Asynchronous games 2: the true concurrency of innocence

In game semantics, the higher-order value passing mechanisms of the lambda-calculus are decomposed as sequences of atomic actions exchanged by a Player and its Opponent. Seen from this angle, game semantics is reminiscent of trace semantics in concurrency theory, where a process is identified to the sequences of requests it generates in the course of time. Asynchronous game semantics is an attempt to bridge the gap between the two subjects, and to see mainstream game semantics as a refined and interactive form of trace semantics. Asynchronous games are positional games played on Mazurkiewicz traces, which reformulate (and generalize) the familiar notion of arena game. The interleaving semantics of lambda-terms, expressed as innocent strategies, may be analyzed in this framework, in the perspective of true concurrency. The analysis reveals that innocent strategies are positional strategies regulated by forward and backward confluence properties. This captures, we believe, the essence of innocence. We conclude the article by defining a non uniform variant of the lambda-calculus, in which the game semantics of a lambda-term is formulated directly as a trace semantics, performing the syntactic exploration or parsing of that lambda-term

Focusing in Asynchronous Games

Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically interested here in relating two such semantics of linear logic, of very different flavor, which both take in account concurrent features of the proofs: asynchronous games and concurrent games. Interestingly, we show that associating a concurrent strategy to an asynchronous strategy can be seen as a semantical counterpart of the focusing property of linear logic

Full abstraction for fair testing in CCS

In previous work with Pous, we defined a semantics for CCS which may both be viewed as an innocent presheaf semantics and as a concurrent game semantics. It is here proved that a behavioural equivalence induced by this semantics on CCS processes is fully abstract for fair testing equivalence. The proof relies on a new algebraic notion called playground, which represents the 'rule of the game'. From any playground, two languages, equipped with labelled transition systems, are derived, as well as a strong, functional bisimulation between them.Comment: 15 pages, to appear in CALCO '13. To appear Lecture notes in computer science (2013

A Nice Labelling for Tree-Like Event Structures of Degree 3

We address the problem of finding nice labellings for event structures of degree 3. We develop a minimum theory by which we prove that the labelling number of an event structure of degree 3 is bounded by a linear function of the height. The main theorem we present in this paper states that event structures of degree 3 whose causality order is a tree have a nice labelling with 3 colors. Finally, we exemplify how to use this theorem to construct upper bounds for the labelling number of other event structures of degree 3

A Nice Labelling for Tree-Like Event Structures of Degree 3 (Extended Version)

We address the problem of finding nice labellings for event structures of degree 3. We develop a minimum theory by which we prove that the labelling number of an event structure of degree 3 is bounded by a linear function of the height. The main theorem we present in this paper states that event structures of degree 3 whose causality order is a tree have a nice labelling with 3 colors. Finally, we exemplify how to use this theorem to construct upper bounds for the labelling number of other event structures of degree 3

Distributed Synthesis for Acyclic Architectures

The distributed synthesis problem is about constructing correct distributed systems, i.e., systems that satisfy a given specification. We consider a slightly more general problem of distributed control, where the goal is to restrict the behavior of a given distributed system in order to satisfy the specification. Our systems are finite state machines that communicate via rendez-vous (Zielonka automata). We show decidability of the synthesis problem for all omega-regular local specifications, under the restriction that the communication graph of the system is acyclic. This result extends a previous decidability result for a restricted form of local reachability specifications

Innocent strategies as presheaves and interactive equivalences for CCS

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of plays, and a subcategory V of views. We argue that presheaves on V adequately represent innocent strategies, in the sense of game semantics. We then equip innocent strategies with a simple notion of interaction. This results in an interpretation of CCS. Based on this, we propose a notion of interactive equivalence for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework we prove that the analogues of fair and must testing equivalences coincide, while they differ in the standard setting.Comment: In Proceedings ICE 2011, arXiv:1108.014

Quantitative testing semantics for non-interleaving

This paper presents a non-interleaving denotational semantics for the ?-calculus. The basic idea is to define a notion of test where the outcome is not only whether a given process passes a given test, but also in how many different ways it can pass it. More abstractly, the set of possible outcomes for tests forms a semiring, and the set of process interpretations appears as a module over this semiring, in which basic syntactic constructs are affine operators. This notion of test leads to a trace semantics in which traces are partial orders, in the style of Mazurkiewicz traces, extended with readiness information. Our construction has standard may- and must-testing as special cases

Probabilistic pi-calculus and Event Structures

Accepté pour le workshop QAPL 2007, associé à ETAPSInternational audienceThis paper proposes two semantics of a probabilistic variant of the pi-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 pi-calculus