Proving probabilistic correctness statements: the case of Rabin's algorithm for mutual exclusion
PODC '92 Proceedings of the eleventh annual ACM symposium on Principles of distributed computing
Randomized mutual exclusion algorithms revisited
PODC '92 Proceedings of the eleventh annual ACM symposium on Principles of distributed computing
Knowledge, probability, and adversaries
Journal of the ACM (JACM)
Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
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)
A Formal Approach to Probabilistic Termination
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
MPC '00 Proceedings of the 5th 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)
Towards automated proof support for probabilistic distributed systems
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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
Refinement Algebra for Probabilistic Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Automating refinement checking in probabilistic system design
ICFEM'07 Proceedings of the formal engineering methods 9th international conference on Formal methods and software engineering
A non-probabilistic relational model of probabilistic Kleene algebras
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Reactive probabilistic programs and refinement algebra
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Towards an algebra of routing tables
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
On probabilistic kleene algebras, automata and simulations
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
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
Hi-index | 0.00 |
We describe pKA, a probabilistic Kleene-style algebra, based on a well known model of probabilistic/demonic computation [3,16,10]. Our technical aim is to express probabilistic versions of Cohen's separation theorems. Separation theorems simplify reasoning about distributed systems, where with purely algebraic reasoning they can reduce complicated interleaving behaviour to “separated” behaviours each of which can be analysed on its own. Until now that has not been possible for probabilistic distributed systems. Algebraic reasoning in general is very robust, and easy to check: thus an algebraic approach to probabilistic distributed systems is attractive because in that “doubly hostile” environment (probability and interleaving) the opportunities for subtle error abound. Especially tricky is the interaction of probability and the demonic or “adversarial” scheduling implied by concurrency. Our case study — based on Rabin's Mutual exclusion with bounded waiting — is one where just such problems have already occurred: the original presentation was later shown to have subtle flaws [15]. It motivates our interest in algebras, where assumptions relating probability and secrecy are clearly exposed and, in some cases, can be given simple characterisations in spite of their intricacy.