Abstract. We introduce a game model for a procedural programming language extended with primitives for parallel composition and synchronization on binary semaphores. The model uses an interleaved version of Hyland-Ong-style games, where most of the original combinatorial constraints on positions are replaced with a simple principle naturally related to static process creation. The model is fully abstract for mayequivalence. 1 Introduction The two major paradigms of concurrent programming are message-passing and shared-variable. The latter style of programming is closer to the underlying machine model, which makes it both more popular and more "low-level " (and more error-prone) than the former. This constitutes very good motivation for the study of such languages. Concurrent shared-variable programming languages themselves can come in several varieties:- Fine-grained languages have designated atomic actions which are implemented directly by the hardware on which the program is executed. In contrast, coarse-grained programming languages can specify sequences of actions to appear as indivisible.- Languages with static process creation execute statements in parallel and

Abstract not found

Abstract—A bicategory of very general nondeterministic concurrent games and strategies is presented. The intention is to formalize distributed games in which both Player (or a team of players) and Opponent (or a team of opponents) can interact in highly distributed fashion, without, for instance, enforcing that their moves alternate. I.

Event structures, Game Semantics strategies and Linear Logic proof-nets arise in different domains (concurrency, semantics, proof-theory) but can all be described by means of directed acyclic graphs (dag’s). They are all equipped with a specific notion of composition, interaction or normalization. We report on-going work, aiming to investigate the common dynamics which seems to underly these different structures. In this paper we focus on confusion free event structures on one side, and linear strategies [Gir01,FM05] on the other side. We introduce an abstract machine which is based on (and generalizes) strategies interaction; it processes labelled dag’s, and provides a common presentation of the composition at work in these different settings. 1

Abstract—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. I.

This paper proposes two semantics of a probabilistic variant of the π-calculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of non-deterministic probabilistic behaviours which can preserve a compositionality of the parallel operator in the event structures and the calculus. We show an operational correspondence between the two semantics. This allows us to prove a “probabilistic confluence” result, which generalises the confluence of the linearly typed π-calculus.

The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of the misleading conception that linear logic is more primitive than game semantics. Here, we defend the opposite view, and thus advocate that game semantics is conceptually more primitive than linear logic. This revised point of view leads us to introduce tensor logic, a primitive variant of linear logic where negation is not involutive. After formulating its categorical semantics, we interpret tensor logic in a model based on Conway games equipped with a notion of payoff, in order to reflect the various resource policies of the logic: linear, affine, relevant or exponential.

This article opens a series of papers on asynchronous games semantics, which aims at a concurrent and geometric account of interference and states in programming languages. In order to develop our theory, we need to reformulate arena games in a simpler algebraic vocabulary, inspired by Girard's Geometry of Interaction and Abramsky, Jagadeesan and Malacaria (AJM) token games. This is precisely the task of this article, which prepares the field for the positional / homotopic account of innocence in (Mellies 2004). 1.

We present a setting in which the search for a proof of B or a refutation of B (i.e., a proof of ¬B) can be carried out simultaneously: in contrast, the usual approach in automated deduction views proving B or proving ¬B as two, possibly unrelated, activities. Our approach to proof and refutation is described as a two-player game in which each player follows the same rules. A winning strategy translates to a proof of the formula and a counter-winning strategy translates to a refutation of the formula. The game is described for multiplicative and additive linear logic (MALL). A game theoretic treatment of the multiplicative connectives is intricate and our approach to it involves two important ingredients. First, labeled graph structures are used to represent positions in a game and, second, the game playing must deal with the failure of a given player and with an appropriate resumption of play. This latter ingredient accounts for the fact that neither player might win (that is, neither B nor ¬B might be provable).

Game semantics was introduced in order to capture the dynamic behaviour of proofs and programs. In these semantics, the interaction between a program and its environment is modeled by a series of moves exchanged between two players in a game. Every program thus induces a strategy describing how it reacts when it is provided information by its environment. Traditionally, strategies considered in game semantics are alternating: the two protagonists play a move one after the other. This property is very natural when modeling sequential programming languages, but is not desirable for programs with concurrent features, since interactions cannot be synchronized globally anymore. Extending fundamental notions of game semantics to a non-alternating setting is far from being straightforward and requires to deeply rethink the definition of strategies. Recently, a series of interactive models, such as concurrent games where strategies are closure operators, were introduced in order to give denotational semantics of programming languages or logics with concurrent features. However, these models were poorly connected with traditional game semantics. We show here that asynchronous games, which combine true concurrency and game semantics, can be used to provide a precise link between these two kind of interactive semantics, thus laying foundations for game semantics of concurrent systems. 1