Algebras of modal operators and partial correctness

Theoretical Computer Science

Volumn 351, Issue 2, 2006, Pages 221-239

  Möller, Bernhard ^a   Struth, Georg ^b  

^a UNIVERSITY OF AUGSBURG   (Germany)

^b BUNDESWEHR UNIVERSITY MUNICH   (Germany)

Author keywords

Hoare logic; Kleene algebra; Modal operators; Partial correctness; Semirings

Indexed keywords

DIAMONDS; MATHEMATICAL PROGRAMMING; MATHEMATICAL TECHNIQUES; MODAL ANALYSIS; SEMANTICS; THEOREM PROVING;

HOARE LOGIC; KLEENE ALGEBRA; MODAL OPERATORS; PARTIAL CORRECTNESS; SEMIRINGS;

ALGEBRA;

EID: 31544443223     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2005.09.069     Document Type: Conference Paper

References (28)

1. K.-R. Apt, and E.-R. Olderog Verification of Sequential and Concurrent Programs second ed. 1997 Springer Berlin
2. R. Backhouse, and J. van der Woude Demonic operators and monotype factors Math. Struct. Comput. Sci. 3 4 1993 417 433
3. G. Birkhoff, Lattice Theory, Vol. 25, Colloquium Publications, American Mathematical Society, Providence, RI, 1984 (Reprint).
4. E. Cohen, Separation and reduction, in: R. Backhouse, J.N. Oliveira (Eds.), Proc. Mathematics of Program Construction, Fifth Internat. Conf., MPC 2000, Lecture Notes in Computer Science, Vol. 1837, Springer, Berlin, 2000, pp. 45-59.
5. P. Cousot, and R. Cousot Systematic design of program analysis frameworks Sixth POPL 1979 ACM Press New York 269 282
6. J. Desharnais, and B. Möller Characterizing determinacy in Kleene algebras Inform. Sci. 139 3-4 2001 253 273
7. J. Desharnais, B. Möller, and G. Struth Applications of modal Kleene algebra - a survey J. Relat. Methods Comput. Sci. 1 2004 93 131
8. J. Desharnais, B. Möller, and G. Struth Termination in modal Kleene algebra J.-J. Lévy E. Mayr J. Mitchell Exploring New Frontiers of Theoretical Informatics, IFIP International Federation for Information Processing Series Vol. 155 2004 Kluwer Dordrecht 653 666
9. J. Desharnais, B. Möller, G. Struth, Kleene algebra with domain, ACM Trans. Comput. Logic 2006, in press.
10. T. Ehm, B. Möller, G. Struth, Kleene modules, in: R. Berghammer, B. Möller, G. Struth (Eds.), Relational and Kleene-Algebraic Methods in Computer Science, Lecture Notes in Computer Science, Vol. 3051, Springer, Berlin, 2004, pp. 112-123.
11. C. Hardin, D. Kozen, On the elimination of hypotheses in Kleene algebra with tests, Technical Report 2002-1879, Computer Science Department, Cornell University, 2002.
12. D. Harel, D. Kozen, and J. Tiuryn Dynamic Logic 2000 MIT Press Cambridge, MA
13. B. Jónsson, and A. Tarski Boolean algebras with operators, Part I Amer. J. Math. 73 1951 891 939
14. D. Kozen, On Kleene algebras and closed semirings, in: B. Rovan (Ed.), Proc. MFCS'90, Lecture Notes in Computer Science, Vol. 452, Springer, Berlin, 1990, pp. 26-47.
15. D. Kozen A completeness theorem for Kleene algebras and the algebra of regular events Inform. Comput. 110 2 1994 366 390
16. D. Kozen Kleene algebra with tests Trans. Program. Languages Systems 19 3 1997 427 443
17. D. Kozen On Hoare logic and Kleene algebra with tests Trans. Comput. Logic 1 1 2001 60 76
18. D. Kozen Some results in dynamic model theory Sci. Comput. Program. 51 1-2 2004 3 22
19. J. Loeckx, and K. Sieber The Foundations of Program Verification second ed. 1987 Wiley, Teubner
20. B. Möller, Lazy Kleene algebra, in: D. Kozen (Ed.), Mathematics of Program Construction, Lecture Notes in Computer Science, Vol. 3125, Springer, Berlin, 2004, pp. 252-273.
21. B. Möller, G. Struth, Modal Kleene algebra and partial correctness, in: C. Rattray, S. Maharaj, C. Shankland (Eds.), Algebraic Methodology and Software Technology, Lecture Notes in Computer Science, Vol. 3116, Springer, Berlin, 2004, pp. 379-393.
22. B. Möller, G. Struth, WP is WLP, in: Participants' Proc. Eighth Internat. Seminar on Relational Methods in Computer Science (RelMiCS 8) and Third Internat. Workshop on Applications of Kleene Algebra, 22-26 February, 2005, St. Catharines, Ont., Canada, 2005, pp. 171-178.
23. Extended version in Technical Report 2004-14, Institute of Computer Science, University of Augsburg, October 2004.
24. G. Nelson A generalization of Dijkstra's calculus ACM Trans. Program. Languages Systems 11 1989 517 561
25. V. Pratt Dynamic algebras: examples, constructions, applications Stud. Logica 50 1991 571 605
26. G. Schmidt, and T. Ströhlein Relations and Graphs: Discrete Mathematics for Computer Scientists, EATCS Monographs on Theoretical Computer Science 1993 Springer Berlin
27. B. von Karger Temporal algebra Math. Struct. Comput. Sci. 8 3 1998 277 320
28. J. von Wright, From Kleene algebra to refinement algebra, in: B. Möller, E. Boiten (Eds.), Mathematics of Program Construction, Sixth Internat. Conf., MPC 2002, Lecture Notes in Computer Science, Vol. 2386, Springer, Berlin, 2002, pp. 233-262.