From asynchronous games to concurrent games

1999

The aim of this chapter is to give an introduction to some recent work on the application of game semantics to the study of programming languages. An initial success for game semantics was its use in giving the first syntax-free descriptions of the fully abstract model for the functional programming language PCF [1,16,29]. One goal of semantics is to characterize the "universe of discourse" implicit in a programming language or a logic.

2012 27th Annual IEEE Symposium on Logic in Computer Science, 2012

A bicategory of concurrent games, where nondeterministic strategies are formalized as certain maps of event structures, was introduced recently. This paper studies an extension of concurrent games by winning conditions, specifying players' objectives. The introduction of winning conditions raises the question of whether such games are determined, that is, if one of the players has a winning strategy. This paper gives a positive answer to this question when the games are well-founded and satisfy a structural property, race-freedom, which prevents one player from interfering with the moves available to the other. Uncovering the conditions under which concurrent games with winning conditions are determined opens up the possibility of further applications of concurrent games in areas such as logic and verification, where both winning conditions and determinacy are most needed. A concurrent-game semantics for predicate calculus is provided as an illustration.

2007

We make a proposal for formalizing simultaneous games at the abstraction level of player's powers, combining ideas from dynamic logic of sequential games and concurrent dynamic logic. We prove completeness for a new system of 'concurrent game logic' CDGL with respect to finite non-determined games. We also show how this system raises new mathematical issues, and throws light on branching quantifiers and independencefriendly evaluation games for first-order logic.

Information and Control

We briefly present a new representation theory for game semantics which is very concrete: instead of playing in an arena game in which P plays the innocent strategy given by a term, the same game is played out over (a souped up version of) the abstract syntax tree of the term itself. The plays that are thus traced out are called traversals. More abstractly, traversals are the justified sequences that are obtained by performing parallel-composition less the hiding. After stating and explaining a number of Path-Traversal Correspondence Theorems, we present a tool for game semantics based on the new representation.

1996

The manipulation of objects with state which changes over time is all-pervasive in computing. Perhaps the simplest example of such objects are the program variables of classical imperative languages. An important strand of work within the study of such languages, pioneered by John Reynolds, focuses on “Idealized Algol”, an elegant synthesis of imperative and functional features. We present a novel semantics for Idealized Algol using games, which is quite unlike traditional denotational models of state.

Synthese, 2008

We make a proposal for formalizing simultaneous games at the abstraction level of player's powers, combining ideas from dynamic logic of sequential games and concurrent dynamic logic. We prove completeness for a new system of 'concurrent game logic' CDGL with respect to finite non-determined games. We also show how this system raises new mathematical issues, and throws light on branching quantifiers and independence-friendly evaluation games for first-order logic.

2001

BIT, 1986

We give transformation rules for the concurrent parts of Hoare's language CSP, transforming concurrent CSP programs into nondeterministic, sequential programs. On the basis of these transformations we define an axiomatic semantics for CSP with nested concurrency. This axiomatic system includes a rule for binary, associative process composition, enabling modular verification dealing with parts of concurrent systems as well as full programs. The proof system is fully abstract, in the sense that the internal structure of processes is irrelevant in the specification inasmuch it is not externally observable. An outline of a verification of a recursive, concurrent sorter is given as an example.

FME'94: Industrial Benefit of Formal Methods, 1994

This paper is about the recently-developed framework of action semantics. The pragmatic qualities of action semantic descriptions are particularly good, which encourages their use in industrial-scale applications where semantic descriptions are needed, e.g., compiler development.

Synthese, 2008

We make a proposal for formalizing simultaneous games at the abstraction level of player's powers, combining ideas from dynamic logic of sequential games and concurrent dynamic logic. We prove completeness for a new system of 'concurrent game logic' CDGL with respect to finite non-determined games. We also show how this system raises new mathematical issues, and throws light on branching quantifiers and independence-friendly evaluation games for first-order logic. ∀x∃y J J J J Rxyzu ∀z∃u s s s s

Software: Practice and Experience, 1992

LOTOS is one of the most recent formal description languages to appear and one of very few with a standard definition. It has both a process algebra and an abstract data-type component, and these facilities are used in combination to describe the behaviour of concurrent systems. The purpose of this paper is to examine, in a tutorial style, what is involved in constructing and taking benefit from such descriptions. The presentation is illustrated through the development of two formal descriptions for the children's game of pass-the-parcel. These descriptions and a concise summary of the main features of LOTOS are given as appendices. Many of the points made in the paper apply equally well to other process-oriented languages such as CCS and CSP.

1999

Concurrent constraint programming is classically based on asynchronous communication via a shared store. In previous work ([1, 2]), we presented a new version of the ask and tell primitives which features synchronicity, our approach being based on the idea of telling new information just in the case that a concurrently running process is asking for it. We turn in this paper to a semantic study of this new framework, called Scc. It is first shown to be different in nature from classical concurrent constraint programming and from CCS, a classical reference in traditional concurrency theory. This suggests the interest of new semantics for Scc. To that end, an operational semantics reporting the steps of the computations is presented. A denotational semantics is then proposed. It uses monotonic sequences of labelled pairs of input-output states, possibly containing gaps, and ending-according to the logic programming tradition-with marks reporting success or failure. This denotational semantics is proved to be correct with respect to the operational semantics as well as fully abstract. L. Brim and M. Křetínský thank the Grant Agency of the Czech Republic, grant 201/97/0456, for supporting their research.

Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One of the main difficulties that has to be faced when constructing such semantics is to make them precise by characterizing definable strategies -that is strategies which actually behave like a proof. This characterization is usually done by restricting to the model to strategies satisfying subtle combinatory conditions such as innocence, whose preservation under composition is often difficult to show. Here, we present an original methodology to achieve this task which requires to combine tools from game semantics, rewriting theory and categorical algebra. We introduce a diagrammatic presentation of definable strategies by the means of generators and relations: those strategies can be generated from a finite set of "atomic" strategies and that the equality between strategies generated in such a way admits a finite axiomatization. These generators satisfy laws which are a variation of bialgebras laws, thus bridging algebra and denotational semantics in a clean and unexpected way. † This work has been supported by the ANR Invariants algébriques des systèmes informatiques (INVAL). Physical address:Équipe PPS, CNRS and Université Paris 7, 2 place Jussieu, case 7017,

Electronic Notes in Theoretical Computer Science, 2018

In this paper, we develop a game-theoretic account of concurrent separation logic. To every execution trace of the Code confronted to the Environment, we associate a specification game where Eve plays for the Code, and Adam for the Environment. The purpose of Eve and Adam is to decompose every intermediate machine state of the execution trace into three pieces: one piece for the Code, one piece for the Environment, and one piece for the available shared resources. We establish the soundness of concurrent separation logic by interpreting every derivation tree of the logic as a winning strategy of this specification game.