The Stochastic Geometric Machine Model
DOI:
https://doi.org/10.5540/tema.2004.05.02.0307Abstract
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! 1), induced by the Coherence Space of Processes D! 1, 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.References
[1] G.P. Dimuro, A.C.R. Costa and D.M. Claudio, A Coherence Space of Rational Intervals for a Construction of IR, Reliable Computing, 6, No. 2 (2000), 139-178.
J. -Y. Girard, Linear Logic, Theoretical Computer Science, 1 (1987), 187-212.
S. Markov, On the Algebraic Properties of Intervals and Some Applications, Reliable Computing, 7, No. 2 (2001), 113-127.
S. Markov and R. Alt, Stochastic Arithmetic: Addition and Multiplication by Scalars, Applied and Numerical Mathematics, 50 (2004), 475-488.
R.E. Moore, “Methods and Applications of Interval Analysis”, SIAM, 1979.
R.H.S. Reiser, A.C.R. Costa and G.P. Dimuro, First steps in the construction of the Geometric Machine, em “Seleta do XXIV CNMAC” (E.X.L. de Andrade, J.M. Balthazar, S.M. Gomes, G.N. Silva and A. Sri Ranga, eds.), Tendências em Matemática Aplicada e Computacional, Vol. 3, pp. 183-192, SBMAC, 2002.
R.H.S. Reiser, A.C.R. Costa and G.P. Dimuro, A programming language for the Interval GeometricMachine, Electronic Notes in Theoretical Computer Science, 84 (2003), 1-12.
R.H.S. Reiser, G. P. Dimuro and AC. R. Costa, The Interval Geometric Machine Model, Numerical Algorithms, 37, No. 4 (2004), 357-366.
D. Scott, Some definitional suggestions for automata theory, Journal of Computer and System Sciences, 1, No. 1 (1967), 187-212.
V. Stoltenberg-Hansen, I. Lindstr¨om and E. R. Griffor, “Mathematical Theory of Domains”, Cambridge University Press, Cambridge, 1994.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.