ACM Transactions on Programming Languages and Systems (TOPLAS)
A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Making a fair roulette from a possibly biased coin
Information Processing Letters
Programming from specifications (2nd ed.)
Programming from specifications (2nd ed.)
Competitive Markov decision processes
Competitive Markov decision processes
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)
Abstract Interpretation of Probabilistic Semantics
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
SLIPE '85 Proceedings of the ACM SIGPLAN 85 symposium on Language issues in programming environments
Performance analysis of probabilistic action systems
Formal Aspects of Computing
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Probabilistic guarded commands mechanized in HOL
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Tank monitoring: a pAMN case study
Formal Aspects of Computing
Towards automated proof support for probabilistic distributed systems
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Reasoning algebraically about probabilistic loops
ICFEM'06 Proceedings of the 8th international conference on Formal Methods and Software Engineering
Compositional specification and analysis of cost-based properties in probabilistic programs
FM'05 Proceedings of the 2005 international conference on Formal Methods
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Development via refinement in probabilistic b: foundation and case study
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
Quantitative refinement and model checking for the analysis of probabilistic systems
FM'06 Proceedings of the 14th international conference on Formal Methods
Using probabilistic kleene algebra for protocol verification
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Proofs and Refutations for Probabilistic Refinement
FM '08 Proceedings of the 15th international symposium on Formal Methods
Security, Probability and Nearly Fair Coins in the Cryptographers' Café
FM '09 Proceedings of the 2nd World Congress on Formal Methods
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Refinement plays a crucial role in "top-down" styles of verification, such as the refinement calculus, but for probabilistic systems proof of refinement is a particularly challenging task due to the combination of probability and nondeterminism which typically arises in partially-specified systems. Whilst the theory of probabilistic refinement is well-known [18] there are few tools to help with establishing refinements between programs. In this paper we describe a tool which provides partial support during refinement proofs. The tool essentially builds small models of programs using an algebraic rewriting system to extract the overall probabilistic behaviour. We use that behaviour to recast refinement-checking as a linear satisfiability problem, which can then be exported to a linear arithmetic solver. One of the major benefits of this approach is the ability to generate counter examples, alerting the prover to a problem in a proposed refinement. We demonstrate the technique on a small case study based on Schneider et al.'s Tank Monitoring [26].