# Probabilistic predicate transformers

@article{Morgan1996ProbabilisticPT, title={Probabilistic predicate transformers}, author={Carroll Morgan and Annabelle McIver and Karen Seidel}, journal={ACM Trans. Program. Lang. Syst.}, year={1996}, volume={18}, pages={325-353} }

Probabilistic predicates generalize standard predicates over a state space; with probabilistic predicate transformers one thus reasons about imperative programs in terms of probabilistic pre- and postconditions. Probabilistic healthiness conditions generalize the standard ones, characterizing “real” probabilistic programs, and are based on a connection with an underlying relational model for probabilistic execution; in both contexts demonic nondeterminism coexists with probabilistic choice…

## Figures from this paper

## 339 Citations

Programming Research Group Probabilistic Predicate Transformers Probabilistic Predicate Transformers

- Computer Science
- 1995

This work brings together independent work of Claire Jones and Jifeng He, showing how their constructions can be made to correspond, and is able to pro-posèprobabilistic healthiness conditions', generalising those of Dijkstra for ordinary predicate transformers.

Programming Research Group Probabilistic Predicate Transformers: Part 2 Probabilistic Predicate Transformers: Part 2

- Computer Science
- 1996

Here the earlier results are extended to innnite state spaces, and several more specialised topics are explored: the characterisation of standard and deterministic programs; and the structure of the extended space generated whenàngelic choice' is added to the system.

Reasoning about efficiency within a probabilistic µ-calculus

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 1999

Reasoning about probabilistic sequential programs in a probabilistic logic

- Computer ScienceActa Informatica
- 2003

A notion of strong monotonicity of probabilistic predicate transformers is introduced, and this notion enables us to establish a normal form theorem for monotone Probabilistic Predicate Transformers, and a notion of probable correctness is introduced.

Proof rules for probabilistic loops

- Computer Science
- 1996

This paper presents practical proof rules, using the probabilistic transformers, for reasoning about iterations when probability is present, and thoroughly illustrated by example: Probabilistic binary chop, faulty factorial, the martingale gambling strategy and Herman's probabilistically self-stabilisation.

Demonic, angelic and unbounded probabilistic choices in sequential programs

- PhysicsActa Informatica
- 2001

In the end, characteristic healthiness conditions for the hierarchies of a system in which deterministic, demonic, probabilistic and angelic choices all coexist are found.

Backwards Abstract Interpretation of Probabilistic Programs

- Computer ScienceESOP
- 2001

This work proposes a general abstract interpretation based method for the static analysis of programs using random generators or random inputs, which allows ordinary non-deterministic inputs, not neces- sarily following a random distribution.

Verifying Probabilistic Programs Using a Hoare Like Logic

- Computer ScienceInt. J. Found. Comput. Sci.
- 2002

A formalism which allows reasoning about programs which can act probabilistically is studied, a basic programming language with an operator for probabilistic choice is introduced and a denotational semantics is given for this language.

Reasoning About States of Probabilistic Sequential Programs

- Computer ScienceCSL
- 2006

TheHoare calculus presented herein is the first probabilistic Hoare calculus with a complete and decidable state logic that has truth-functional propositional (not arithmetical) connectives.

Programming Research Group Proof Rules for Probablistic Loops

- Computer Science
- 1995

This paper presents practical proof rules, using the probabilistic transformers, for reasoning about iterations when probability is present, and thoroughly illustrated by example: probabilistically binary chop, faulty factorial, the martingale gambling strategy and Herman's probabilists self-stabilisation.

## References

SHOWING 1-10 OF 41 REFERENCES

Proof rules for probabilistic loops

- Computer Science
- 1996

This paper presents practical proof rules, using the probabilistic transformers, for reasoning about iterations when probability is present, and thoroughly illustrated by example: Probabilistic binary chop, faulty factorial, the martingale gambling strategy and Herman's probabilistically self-stabilisation.

Semantics of probabilistic programs

- Computer Science20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
- 1979

Representing Nondeterministic and Probabilistic Behaviour in Reactive Processes

- Computer Science
- 1993

This paper presents an operational model for a probabilistic version of CSP, and describes a number of ways of abstracting a denotational semantics from such a model, so as to represent a process by a set of probability functions.

A probabilistic PDL

- MathematicsSTOC
- 1983

A probabilistic analog PPDL of Propositional Dynamic Logic is given and a small model property is proved and a polynomial space decision procedure for formulas involving well-structured programs is given.

Reasoning about probabilistic parallel programs

- Computer ScienceTOPL
- 1994

This paper addresses the problem of specifying and deriving properties of probabilistic parallel programs that either hold deterministically or with probability 1 and shows that such programs can be derived with the same rigor and elegance that has been seen in the derivation of sequential and parallel programs.

Probabilistic Models for the Guarded Command Language

- Computer ScienceSci. Comput. Program.
- 1997

A generalization of Dijkstra's calculus

- Computer ScienceACM Trans. Program. Lang. Syst.
- 1989

This paper gives a self-contained account of the generalized calculus from first principles through the semantics of recursion through the fixpoint method from denotational semantics.

A Theoretical Basis for Stepwise Refinement and the Programming Calculus

- Computer ScienceSci. Comput. Program.
- 1987

A logic for reasoning about probabilities

- Computer Science[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science
- 1988