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Asynchronous Games: Innocence without Alternation
 In Proceedings of CONCUR’05, volume 4703 of LNCS
, 2007
"... Abstract. The notion of innocent strategy was introduced by Hyland and Ong in order to capture the interactive behaviour of λterms and PCF programs. An innocent strategy is defined as an alternating strategy with partial memory, in which the strategy plays according to its view. Extending the defin ..."
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Abstract. The notion of innocent strategy was introduced by Hyland and Ong in order to capture the interactive behaviour of λterms and PCF programs. An innocent strategy is defined as an alternating strategy with partial memory, in which the strategy plays according to its view. Extending the definition to nonalternating strategies is problematic, because the traditional definition of views is based on the hypothesis that Opponent and Proponent alternate during the interaction. Here, we take advantage of the diagrammatic reformulation of alternating innocence in asynchronous games, in order to provide a tentative definition of innocence in nonalternating games. The task is interesting, and far from easy. It requires the combination of true concurrency and game semantics in a clean and organic way, clarifying the relationship between asynchronous games and concurrent games in the sense of Abramsky and Melliès. It also requires an interactive reformulation of the usual acyclicity criterion of linear logic, as well as a directed variant, as a scheduling criterion. 1
From Asynchronous Games to Concurrent Games
, 2008
"... 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 r ..."
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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 nonalternating 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
Pomsets for Local Trace Languages  Recognizability, Logic & Petri Nets
, 2000
"... Mazurkiewicz traces can be seen as equivalence classes of words or as pomsets. Their generalisation by local traces was formalized by Hoogers, Kleijn and Thiagarajan as equivalence classes of step ring sequences. First we introduce a pomset representation for local traces. Extending Büchi's The ..."
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Mazurkiewicz traces can be seen as equivalence classes of words or as pomsets. Their generalisation by local traces was formalized by Hoogers, Kleijn and Thiagarajan as equivalence classes of step ring sequences. First we introduce a pomset representation for local traces. Extending Büchi's Theorem and a previous generalisation to Mazurkiewicz traces, we show then that a local trace language is recognized by a finite step transition system if and only if its class of pomsets is bounded and definable in the Monadic Second Order logic. Finally, using Zielonka's Theorem, we show that each recognizable local trace language is described by a finite safe labelled Petri net.
This document in subdirectoryRS/98/8/ Distributed Versions of Linear Time Temporal Logic: A Trace Perspective ∗
, 1998
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
On Recognizable Languages in Left Divisibility Monoids
, 1998
"... We describe a class of monoids where crational languages can be defined analogously to trace theory and where these languages are precisely the recognizable ones. The proofs rely on Ramsey's theorem, distributive lattice theory and on Hashigushi's rank function generalized to our left ..."
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We describe a class of monoids where crational languages can be defined analogously to trace theory and where these languages are precisely the recognizable ones. The proofs rely on Ramsey's theorem, distributive lattice theory and on Hashigushi's rank function generalized to our left divisibility monoids. We obtain Ochma'nski's theorem on recognizable languages in free partially commutative monoids as a consequence. 1 Introduction In the literature, Kleene's theorem on recognizable languages of finite words has been generalized in several directions, e.g. to formal power series by Schutzenberger [23], to infinite words by Buchi [4], and to infinite trees by Rabin [21]. More recently, Sakarovitch [22] investigated rational monoids, in which the recognizable languages coincide with the rational ones. Also, several authors (Cori & Perrin [7], Cori & M'etivier [6], and M'etivier [17], among others) investigated recognizable languages in trace monoids (free partially commutative mo...