Titlebook: Directed Algebraic Topology and Concurrency; Lisbeth Fajstrup,Eric Goubault,Martin Raussen Book 2016 Springer International Publishing Swi

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https://doi.org/10.1007/978-3-642-34730-6ecent architectures (processors with many cores, clouds, etc.), but they are notoriously difficult to design and to reason about: one has to ensure that the program will not go wrong, regardless of the way the different processes composing the program are scheduled. In principle, in order to achieve

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Springer Lexikon Physiotherapieg language through which we demonstrate the main ideas of this book. We begin by introducing the language. We then describe its operational semantics, which formalizes the way programs are to be executed. Finally, we describe the correctness properties that we will be interested in.

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Springer Lexikon Physiotherapies commute or not. In this chapter, we introduce truly concurrent models which incorporate this information. We begin by extending our programming languages with resources and restrict ourselves to conservative programs, in which resource consumption only depends on the current state. We then general

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Springer Lexikon Physiotherapie of concurrent programs. In those models, the state space of a program is described as a topological space, and an execution corresponds naturally to a path in this space. To rensure that models reflect order properties, we are led to enrich the concept of a topological space so that it takes causal

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Springer Lexikon Physiotherapiea method that allows one to “compress” this space in the case of simple programs, and to provide a finite combinatorial description of it which retains its essential topological characteristics: we compute a combinatorial model of this space, whose geometric realization is homotopy equivalent to it.

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Springer Lexikon PhysiotherapieWe hope that this panorama of relationships between directed algebraic topology and concurrency has given the reader an impression of the profound links between the two fields.