From linear time to branching time

ACM Transactions on Computational Logic

Volumn 6, Issue 2, 2005, Pages 273-294

  Kupferman, Orna ^a   Vardi, Moshe Y ^b,c  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b RICE UNIVERSITY   (United States)

^c Rice University   (United States)

Author keywords

Alternation free calculus; Linear temporal logic

Indexed keywords

ALTERATION-FREE Μ-CALCULUS; BRANCHING TIME; LINEAR TEMPORAL LOGIC; LINEAR TIME;

AUTOMATA THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; LINEAR SYSTEMS; MATHEMATICAL MODELS; PROBLEM SOLVING; SYNTACTICS; THEOREM PROVING; TREES (MATHEMATICS);

FORMAL LOGIC;

EID: 16644363102     PISSN: 15293785     EISSN: None     Source Type: Journal    
DOI: 10.1145/1055686.1055689     Document Type: Article

References (52)

1. ARNOLD, A. AND NIWIŃSKI, D. 1992. Fixed point characterization of weak monadic logic definable sets of trees. In Tree Automata and Languages, M. Nivat and A. Podelski, Eds. Elsevier, Amsterdam, The Netherlands, 159-188.
2. BHAT, G. AND CLEAVLAND, R. 1996. Efficient model checking via the equational μ-calculus. In Proceedings of the 11th IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., 304-312.
3. BLOEM, R., RAVI, K., AND SOMENZI, F. 1999. Efficient decision procedures for model checking of linear time logic properties. In Computer-Aided Verification, Proceedings of the 11th International Conference. Lecture Notes in Computer Science, vol. 1633. Springer-Verlag, New York, 222-235.
4. BRAYTON, R., HACHTEL, G., SANGIOVANNI-VINCENTELLI, A., SOMENZI, F., AZIZ, A., CHENG, S.-T., EDWARDS, S., KHATRI, S., KUKIMOTO, T., PARDO, A., QADEER, S., RANJAN, R., SARWARY, S., SHIPLE, T., SWAMY, G., AND VILLA, T. 1996. VIS: a system for verification and synthesis. In Computer-Aided Verification, Proceedings of the 8th International Conference. Lecture Notes in Computer Science, vol. 1102. Springer-Verlag, New York, 428-432.
5. BRYANT, R. 1986. Graph-based algorithms for Boolean-function manipulation. IEEE Trans. Comput. C-35, 8.
6. BÜCHI, J. 1962. On a decision method in restricted second-order arithmetic. In Proceedings of the International Congress on Logic, Method, and Philosophy of Science. Stanford University Press, Stanford, Calif., 1-12.
7. 20 states and beyond. Inf. Comput. 98, 2 (June), 142-170.
8. CADENCE. SMV. http://www.cadence.com/company/cadence_labs_research.html.
9. CHANDRA, A., KOZEN, D., AND STOCKMEYER, L. 1981. Alternation. J. ACM 28, 1 (Jan.), 114-133.
10. CLARKE, E. AND DRAGHICESCU, I. 1988. Expressibility results for linear-time and branching-time logics. In Proceedings of the Workshop on Linear Time, Branching Time, and Partial Order in Logics and Models for Concurrency, J. de Bakker, W. de Roever, and G. Rozenberg, Eds. Lecture Notes in Computer Science, vol. 354. Springer-Verlag, New York, 428-437.
11. CLARKE, E., EMERSON, E., AND SISTLA, A. 1986. Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Prag. Lang. Syst. 8, 2 (Jan.), 244-263.
12. CLARKE, E., GRUMBERG, O., AND PELED, D. 1999. Model Checking. MIT Press.
13. CLEAVELAND, R. AND STEFFEN, B. 1991. A linear-time model-checking algorithm for the alternation-free modal μ-calculus. In Proceedings of the 3rd International Conference on Computer-Aided Verification. Lecture Notes in Computer Science, vol. 575. Springer-Verlag, New York, 48-58.
14. EMERSON, E. AND HALPERN, J. 1986. Sometimes and not never revisited: On branching versus linear time. J. ACM 33, 1, 151-178.
15. EMERSON, E. AND LEI, C.-L. 1985. Temporal model checking under generalized fairness constraints. In Proceedings of the 18th Hawaii International Conference on System Sciences. Western Periodicals Company, North Hollywood, Calif.
16. EMERSON, E. AND LEI, C.-L. 1986. Efficient model checking in fragments of the propositional μ-calculus. In Proceedings of the 1st Symposium on Logic in Computer Science (Cambridge, Mass.). 267-278.
17. HAFER, T. AND THOMAS, W. 1987. Computation tree logic CTL* and path quantifiers in the monadic theory of the binary tree. In Proceedings of the 14th International Colloquium, on Automata, Languages, and Programming. Lecture Notes in Computer Science, vol. 267. Springer-Verlag, New York, 269-279.
18. HARDIN, R., HAR'EL, Z., AND KURSHAN, R. 1996. COSPAN. In Computer Aided Verification, Proceedings of the 8th International Conference. Lecture Notes in Computer Science, vol. 1102. Springer-Verlag, New York, 423-427.
19. HARDIN, R., KURSHAN, R., SHUKLA, S., AND VARDI, M. 2001. A new heuristic for bad cycle detection using BDDs. Form. Meth. Syst. Des. 18, 131-140.
20. HOLZMANN, G. 1997. The model checker SPIN. IEEE Trans. Softw. Eng. 23, 5 (May), 279-295. (Special issue on Formal Methods in Software Practice.)
21. JANIN, D. AND WALUKIEWICZ, I. 1995. Automata for the modal μ-calculus and related results. In Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science. Lecture Notes in Computer Science. Springer-Verlag, New York, 552-562.
22. JONES, N. 1975. Space-bounded reducibility among combinatorial problems. J. Comput. Syst. Sci. 11, 68-75.
23. KOZEN, D. 1983. Results on the propositional μcalculus. Theoret. Comput. Sci. 27, 333-354.
24. KRISHNAN, S., PURI, A., AND BRAYTON, R. 1994. Deterministic ω-automata vis-a-vis deterministic Büchi automata. In Algorithms and Computations. Lecture Notes in Computer Science, vol. 834. Springer-Verlag, New York, 378-386.
25. KRISHNAN, S., PURI, A., AND BRAYTON, R. 1995a. Structural complexity of ω-automata. In Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science, vol. 900. Springer-Verlag, New York.
26. KRISHNAN, S., PURI, A., BRAYTON, R., AND VARAIYA, P. 1995b. The Rabin index and chain automata, with applications to automata and games. In Computer Aided Verification, Proceedings of the 7th International Conference (Liege). 253-266.
27. KUPFERMAN, O. AND GRUMBERG, O. 1996. Buy one, get one free!!! J. Logic Comput. 6, 4, 523-539.
28. KUPFERMAN, O., SAFRA, S., AND VARDI, M. 1996. Relating word and tree automata. In Proceedings of the 11th IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., 322-333.
29. KUPFERMAN, O. AND VARDI, M. 1998. Relating linear and branching model checking. In Proceedings of the IFIP Working Conference on Programming Concepts and Methods. Chapman & Hall, New York, 304-326.
30. KUPFERMAN, O. AND VARDI, M. 2001. Weak alternating automata are not that weak. ACM Trans. Computat. Logic 2, (July), 408-429.
31. KUPFERMAN, O., VARDI, M., AND WOLPER, P. 2000. An automata-theoretic approach to branching-time model checking. J. ACM 47, 2 (Mar.), 312-360.
32. KURSHAN, R. 1987. Complementing deterministic Büchi automata in polynomial time. J. Comput. Syst. Sci. 35, 59-71.
33. KURSHAN, R. 1994. Computer Aided Verification of Coordinating Processes. Princeton University Press, Princeton, N.J.
34. LANDWEBER, L. 1969. Decision problems for ω-automata. Math. Syst. Theory 3, 376-384.
35. LICHTENSTEIN, O. AND PNUELI, A. 1985. Checking that finite state concurrent programs satisfy their linear specification. In Proceedings of the 12th ACM Symposium on Principles of Programming Languages (New Orleans, La). ACM, New York, 97-107.
36. MAIDL, M. 2000. The common fragment of CTL and LTL. In Proceedings of the 41th Annual Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., 643-652.
37. MCMILLAN, K. 1993. Symbolic Model Checking. Kluwer Academic Publishers.
38. MEYER, A. AND STOCKMEYER, L. 1972. The equivalence problem for regular expressions with squaring requires exponential time. In Proceedings of the 13th IEEE Symposium on Switching and Automata Theory. IEEE Computer Society Press, Los Alamitos, Calif., 125-129.
39. MULLER, D., SAOUDI, A., AND SCHUPP, P. 1986. Alternating automata, the weak monadic theory of the tree and its complexity. In Proceedings of the 13th International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science, vol. 226. Springer-Verlag, New York.
40. MULLER, D. AND SCHUPP, P. 1987. Alternating automata on infinite trees. Theoret. Comput. Sci. 54, 267-276.
41. PNUELI, A. 1981. The temporal semantics of concurrent programs. Theoret. Comput. Sci. 13, 45-60.
42. RABIN, M. 1970. Weakly definable relations and special automata. In Proceedings of the Symposium on Mathematical Logic and Foundations of Set Theory. North Holland, 1-23.
43. RABIN, M. AND SCOTT, D. 1959. Finite automata and their decision problems. IBMJ. Res. Devel. 3, 115-125.
44. SAFRA, S. 1988. On the complexity of ω-automata. In Proceedings of the 29th IEEE Symposium on Foundations of Computer Science (White Plains, N.Y.). IEEE Computer Society Press, Los Alamitos, Calif., 319-327.
45. SAFRA, S. 1989. Complexity of automata on infinite objects. Ph.D. dissertation, Weizmann Institute of Science, Rehovot, Israel.
46. SAFRA, S. 1992. Exponential determinization for ω-automata with strong-fairness acceptance condition. In Proceedings of the 24th ACM Symposium on Theory of Computing (Victoria, B.C., Canada). ACM, New York.
47. SCHNEIDER, K. 1997. CTL and equivalent sublanguages of CTL*. In Proceedings of IFIP Conference on Computer Hardware Description Languages and Applications (Toledo, Ohio). Chapman and Hall, Toledo, 40-59.
48. THOMAS, W. 1990. Automata on infinite objects. Hand. Theoret. Comput. Sci., 165-191.
49. VARDI, M. AND WOLPER, P. 1986. An automata-theoretic approach to automatic program verification. In Proceedings of the 1st Symposium on Logic in Computer Science. Cambridge, 332-344.
50. VARDI, M. AND WOLPER, P. 1994. Reasoning about infinite computations. Inf. Comput. 115, 1 (Nov.), 1-37.
51. + is exponentially more succinct than CTL. In Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science, C. P. Ragan, V. Raman, and R. Ramanujam, Eds. Lecture Notes in Computer Science, vol. 1738. Springer-Verlag, New York, 110-121.
52. WOLPER, P. 1982. Synthesis of communicating processes from temporal logic specifications. Ph.D. dissertation, Stanford University, Stanford, Calif.