First Steps in the Construction of the Geometric Machine Model

Authors

  • R.H.S. REISER
  • A.C.R. COSTA
  • G.P. DIMURO

DOI:

https://doi.org/10.5540/tema.2002.03.01.0183

Abstract

This work introduces the Geometric Machine (GM) – a computational model for the construction and representation of concurrent and non-deterministic processes, preformed in a synchronized way, with infinite memory whose positions are labelled by the points of a geometric space. The ordered structure of the GM model is based on Girard’s Coherence Spaces. Starting with a coherence space of elementary processes, the inductive domain-theoretic structure of this model is step-wise and systematically constructed and the procedure completion ensures the existence of temporally and spatially infinite computations. A particular aim of our work is to apply this coherence-space-based interpretation to the semantic modelling parallelism and distributed computation over array structures.

References

[1] G.P. Dimuro, A.C.R. Costa and D.M. Claudio, A coherence space of rational intervals for a construction of IR, Journal of Reliable Computing, 6 (2000), 139-178.

J.-Y. Girard, The system F of variable types, fifteen years later, Theoretical Computer Science, 45 (1986), 159-192.

J.-Y. Girard, Linear logic, Theoretical Computer Science, 1 (1987), 187-212.

R.H.S. Reiser, “The Geometric Machine - a Computational Model for Con- currence and Non-determinism Based on Coherence Spaces”, Ph.D. Thesis (in portuguese), PPGC, UFRGS, Porto Alegre, RS, Brazil, 2002. (avaliable in http://gmc.ucpel.tche.br/imqd)

D. Scott, Some definitional suggestions for automata theory, Journal of Com- puter and System Sciences, 188 (1967), 311-372.

D. Scott, The lattice of flow diagrams, Lecture Notes in Mathematics, 188 (1971), 311-372.

A.S. Troeltra, Lectures on Linear Logic, in “CSLI Lecture Notes”, Vol. 29, 1992.

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Published

2002-06-01

How to Cite

REISER, R., COSTA, A., & DIMURO, G. (2002). First Steps in the Construction of the Geometric Machine Model. Trends in Computational and Applied Mathematics, 3(1), 183–192. https://doi.org/10.5540/tema.2002.03.01.0183

Issue

Vol. 3 No. 1 (2002)

Section

Original Article

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