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

Programming Research Group Probabilistic Predicate Transformers Probabilistic Predicate Transformers
TLDR
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
TLDR
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 probabilistic sequential programs in a probabilistic logic
  • M. Ying
  • Computer Science
    Acta Informatica
  • 2003
TLDR
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.
Reasoning about efficiency within a probabilistic µ-calculus
Proof rules for probabilistic loops
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
  • D. Kozen
  • Computer Science
    20th Annual Symposium on Foundations of Computer Science (sfcs 1979)
  • 1979
Representing Nondeterministic and Probabilistic Behaviour in Reactive Processes
TLDR
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
TLDR
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
TLDR
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.
Data Refinement of Predicate Transformers
A generalization of Dijkstra's calculus
  • Greg Nelson
  • Computer Science
    ACM Trans. Program. Lang. Syst.
  • 1989
TLDR
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
A logic for reasoning about probabilities
...
...