A polynomial-time algorithm for the equivalence of probabilistic automata
SIAM Journal on Computing
Probabilistic and prioritized models of timed CSP
MFPS '92 Selected papers of the meeting on Mathematical foundations of programming semantics
Randomized algorithms
Modeling and verification of randomized distributed real-time systems
Modeling and verification of randomized distributed real-time systems
On full abstraction for PCF: I, II, and III
Information and Computation
ACM Transactions on Computational Logic (TOCL)
Semiring frameworks and algorithms for shortest-distance problems
Journal of Automata, Languages and Combinatorics
Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Reasoning about Idealized ALGOL Using Regular Languages
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
Games for complexity of second-order call-by-name programs
Theoretical Computer Science - Game theory meets theoretical computer science
On automated verification of probabilistic programs
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Language equivalence for probabilistic automata
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Best probabilistic transformers
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
On the complexity of the equivalence problem for probabilistic automata
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
APEX: an analyzer for open probabilistic programs
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Algorithmic probabilistic game semantics
Formal Methods in System Design
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We study notions of equivalence and refinement for probabilistic programs formalized in the second-order fragment of Probabilistic Idealized Algol. Probabilistic programs implement randomized algorithms: a given input yields a probability distribution on the set of possible outputs. Intuitively, two programs are equivalent if they give rise to identical distributions for all inputs. We show that equivalence is decidable by studying the fully abstract game semantics of probabilistic programs and relating it to probabilistic finite automata. For terms in β-normal form our decision procedure runs in time exponential in the syntactic size of programs; it is moreover fully compositional in that it can handle open programs (probabilistic modules with unspecified components).In contrast, we show that the natural notion of program refinement, in which the input-output distributions of one program uniformly dominate those of the other program, is undecidable.