Using formal tools in computer science to describe games is an interesting problem. We give games, exactly two person games, an axiomatical foundation based on the process algebra ACP (Algebra of Communicating Process). A fresh operator called opponent's alternative composition operator (OA) is introduced into ACP to describe game trees and game strategies, called GameACP. And its sound and complete axiomatical system is naturally established. To model the outcomes of games (the co-action of the player and the opponent), correspondingly in GameACP, the execution of GameACP processes, another operator called playing operator (PO) is extended into GameACP. We also establish a sound and complete axiomatical system for PO. Finally, we give the correctness theorem between the outcomes of games and the deductions of GameACP processes.
Game semantics has gained great successes in modeling computations, such as an initial success of modeling the functional programming language PCF (Programming Computable Functions) @cite_12 @cite_17 @cite_4 , multiplicative linear logic @cite_13 , idealized Algol @cite_14 , general reference @cite_3 , etc. To model concurrency in computer science with game semantics, a new kind of game semantics called asynchronous game @cite_15 @cite_27 @cite_9 @cite_25 @cite_11 is established and a bridge between the asynchronous game and traditional game semantics is founded. Moreover, asynchronous games perfectly model propositional linear logic and get a full completeness result. Another kind of game semantics to describe concurrency is concurrent game @cite_1 @cite_23 , and a work to bridge asynchronous game and concurrent game is introduced in @cite_18 .
@cite_18 @cite_14 @cite_4 @cite_11 @cite_9 @cite_1 @cite_3 @cite_27 @cite_23 @cite_15 @cite_13 @cite_25 @cite_12 @cite_17
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A new concurrent form of game semantics is introduced. This overcomes the problems which had arisen with previous, sequential forms of game semantics in modelling Linear Logic. It also admits an elegant and robust formalization. A Full Completeness Theorem for Multiplicative-Additive Linear Logic is proved for this semantics. In game semantics, the higher-order value passing mechanisms of the λ-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 λ-terms, expressed as innocent strategies, may be analysed 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 λ-calculus, in which the game semantics of a λ-term is formulated directly as a trace semantics, performing the syntactic exploration or parsing of that λ-term. We present automatic verification techniques for concurrent stochastic multi-player games (CSGs) with rewards. To express properties of such models, we adapt the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards), originally introduced for the simpler model of turn-based games, which enables quantitative reasoning about the ability of coalitions of players to achieve goals related to the probability of an event or reward measures. We propose and implement a modelling approach and model checking algorithms for property verification and strategy synthesis of CSGs, as an extension of PRISM-games. We evaluate the performance, scalability and applicability of our techniques on case studies from domains such as security, networks and finance, showing that we can analyse systems with probabilistic, cooperative and competitive behaviour between concurrent components, including many scenarios that cannot be analysed with turn-based models. A games model of a programming language with higher-order store in the style of ML-references is introduced. The category used for the model is obtained by relaxing certain behavioural conditions on a category of games previously used to provide fully abstract models of pure functional languages. The model is shown to be fully abstract by means of factorization arguments which reduce the question of definability for the language with higher-order store to that for its purely functional fragment.