The Stochastic Geometric Machine Model

R.H.S. Reiser, G.P. Dimuro, A.C.R. Costa

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! 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.




DOI: https://doi.org/10.5540/tema.2004.05.02.0307

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia