Abstract
We present a theory of designs based on functions from the state space to real numbers, which we term distributions. This theory uses predicates, in the style of UTP, based on homogeneous relations between distributions, and is richer than the standard UTP theory of designs as it allows us to reason about probabilistic programs; the healthiness conditions H1–H4 of the standard theory are implicitly accounted for in the distributional theory we present. In addition we propose a Galois connection linkage between our distribution-based model of probabilistic designs, and the standard UTP model of (non-probabilistic) designs.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Healthiness Condition
- Probabilistic Choice
- Probabilistic Program
- Homogeneous Relation
- Nondeterministic Choice
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bresciani, R., Butterfield, A.: Towards a UTP-style framework to deal with probabilities. Technical Report TCD-CS-2011-09, FMG, Trinity College Dublin, Ireland (August 2011)
Bresciani, R., Butterfield, A.: A UTP Semantics of pGCL as a Homogeneous Relation. In: Derrick, J., Gnesi, S., Latella, D., Treharne, H. (eds.) IFM 2012. LNCS, vol. 7321, pp. 191–205. Springer, Heidelberg (2012)
Butterfield, A. (ed.): UTP 2008. LNCS, vol. 5713. Springer, Heidelberg (2010)
Chen, Y., Sanders, J.W.: Unifying Probability with Nondeterminism. In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 467–482. Springer, Heidelberg (2009)
Dunne, S., Stoddart, B. (eds.): UTP 2006. LNCS, vol. 4010. Springer, Heidelberg (2006)
Halmos, P.R.: Measure Theory. University Series in Higher Mathematics. D. Van Nostrand Company, Inc., Princeton (1950)
He, J.: A probabilistic bpel-like language. In: Qin [Qin10], pp. 74–100
Hehner, E.C.R.: Predicative programming part i,&,ii. Commun. ACM 27(2), 134–151 (1984)
Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall International Series in Computer Science (1998)
Hoare, C.A.R.: Programs are predicates. In: Proceedings of a Discussion Meeting of the Royal Society of London on Mathematical Logic and Programming Languages, pp. 141–155. Prentice-Hall, Upper Saddle River (1985)
He, J., Sanders, J.W.: Unifying probability. In: Dunne and Stoddart [ds06], pp. 173–199
McIver, A., Morgan, C.: Abstraction, Refinement and Proof For Probabilistic Systems. Monographs in Computer Science. Springer (2004)
Qin, S. (ed.): UTP 2010. LNCS, vol. 6445. Springer, Heidelberg (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bresciani, R., Butterfield, A. (2013). A Probabilistic Theory of Designs Based on Distributions. In: Wolff, B., Gaudel, MC., Feliachi, A. (eds) Unifying Theories of Programming. UTP 2012. Lecture Notes in Computer Science, vol 7681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35705-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-35705-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35704-6
Online ISBN: 978-3-642-35705-3
eBook Packages: Computer ScienceComputer Science (R0)