Probabilistic non-determinism
Operational semantics and generalized weakest preconditions
Science of Computer Programming - Special issue on mathematics of program construction
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)
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
A Discipline of Programming
An Operational Semantics for the Guarded Command Language
Proceedings of the Second International Conference on Mathematics of Program Construction
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Cost-based analysis of probabilistic programs mechanised in HOL
Nordic Journal of Computing
Principles of Model Checking (Representation and Mind Series)
Principles of Model Checking (Representation and Mind Series)
Program Analysis Probably Counts
The Computer Journal
Linear-invariant generation for probabilistic programs: automated support for proof-based methods
SAS'10 Proceedings of the 17th international conference on Static analysis
Probabilistic reachability for parametric Markov models
International Journal on Software Tools for Technology Transfer (STTT) - SPIN 2009
Probabilistic relational reasoning for differential privacy
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Operational Versus Weakest Precondition Semantics for the Probabilistic Guarded Command Language
QEST '12 Proceedings of the 2012 Ninth International Conference on Quantitative Evaluation of Systems
PRINSYS: on a quest for probabilistic loop invariants
QEST'13 Proceedings of the 10th international conference on Quantitative Evaluation of Systems
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This paper proposes a simple operational semantics of pGCL, Dijkstra's guarded command language extended with probabilistic choice, and relates this to pGCL's wp-semantics by McIver and Morgan. Parametric Markov decision processes whose state rewards depend on the post-expectation at hand are used as the operational model. We show that the weakest pre-expectation of a pGCL-program w.r.t. a post-expectation corresponds to the expected cumulative reward to reach a terminal state in the parametric MDP associated to the program. In a similar way, we show a correspondence between weakest liberal pre-expectations and liberal expected cumulative rewards. The verification of probabilistic programs using wp-semantics and operational semantics is illustrated using a simple running example.