Verification of multiprocess probabilistic protocols
Distributed Computing
Parallel program design: a foundation
Parallel program design: a foundation
A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Predicate calculus and program semantics
Predicate calculus and program semantics
Probabilistic self-stabilization
Information Processing Letters
Token management schemes and random walks yield self-stabilizing mutual exclusion
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Equivalences, congruences, and complete axiomatizations for probabilistic processes
CONCUR '90 Proceedings on Theories of concurrency : unification and extension: unification and extension
Building on the unity experience: compositionality, fairness and probability in parallelism
Building on the unity experience: compositionality, fairness and probability in parallelism
Termination of Probabilistic Concurrent Program
ACM Transactions on Programming Languages and Systems (TOPLAS)
Guarded commands, nondeterminacy and formal derivation of programs
Communications of the ACM
POPL '81 Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Another advantage of free choice (Extended Abstract): Completely asynchronous agreement protocols
PODC '83 Proceedings of the second annual ACM symposium on Principles of distributed computing
Verification of multiprocess probabilistic protocols
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed computing
Probabilistic temporal logics for finite and bounded models
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
On the extremely fair treatment of probabilistic algorithms
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Eventual Determinism: Using Probabilistic Means to Achieve DeterministicEnds
Eventual Determinism: Using Probabilistic Means to Achieve DeterministicEnds
Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Almost-certain eventualities and abstract probabilities in the quantitative temporal logic qTL
Theoretical Computer Science
Abstract compositional analysis of iterated relations: a structural approach to complex state transition systems
Probabilistic termination in B
ZB'03 Proceedings of the 3rd international conference on Formal specification and development in Z and B
Reasoning about almost-certain convergence properties using Event-B
Science of Computer Programming
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The use of randomization in the design and analysis of algorithms promises simple and efficient algorithms to difficult problems, some of which may not have a deterministic solution. This gain in simplicity, efficiency, and solvability results in a trade-off of the traditional notion of absolute correctness of algorithms for a more quantitative notion: correctness with a probability between 0 and 1. The addition of the notion of parallelism to the already unintuitive idea of randomization makes reasoning about probabilistic parallel programs all the more tortuous and difficult.In this paper we address the problem of specifying and deriving properties of probabilistic parallel programs that either hold deterministically or with probability 1. We present a proof methodology based on existing proof systems for probabilistic algorithms, the theory of the predicate transformer, and the theory of UNITY. Although the proofs of probabilistic programs are slippery at best, we show that such programs can be derived with the same rigor and elegance that we have seen in the derivation of sequential and parallel programs. By applying this methodology to derive probabilistic programs, we hope to develop tools and techniques that would make randomization a useful paradigm in algorithm design.