Automata and fixed point logic: A coalgebraic perspective

Information and Computation

Volumn 204, Issue 4, 2006, Pages 637-678

  Venema, Yde ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Automata; Bisimulation; Coalgebra; Fixed point operators; Game semantics; Modal logic; Parity games

Indexed keywords

AUTOMATA THEORY; SEMANTICS;

AUTOMATA; BISIMULATIONS; COALGEBRAS; FIXED POINT OPERATOR; GAME SEMANTICS; MODAL LOGIC; PARITY GAMES;

COMPUTER CIRCUITS;

EID: 84855206619     PISSN: 08905401     EISSN: 10902651     Source Type: Journal    
DOI: 10.1016/j.ic.2005.06.003     Document Type: Review

References (29)

1. S. Abramsky. A Cook's Tour of the Finitary Non-Well-Founded Sets. Invited Lecture at BCTCS 1988.
2. J. Adámek, V. Trnková, Automata and Algebras in Categories, Kluwer Academic Publishers, Dordrecht, 1990.
3. A. Baltag, A logic for coalgebraic simulation, in: H. Reichel (Ed.), Coalgebraic Methods in Computer Science (CMCS'00), 2000, pp. 41-60.
4. J. Barwise, L. Moss, in: Vicious Circles, CSLI Lecture Notes, vol. 60, CSLI Publications, 1996.
5. A. Carboni, G. Kelly, R. Wood, A 2-categorical approach to change of base and geometric morphisms I, Technical Report 90-1, Department of Pure Mathematics, University of Sydney, 1990.
6. E. Clarke, O. Grumberg, D. Peled, (Eds.), Model Checking, The MIT Press, Cambridge, USA, 2000.
7. E. Graedel, W. Thomas, T. Wilke (Eds.), in: Automata, Logic, and Infinite Games, Lecture Notes in Computer Series, vol. 2500, Springer, Berlin, 2002.
8. E. Emerson, C. Jutla, Tree automata, mu-calculus and determinacy, in: Proceedings of the 32nd IEEE Symposium on Foundations of Computer Science (FoCS'91), IEEE Computer Society Press, 1991, pp. 368-377.
9. B. Jacobs, Exercises in coalgebraic specification, in: R. Backhouse, R. Crole, J. Gibbons (Eds.), Algebraic and Coalgebraic Methods in the Mathematics of Program Construction, Springer, Berlin, 2002, pp. 237-280.
10. B. Jacobs, Many-sorted coalgebraic modal logic: a model-theoretic study, Theoretical Informatics and Applications 35(1) (2001) 31-59. (Pubitemid 32657786)
11. B. Jacobs, The temporal logic of coalgebras via Galois algebras, Mathematical Structure in Computer Science 12(2002) 875-903. (Pubitemid 36047810)
12. D. Janin, I. Walukiewicz, Automata for the modal μ-calculus and related results, in: Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science (MFCS'95), Springer, Berlin, 1995, pp. 552-562.
13. D. Janin, I. Walukiewicz, On the expressive completeness of the propositional mu-calculus with respect to monadic second order logic, in: CONCUR'96: Concurrency Theory, 7th International Conference, Springer, Berlin, 1996, pp. 263-277. (Pubitemid 126117767)
14. C. Kupke, Y. Venema, Closure properties of coalgebra automata, in: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science (LICS 2005), 2005, pp. 199-208. (Pubitemid 41462567)
15. A. Kurz, A co-variety-theorem for modal logic, in: M. Zakharyaschev, K. Segerberg, M. de Rijke, H. Wansing (Eds.), Advances in Modal Logic 2, Center for the Study of Language and Information, Stanford University, 2001.
16. D. Martin, Borel determinacy, Annals of Mathematics 102(1975) 363-371.
17. L. Moss, Coalgebraic logic, Annals of Pure and Applied Logic 96(1999) 277-317
18. (Erratum published APAL 99:241-259, 1999.
19. A. Mostowski, Games with Forbidden Positions, Technical Report 78, Instytut Matematyki, Uniwersytet Gdański, Poland, 1991.
20. D. Muller, P. Schupp, Simulating alternating tree automata by nondeterministic ones: new results and new proofs of the theorems of Rabin, McNaughton and Safra, Theoretical Computer Science 141(1995) 69-107.
21. D. Niwiński, Fixed point characterization of infinite behavior of finite-state systems, Theoretical Computer Science 189(1997) 1-69. (Pubitemid 127451557)
22. D. Pattinson, Semantical principles in the modal logic of coalgebras, in: H. Reichel, A. Ferreira (Eds.), Proceedings of the 18th International Symposium on Theoretical Aspects of Computer Science (STACS 2001), Springer, Berlin, 2001.
23. M. Rabin, Decidability of second-order theories and automata on infinite trees, Transactions of the American Mathematical Society 141(1969) 1-35.
24. M. Rößiger, Coalgebras and modal logic, in: H. Reichel (Ed.), Coalgebraic Methods in Computer Science (CMCS'00), 2000, pp. 299-320.
25. J. Rutten, Automata and coinduction (an exercise in coalgebra), in: D. Sangiorigi, R. de Simone (Eds.), Proceedings of the 9th International Conference on Concurrency Theory (CONCUR'98), Springer, Berlin, 1998, pp. 194-218. (Pubitemid 128125357)
26. J. Rutten, Behavioural differential equations: a coinductive calculus of streams, automata, and power series, Theoretical Computer Science 308(2003) 1-53.
27. J. Rutten, Relators and metric bisimulations, in:B. Jacobs, L. Moss, H. Reichel, J. Rutten (Eds.), Coalgebraic Methods in Computer Science (CMCS'98), 1998, pp. 257-263.
28. V. Trnková, Relational automata in a category and theory of languages, in: M. Karpinski (Ed.), Fundamentals of Computation Theory: Proceedings of the 1977 International FCT-conference, Springer, Berlin, 1977, pp. 340-355.
29. Y. Venema, Automata and fixed point logics for coalgebras, Electronic Notes in Theoretical Computer Science 106(2004) 355-375. (Pubitemid 40536134)