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**1 - 2**of**2**### VirD-GM: Towards to a Grid Computing Environment ∗

"... This work describes the integration of the Geometric Machine model (GM) with the execution environment for pervasive and grid computing EXEHDA. The model is responsible for the logical structure of the process which graphic expressions may be constructed in the interface of the Visual Programming En ..."

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This work describes the integration of the Geometric Machine model (GM) with the execution environment for pervasive and grid computing EXEHDA. The model is responsible for the logical structure of the process which graphic expressions may be constructed in the interface of the Visual Programming Environment related to the Geometric Machine model (VPE-GM), while the middleware EXEHDA carries out its parallel and distributed execution. The resulting environment is a simple and reliable framework where the performance of several parallel programming tasks can be analyzed in an uniform way. VPE-GM handles the entire workflow, from modelling to execution of algorithms of scientific computations, and it is especially useful for partial, concurrent and non-deterministic programs. The simulator validates the graphic representation in the environment, including the control of process constructors and memory configurations. This means that encoding processes free from semantic errors can be exported to the execution module in a higher abstraction level. 1

### c ○ Uma Publicação da Sociedade Brasileira de Matemática Aplicada e Computacional. The Stochastic Geometric Machine Model 1

"... Abstract. This paper introduces the stochastic version of the Geometric Machine Model for the modelling of sequential, alternative, parallel (synchronous) and nondeterministic computations with stochastic numbers stored in a (possibly infinite) shared memory. The programming language L(D → ∞), induc ..."

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Abstract. This paper introduces the stochastic version of the Geometric Machine Model for the modelling of sequential, alternative, parallel (synchronous) and nondeterministic computations with stochastic numbers stored in a (possibly infinite) shared memory. The programming language L(D → ∞), induced by the Coherence Space of Processes D → ∞, can be applied to sequential and parallel products in order to provide recursive definitions for such processes, together with a domain-theoretic semantics of the Stochastic Arithmetic. We analyze both the spacial (ordinal) recursion, related to spacial modelling of the stochastic memory, and the temporal (structural) recursion, given by the inclusion relation modelling partial objects in the ordered structure of process construction. 1.