Abstract
A complete and decidable Hoare-style calculus for iteration-free probabilistic sequential programs is presented using a state logic with truth-functional propositional (not arithmetical) connectives.
- [1] Abadi, M. and Halpern, J.Y., Decidability and expressiveness for first-order logics of probability. Information and Computation. v112 i1. 1-36. Google ScholarDigital Library
- [2] Ambainis, A., Mosca, M., Tapp, A. and de Wolf, R., Private quantum channels. In: FOCS¿00: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, IEEE Computer Society. pp. 547 Google ScholarDigital Library
- [3] Baltazar, P., Chadha, R., Mateus, P. and Sernadas, A., Towards model-checking quantum security protocols. In: Dini, P. (Ed.), Proceedings of the First Workshop on Quantum Security: QSec¿07, IEEE Press. Google ScholarDigital Library
- [4] Basu, S., Pollack, R. and Marie-Françoise, R., Algorithms in Real Algebraic Geometry. 2003. Springer Verlag. Google ScholarDigital Library
- [5] Ben-Or, M., Kozen, D. and Reif, J., The complexity of elementary algebra and geometry. Journal of Computer and System Sciences. v18. 251-264. Google ScholarDigital Library
- [6] Caleiro, C., Mateus, P., Sernadas, A. and Sernadas, C., Quantum institutions. In: Futatsugi, K., Jouannaud, J.-P., Meseguer, J. (Eds.), Lecture Notes in Computer Science, vol. 4060. Springer Verlag. pp. 50-64.Google Scholar
- [7] Chadha, R., Mateus, P. and Sernadas, A., Reasoning about quantum imperative programs. Electronic Notes in Theoretical Computer Science. v158. 19-40.Google Scholar
- [8] Chadha, R., Mateus, P. and Sernadas, A., Reasoning about states of probabilistic sequential programs. In: Ésik, Z. (Ed.), Lecture Notes in Computer Science, vol. 4207. Springer-Verlag. pp. 240-255. Google ScholarDigital Library
- [9] R. Chadha, P. Mateus, A. Sernadas, C. Sernadas, Extending classical logic for reasoning about quantum systems, CLC, Department of Mathematics, Instituto Superior Técnico, 2005. Invited submission to the Handbook of Quantum Logic. PreprintGoogle Scholar
- [10] den Hartog, J.I. and de Vink, E.P., Verifying probabilistic programs using a Hoare like logic. International Journal of Foundations of Computer Science. v13 i3. 315-340.Google Scholar
- [11] Fagin, R., Halpern, J.Y. and Megiddo, N., A logic for reasoning about probabilities. Information and Computation. v87 i1¿2. 78-128. Google ScholarDigital Library
- [12] Feldman, Y.A., A decidable propositional dynamic logic with explicit probabilities. Information and Control. v63 i1¿2. 11-38. Google ScholarDigital Library
- [13] Feldman, Y.A. and Harel, D., A probabilistic dynamic logic. Journal of Computer and System Sciences. v28. 193-215.Google Scholar
- [14] Hansson, H. and Jonsson, B., A logic for reasoning about time and reliability. Formal Aspects of Computing. v6. 512-535.Google Scholar
- [15] Hoare, C., An axiomatic basis for computer programming. Communications of the ACM. v12. 576-583. Google ScholarDigital Library
- [16] Hodges, W., Model Theory. 1993. Cambridge University Press.Google Scholar
- [17] M. Huth, M. Kwiatkowska, Quantitative analysis and model checking, in: 12th Annual IEEE Symposium on Logic in Computer Science, LICS¿97, 1997, pp. 111¿122 Google ScholarDigital Library
- [18] C. Jones, Probabilistic non-determinism, Ph.D. Thesis, U. Edinburgh, 1990 Google ScholarDigital Library
- [19] Jones, C. and Plotkin, G.D., A probabilistic powerdomain of evaluations. In: Proceedings of the Fourth Annual Symposium on Logic in Computer Science, IEEE Computer Society. pp. 186-195. Google ScholarDigital Library
- [20] Kozen, D., Semantics of probabilistic programs. Journal of Computer System Science. v22. 328-350.Google Scholar
- [21] Kozen, D., A probabilistic PDL. Journal of Computer System Science. v30. 162-178.Google Scholar
- [22] J.A. Makowsky, M.L. Tiomkin, Probabilistic propositional dynamic logic, 1980. ManuscriptGoogle Scholar
- [23] Mateus, P. and Sernadas, A., Weakly complete axiomatization of exogenous quantum propositional logic. Information and Computation. v204 i5. 771-794.Google Scholar
- [24] Mateus, P., Sernadas, A. and Sernadas, C., Exogenous semantics approach to enriching logics. In: Sica, G. (Ed.), Advanced Studies in Mathematics and Logic, vol. 1. Polimetrica. pp. 165-194.Google Scholar
- [25] Morgan, C., McIver, A. and Seidel, K., Probabilistic predicate transformers. ACM Transactions on Programming Languages and Systems. v18 i3. 325-353. Google ScholarDigital Library
- [26] Moshier, M.A. and Jung, A., A logic for probabilities in semantics. In: Lecture Notes in Computer Science, vol. 2471. Springer Verlag. pp. 216-231. Google ScholarDigital Library
- [27] Narasimha, M., Cleaveland, R. and Iyer, P., Probabilistic temporal logics via the modal mu-calculus. In: Lecture Notes in Computer Science, vol. 1578. Springer Verlag. pp. 288-305. Google ScholarDigital Library
- [28] Nilsson, N.J., Probabilistic logic. Artificial Intelligence. v28 i1. 71-87. Google ScholarDigital Library
- [29] Nilsson, N.J., Probabilistic logic revisited. Artificial Intelligence. v59 i1¿2. 39-42.Google Scholar
- [30] Parikh, R. and Mahoney, A., A theory of probabilistic programs. In: Lecture Notes in Computer Science, vol. 64. Springer Verlag. pp. 396-402. Google ScholarDigital Library
- [31] L.H. Ramshaw, Formalizing the analysis of algorithms, Ph.D. Thesis, Stanford University, 1979 Google ScholarDigital Library
- [32] J.H. Reif, Logics for probabilistic programming (extended abstract), in: STOC¿80: Proceedings of the Twelfth Annual ACM Symposium on Theory of Computing, 1980, pp. 8¿13 Google ScholarDigital Library
- [33] Tix, R., Keimel, K. and Plotkin, G.D., Semantic domains for combining probability and non-determinism. Electronic Notes in Theoretical Computer Science. v129. 1-104.Google Scholar
Index Terms
- Reasoning about probabilistic sequential programs
Recommendations
Completeness and decidability of converse PDL in the constructive type theory of Coq
CPP 2018: Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and ProofsThe completeness proofs for Propositional Dynamic Logic (PDL) in the literature are non-constructive and usually presented in an informal manner. We obtain a formal and constructive completeness proof for Converse PDL by recasting a completeness proof ...
Completeness and Decidability Results for CTL in Constructive Type Theory
We prove completeness and decidability results for the temporal logic CTL in Coq/Ssreflect. Our main result is a constructive proof that for every formula one can obtain either a finite model satisfying the formula or a proof in a Hilbert system ...
On graph reasoning
In this paper, we study the (positive) graph relational calculus. The basis for this calculus was introduced by Curtis and Lowe in 1996 and some variants, motivated by their applications to semantics of programs and foundations of mathematics, appear ...
Comments