Reasoning About States of Probabilistic Sequential Programs

1. Abadi, M., Halpern, J.Y.: Decidability and expressiveness for first-order logics of probability. Information and Computation 112(1), 1–36 (1994)

   Article  MATH  MathSciNet  Google Scholar 

2. Ambainis, A., Mosca, M., Tapp, A., de Wolf, R.: Private quantum channels. In: FOCS 2000: Proceedings of the 41st Annual Symposium on Foundations of Computer Science, p. 547. IEEE Computer Society Press, Los Alamitos (2000)

   Chapter  Google Scholar 

3. Basu, S., Pollack, R., Marie-Françoise, R.: Algorithms in Real Algebraic Geometry. Springer, Heidelberg (2003)

   MATH  Google Scholar 

4. Chadha, R., Mateus, P., Sernadas, A.: Reasoning about quantum imperative programs. Electronic Notes in Theoretical Computer Science 158, 19–40 (2006) (Invited talk at the Twenty-Second Conference on the Mathematical Foundations of Programming Semantics)

   Article  Google Scholar 

5. Chadha, R., Mateus, P., Sernadas, A., Sernadas, C.: Extending classical logic for reasoning about quantum systems. CLC, Department of Mathematics, Instituto Superior Técnico (preprint, 2005) (Invited submission to the Handbook of Quantum Logic)

   Google Scholar 

6. den Hartog, J.I., de Vink, E.P.: Verifying probabilistic programs using a hoare like logic. International Journal of Foundations of Computer Science 13(3), 315–340 (2002)

   Article  MATH  MathSciNet  Google Scholar 

7. Fagin, R., Halpern, J.Y., Megiddo, N.: A logic for reasoning about probabilities. Information and Computation 87(1-2), 78–128 (1990)

   Article  MATH  MathSciNet  Google Scholar 

8. Feldman, Y.A.: A decidable propositional dynamic logic with explicit probabilities. Information and Control 63(1/2), 11–38 (1984)

   Article  MATH  MathSciNet  Google Scholar 

9. Feldman, Y.A., Harel, D.: A probabilistic dynamic logic. Journal of Computer and System Sciences 28, 193–215 (1984)

   Article  MATH  MathSciNet  Google Scholar 

10. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6, 512–535 (1995)

    Article  Google Scholar 

11. Hoare, C.: An axiomatic basis for computer programming. Communications of the ACM 12, 576–583 (1969)

    Article  MATH  Google Scholar 

12. Hodges, W.: Model Theory. Cambridge University Press, Cambridge (1993)

    Book  MATH  Google Scholar 

13. Huth, M., Kwiatkowska, M.: Quantitative analysis and model checking. In: 12th Annual IEEE Symposium on Logic in Computer Science (LICS 1997), pp. 111–122 (1997)

    Google Scholar 

14. Jones, C.: Probabilistic Non-determinism. PhD thesis, U. Edinburgh (1990)

    Google Scholar 

15. Jones, C., Plotkin, G.D.: A probabilistic powerdomain of evaluations. In: Proceedings of the Fourth Annual Symposium on Logic in Computer Science, pp. 186–195. IEEE Computer Society Press, Los Alamitos (1989)

    Chapter  Google Scholar 

16. Kozen, D.: Semantics of probabilistic programs. Journal of Computer System Science 22, 328–350 (1981)

    Article  MATH  MathSciNet  Google Scholar 

17. Kozen, D.: A probabilistic PDL. Journal of Computer System Science 30, 162–178 (1985)

    Article  MATH  MathSciNet  Google Scholar 

18. Makowsky, J.A., Tiomkin, M.L.: Probabilistic propositional dynamic logic (manuscript, 1980)

    Google Scholar 

19. Mateus, P., Sernadas, A.: Weakly complete axiomatization of exogenous quantum propositional logic. Information and Computation (to appear)

    Google Scholar 

20. Mateus, P., Sernadas, A., Sernadas, C.: Exogenous semantics approach to enriching logics. In: Essays on the Foundations of Mathematics and Logic. Advanced Studies in Mathematics and Logic, vol. 1, pp. 165–194. Polimetrica (2005)

    Google Scholar 

21. Morgan, C., McIver, A., Seidel, K.: Probabilistic predicate transformers. ACM Transactions on Programming Languages and Systems 18(3), 325–353 (1996)

    Article  Google Scholar 

22. Moshier, M.A., Jung, A.: A logic for probabilities in semantics. In: Bradfield, J.C. (ed.) CSL 2002. LNCS, vol. 2471, pp. 216–231. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

23. Narasimha, M., Cleaveland, W.R., Iyer, P.: Probabilistic temporal logics via the modal mu-calculus. In: Thomas, W. (ed.) FOSSACS 1999. LNCS, vol. 1578, pp. 288–305. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

24. Nilsson, N.J.: Probabilistic logic. Artificial Intelligence 28(1), 71–87 (1986)

    Article  MATH  MathSciNet  Google Scholar 

25. Nilsson, N.J.: Probabilistic logic revisited. Artificial Intelligence 59(1-2), 39–42 (1993)

    Article  MathSciNet  Google Scholar 

26. Parikh, R., Mahoney, A.: A theory of probabilistic programs. In: Proceedings of the Carnegie Mellon Workshop on Logic of Programs. LNCS, vol. 64, pp. 396–402. Springer, Heidelberg (1983)

    Google Scholar 

27. Ramshaw, L.H.: Formalizing the analysis of algorithms. PhD thesis, Stanford University (1979)

    Google Scholar 

28. Reif, J.H.: Logics for probabilistic programming (extended abstract). In: STOC 1980: Proceedings of the Twelfth Annual ACM Symposium on Theory of Computing, pp. 8–13 (1980)

    Google Scholar 

29. Tix, R., Keimel, K., Plotkin, G.D.: Semantic domains for combining probability and non-determinism. Electronic Notes in Theoretical Computer Science 129, 1–104 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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