Nondeterminism in logics of programs
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A dynamic logic of multiprocessing with incomplete information
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Riemann's Hypothesis and tests for primality
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Computational complexity of probabilistic Turing machines
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
A practical decision method for propositional dynamic logic (Preliminary Report)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Formalizing the analysis of algorithms.
Formalizing the analysis of algorithms.
Algebraic approaches to nondeterminism—an overview
ACM Computing Surveys (CSUR)
STOC '82 Proceedings of the fourteenth 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
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A decidable propositional probabilistic dynamic logic
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Reasoning about probabilistic sequential programs
Theoretical Computer Science
Reasoning about states of probabilistic sequential programs
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Probabilistic Relational Reasoning for Differential Privacy
ACM Transactions on Programming Languages and Systems (TOPLAS)
Probabilistic relational verification for cryptographic implementations
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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This paper introduces a logic for probabilistic programming+ PROB-DL (for probabilistic dynamic logic; see Section 2 for a formal definition). This logic has “dynamic” modal operators in which programs appear, as in Pratt's [1976] dynamic logic DL. However the programs of PROB-DL contain constructs for probabilistic branching and looping whereas DL is restricted to nondeterministic programs. The formula {a}&sgr;p of PROB-DL denotes “with measure ≥&sgr;, formula p holds after executing program a.” In Section 3, we show that PROB-DL has a complete and consistent axiomatization, (using techniques derived from Parikh's [1978] completeness proof for the propositional dynamic logic). Section 4 presents a probabilistic quantified boolean logic (PROB-QBF) which also has applications to probabilistic programming.