomised protocols and other open programs, sometimes with an exponential speedup over competing stateoftheart approaches. 1
Applications of Game Semantics: From Program Analysis to Hardware Synthesis
"... After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design. 1. C ..."
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After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design. 1. Chronology, methodology, ideology Game Semantics is a denotational semantics in the conventional sense: for any term, it assigns a certain mathematical object as its meaning, which is constructed compositionally from the meanings of its subterms in a way that is independent of the operational semantics of the object language. What makes Game Semantics particular, peculiar maybe, is that the mathematical objects it operates with