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The Distributed Interval Geometric Machine Model

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Book cover Applied Parallel Computing. State of the Art in Scientific Computing (PARA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3732))

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Abstract

This paper presents a distributed version of the Interval Geometric Machine Model, called Distributed Interval Geometric Machine, whose inductive construction allows recursive definitions for interval algorithms involving possibly infinite distributed and synchronous parallel computations performed over array structures. In addition, the programming language \(\cal{L}(\mathbb{D}_{\infty})\) is extended to model the semantics of sample distributed algorithms applied to Interval Mathematics.

Partially supported by CTINFO/CNPq and FAPERGS.

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References

  1. Dimuro, G.P., Costa, A.C.R., Claudio, D.M.: A Coherence Space of Rational Intervals for a Construction of IR. Reliable Computing 6(2), 139–178 (2000)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  3. Moore, R.E.: Methods and Applications of Interval Analysis. SIAM Publ., Philadelphia (1979)

    MATH  Google Scholar 

  4. Reiser, R.H.S., Costa, A.C.R., Dimuro, G.P.: First steps in the construction of the Geometric Machine. TEMA. RJ: SBMAC 3(1), 183–192 (2002)

    MathSciNet  MATH  Google Scholar 

  5. Reiser, R.H.S., Costa, A.C.R., Dimuro, G.P.: The Interval Geometric Machine. Numerical Algorithms 37, 357–366 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Reiser, R.H.S., Costa, A.C.R., Dimuro, G.P.: A Programming Language for the Interval Geometric Machine Model. Electronic Notes in Theoretical Computer Science 84, 1–12 (2003)

    Article  Google Scholar 

  7. Reiser, R.H.S., Costa, A.C.R., Dimuro, G.P.: Programming in the Geometric Machine. Frontiers in Artificial Intelligence and Its Applications 101, 95–102 (2003)

    Google Scholar 

  8. Scott, D.: Some Definitional Suggestions for Automata Theory. Journal of Computer and System Sciences 1, 187–212 (1967)

    Article  MATH  Google Scholar 

  9. Scott, D.: The lattice of flow diagrams, Lecture Notes. Berlin: Springer Verlag 188, 311–372 (1971)

    Google Scholar 

  10. Stoll, R.R.: Set Theory and Logic, p. 474. Dover Publication Inc., New York (1961)

    Google Scholar 

  11. Troelstra, S.: Lectures on Linear Logic, Lecture Notes. Stanford: CSLI/Leland Stanford Junior University 29 (1992)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Escola de Informática, Universidade Católica de Pelotas, 96010-000, Pelotas, Brazil

    Renata H. S. Reiser, Antônio C. R. Costa & Graçaliz P. Dimuro

  2. Programa de Pós-Graduação em Computação, Universidade Federal do Rio Grande do Sul, 90501-970, Porto Alegre, Brazil

    Antônio C. R. Costa

Authors
  1. Renata H. S. Reiser
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  2. Antônio C. R. Costa
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  3. Graçaliz P. Dimuro
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Editor information

Editors and Affiliations

  1. Computer Science Department, University of Tennessee, 37996-3450, Knoxville, TN, USA

    Jack Dongarra

  2. Department of Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Kaj Madsen

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2006 Springer-Verlag Berlin Heidelberg

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Reiser, R.H.S., Costa, A.C.R., Dimuro, G.P. (2006). The Distributed Interval Geometric Machine Model. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_20

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  • DOI: https://doi.org/10.1007/11558958_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29067-4

  • Online ISBN: 978-3-540-33498-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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