Monadic NP and built-in trees

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1258, Issue , 1997, Pages 260-274

  Kreidler, Martin ^a   Seese, Detlef ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Descriptive complexity theory; Ehrenfeucht Fra ss games; Finite model theory; Monadic second order logic

Indexed keywords

FORMAL LOGIC; RECONFIGURABLE HARDWARE;

ARBITRARY DEGREE; DESCRIPTIVE COMPLEXITY THEORY; FINITE MODEL THEORY; GRAPH CONNECTIVITY; MONADIC SECOND-ORDER LOGIC; WINNING STRATEGY;

COMPUTER CIRCUITS;

EID: 84957020957     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-63172-0_44     Document Type: Conference Paper

References (30)

1. M. Ajtai: Σ11-formulae on finite structures, Annals of Pure and Applied Logic, vol. 24, 1983, pp. 1-48.
2. M. Ajtai and R. Fagin: Reachability is harder for directed than for undirected finite graphs, Journal of Symbolic Logic, 55 (1), 1990, pp. 113-150.
3. E. Börger: Berechenbarkeit, Komplexität, Logik, Vieweg 1992.
4. R. Boppana and M. Sipser: The Complexity of Finite Functions. In Handbook of Theoretical Computer Science vol. A (ed. J. van Leeuwen), Elsevier Science Publishers, pp. 757-804, 1990.
5. S. Arora and R. Fagin: On winning strategies in Ehrenfeucht-Fraisse Games. Preprint, 1995.
6. B. Courcelle: Recognizability and second-order definability for sets of finite graphs, Information and Comput. 85, 1990, pp. 12-75.
7. A. Durand, C. Lautemann and T. Schwentick: Fragments of Binary NP, In Proc. IEEE Structures in Complexity Theory, 1995, also presented at CSL’95.
8. H.-D. Ebbinghaus, J. Flum: Finite Model Theory, Springer-Verlag, New York, 1995.
9. H.-D. Ebbinghaus, J. Flum and W. Thomas: Mathematical Logic, Second Edition, Springer-Verlag, New York, 1993.
10. A. Ehrenfeucht: An application of games to the completeness problem for formalized theories, Fund. Math., 49, 1961, pp. 129-141.
11. R. Fagin: Generalized First-Order spectra and polynomial-time recognizable sets, In Complexity of Computation, (ed. R. Karp) SIAM-AMS Proc. 7, 1974, pp. 27-41.
12. R. Fagin: Monadic generalized spectra, in Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 21, 1975, pp. 89-96.
13. R. Fagin: Comparing the Power of Monadic NP Games, in Proc. LCC’94, LNCS 960, Springer-Verlag, 1995 pp. 414-425.
14. R. Fraïssé: Sur quelques classifications des systèmes de relations, Publ. Sci. Univ. Alger. Sr. A, 1, 1954, pp. 35-182.
15. R. Fagin, L. Stockmeyer and M. Vardi: On Monadic NP vs. Monadic co-NP, In Information and Computation, 120, 1995, pp. 18-92.
16. H. Gaifman: On local and nonlocal properties, In J. Stern, editor, Logic Collo-quium’81, North-Holland, 1982, pp. 105-135.
17. Y. Gurevich: Logic and the challenge of computer science, Univ. Michigan Tech. Report CRL-TR-10-85, Sept. 1985.
18. W. Hanf: Model-theoretic methods in the study of elementary logic, In J. Addison, L. Henkin and A. Tarski, editors, The Theory of Models, North Holland, 1965, pp. 132-145.
19. N. Immerman: Languages that capture complexity classes, SIAM J. of Computing, Vol. 16, No. 4, August 1987, pp. 760-778.
20. N. Immerman: Descriptive and computational complexity, Computational Complexity Theory, Proc. Symp. Applied Math. Vol. 38 (J. Hartmanis, ed.), 1989, pp. 75-91.
21. C. Lautemann: Logical Definability of NP-Optimisation Problems with Monadic Auxiliary Predicates, in Proc. CSL’92, San Miniato, Italy, LNCS 702, pp. 327-339, Springer-Verlag, 1993.
22. K. Mehlhorn: Graph Algorithms and NP-Completeness, Springer-Verlag, Berlin, 1984.
23. C. H. Papadimitriou: Computational Complexity, Addison-Wesley Publishing Company, Reading, Massachusetts, 1994.
24. R. Reischuk: Einführung in die Komplexitatstheorie, B.G. Teubner Stuttgart, 1990.
25. M. de Rougemont: Second-order and inductive definability on finite structures, Zeitschrift f. math. Logik und Grundlagen d. Math., Bd. 33, 1987, pp. 47-63.
26. T. Schwentick: On Bijections vs. Unary Functions, In Proc. STACS’96, LNCS 1046, Springer-Verlag, 1996.
27. T. Schwentick: On Winning Ehrenfeucht Games and Monadic NP, Annals of Pur and Applied Logic vol. 79, pp. 61-92, 1996.
28. D. Seese: Linear time computable problems and first-order descriptions, in Math. Struct, in Comp. Sc. vol. 6, pp. 1-22, 1996 (to appear).
29. S. Shelah: The Monadic Theory of Order, Annals of Mathematics, vol. 102, pp. 379-419, 1975.
30. J. Spencer: Threshold spectra via the Ehrenfeucht game, Disc. Appl. Math. 30, pp. 235-252, 1991.