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The Interval Geometric Machine Model

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Abstract

This paper introduces the interval version of the Geometric Machine (GM) model, to model the semantics of algorithms of interval mathematics. Based on coherence spaces, the set of values storable in the GM memory is represented by the bi-structured coherence space of rational intervals, a constructive computational representation of the set of real intervals. Over the inductive ordered structure called the coherence space of processes, the representation of parallel and nondeterministic processes operating on the array structures of the GM memory is obtained. The infinite GM memory, supporting a coherence space of states, is conceived as the set of points of a geometric space. Using this framework, a domain-theoretic semantics of interval algorithms is presented.

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References

  1. S. Abramsky and A. Jung, Domain Theory, in: Handbook of Logic in Computer Science (Clarendon Press, Oxford, 1994).

    Google Scholar 

  2. G.P. Dimuro, A.C.R. Costa and D.M. Claudio, A coherence space of rational intervals for a construction of IR, Reliable Comput. 6(2) (2000) 139–178.

    Google Scholar 

  3. R. Milner, Communication and Concurrency (Prentice-Hall, Englewood Cliffs, NJ, 1990).

    Google Scholar 

  4. R.E. Moore, Methods and Applications of Interval Analysis (SIAM, Philadelphia, PA, 1979).

    Google Scholar 

  5. R.H.S. Reiser, A.C.R. Costa and G.P. Dimuro, First steps in the construction of the geometric machine, in: Seleta do XXIV CNMAC, eds. E.X.L. de Andrade et al., TEMA 3(1) (2002) 183–192.

  6. D. Scott, Some definitional suggestions for automata theory, J. Comput. System Sci. 188 (1967) 311–372.

    Google Scholar 

  7. D. Scott, The lattice of flow diagrams, in: Lecture Notes in Mathemathics, Vol. 188 (Springer, Berlin, 1971) pp. 311–372.

    Google Scholar 

  8. A.S. Troelstra, Lectures on Linear Logic, CSLI Lecture Notes, Vol. 29 (1992).

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Authors and Affiliations

  1. Escola de Informática, Universidade Católica de Pelotas, CP 402, 96010-140, Pelotas, RS, Brazil

    Renata Hax Sander Reiser, Graçaliz Pereira Dimuro & Antônio Carlos da Rocha Costa

  2. Programa de Pós-Graduação em Computação, Universidade Federal do Rio Grande do Sul, CP 15064, 91501-970, Porto Alegre, RS, Brazil

    Antônio Carlos da Rocha Costa

Authors
  1. Renata Hax Sander Reiser
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  2. Graçaliz Pereira Dimuro
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  3. Antônio Carlos da Rocha Costa
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Reiser, R.H.S., Dimuro, G.P. & Costa, A.C.d.R. The Interval Geometric Machine Model. Numerical Algorithms 37, 357–366 (2004). https://doi.org/10.1023/B:NUMA.0000049481.94703.00

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  • DOI: https://doi.org/10.1023/B:NUMA.0000049481.94703.00

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