Communicating sequential processes
Communicating sequential processes
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A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Probabilistic non-determinism
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Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
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Power domains and iterated function systems
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Probabilistic predicate transformers
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Probabilistic models for the guarded command language
Science of Computer Programming - Special issue: on formal specifications: foundations, methods, tools and applications: selected papers from the FMTA '95 conference (29–31 May 1995, Konstancin n. Warsaw, Poland)
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Theoretical Computer Science - Domains
Partial correctness for probabilistic demonic programs
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The Powerdomain of Indexed Valuations
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
The Versatile Continuous Order
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
A Powerdomain for Countable Non-Determinism (Extended Abstract)
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Power Domains and Predicate Transformers: A Topological View
Proceedings of the 10th Colloquium on Automata, Languages and Programming
A Complete System for SCCS with Modal Assertions
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Data Refinement with Probability in Mind
Electronic Notes in Theoretical Computer Science (ENTCS)
Unifying Probability with Nondeterminism
FM '09 Proceedings of the 2nd World Congress on Formal Methods
A Kantorovich-Monadic Powerdomain for Information Hiding, with Probability and Nondeterminism
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Layout Randomization and Nondeterminism
Electronic Notes in Theoretical Computer Science (ENTCS)
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We present domain-theoretic models that support both probabilistic and nondeterministic choice. In [A. McIver and C. Morgan. Partial correctness for probablistic demonic programs. Theoretical Computer Science, 266:513-541, 2001], Morgan and McIver developed an ad hoc semantics for a simple imperative language with both probabilistic and nondeterministic choice operators over a discrete state space, using domain-theoretic tools. We present a model also using domain theory in the sense of D.S. Scott (see e.g. [G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove, and D. S. Scott. Continuous Lattices and Domains, volume 93 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 2003]), but built over quite general continuous domains instead of discrete state spaces. Our construction combines the well-known domains modelling nondeterminism - the lower, upper and convex powerdomains, with the probabilistic powerdomain of Jones and Plotkin [C. Jones and G. Plotkin. A probabilistic powerdomain of evaluations. In Proceedings of the Fourth Annual Symposium on Logic in Computer Science, pages 186-195. IEEE Computer Society Press, 1989] modelling probabilistic choice. The results are variants of the upper, lower and convex powerdomains over the probabilistic powerdomain (see Chapter 4). In order to prove the desired universal equational properties of these combined powerdomains, we develop sandwich and separation theorems of Hahn-Banach type for Scott-continuous linear, sub- and superlinear functionals on continuous directed complete partially ordered cones, endowed with their Scott topologies, in analogy to the corresponding theorems for topological vector spaces in functional analysis (see Chapter 3). In the end, we show that our semantic domains work well for the language used by Morgan and McIver.