Describing parameterized complexity classes

Information and Computation

Volumn 187, Issue 2, 2003, Pages 291-319

  Flum, Jörg ^a   Grohe, Martin ^b  

^a UNIVERSITY OF FREIBURG   (Germany)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; DATABASE SYSTEMS; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING;

FIXED-PARAMETER TRACTABILITY; PARAMETERIZED INTRACTABILITY;

COMPUTATIONAL COMPLEXITY;

EID: 0348226423     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0890-5401(03)00161-5     Document Type: Article

References (28)

1. K.A. Abrahamson, R.G. Downey, M.R. Fellows, Fixed-parameter tractability and completeness IV: on completeness for W[P] and PSPACE analogs, Ann. Pure Appl. Logic 73 (1995) 235-276.
2. M. Alekhnovich, A. Razborov, Resolution is not automatizable unless W[P] is tractable, in: Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, 2001, pp. 210-219.
3. H.L. Bodlaender, R. G. Downey, M.R. Fellows, M.T. Hallett, H.T. Wareham, Parameterized complexity analysis in computational biology, Comput. Appl. Biosci. 11 (1995) 49-57.
4. J.R. Büchi, Weak second-order arithmetic and finite automata, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 6 (1960) 66-92.
5. L. Cai, J. Chen, R. G. Downey, M.R. Fellows, Advice classes of parameterized tractability, Ann. Pure Appl. Logic 84 (1997) 119-138.
6. Y. Chen, J. Flum, Machine characterizations of the classes of the W-hierarchy, in: Proceedings of the 17th International Workshop on Computer Science Logic, Lecture Notes in Computer Science, Springer-Verlag, 2003, to appear.
7. Y. Chen, J. Flum, M. Grohe, Bounded nondeterminism and alternation in parameterized complexity theory, in: Proceedings of the 18th IEEE Conference on Computational Complexity, pp. 13-29, 2003.
8. R.G. Downey, M.R. Fellows, Fixed-parameter tractability and completeness I: basic results, SIAM J. Comput. 24 (1995) 873-921.
9. R.G. Downey, M.R. Fellows, Parameterized Complexity, Springer, Berlin, 1999.
10. R.G. Downey, M.R. Fellows, K. Regan, Descriptive complexity and the W-hierarchy, in: P. Beame, S. Buss (Eds.), Proof Complexity and Feasible Arithmetic, AMS-DIMACS Volume Series, vol. 39, AMS, Providence, RI, 1998, pp. 119-134.
11. R.G. Downey, M.R. Fellows, K. Taylor, The parameterized complexity of relational database queries and an improved characterization of W[1], In: D.S. Bridges, C. Calude, P. Gibbons, S. Reeves, I.H. Witten (Eds.), Combinatorics, Complexity, and Logic - Proceedings of DMTCS '96, Springer, Berlin, 1996, pp. 194-213.
12. H.-D. Ebbinghaus, J. Flum, Finite Model Theory, second ed., Springer, Berlin, 1999.
13. H.-D. Ebbinghaus, J. Flum, W. Thomas, Mathematical Logic, second ed., Springer, Berlin, 1994.
14. R. Fagin, Generalized first-order spectra and polynomial-time recognizable sets, In: R.M. Karp (Ed.), Complexity of Computation, SIAM-AMS Proceedings, vol. 7, 1974, pp. 43-73.
15. J. Flum, M. Grohe, Fixed-parameter tractability, definability, and model checking, SIAM J. Comput. 31 (1) (2001) 113-145.
16. H. Gaifman, On local and non-local properties, in: J. Stern (Ed.), Proceedings of the Herbrand Symposium, Logic Colloquium '81, North Holland, 1982, pp. 105-135.
17. G. Gottlob, N. Leone, M. Sideri, Fixed-parameter complexity in AI and nonmonotonic reasoning, in: M. Gelfond, N. Leone, G. Pfeifer (Eds.), Logic Programming and Nonmonotonic Reasoning, 5th International Conference, LPNMR'99, Lecture Notes in Computer Science, vol. 1730, Springer, Berlin, 1999, pp. 1-18.
18. M. Grohe, Generalized model-checking problems for first-order logic, in: H. Reichel, A. Ferreira (Eds.), Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Computer Science, vol. 2010, Springer, Berlin, 2001, pp. 12-26.
19. M. Grohe, The parameterized complexity of database queries, in: Proceedings of the 20th ACM Symposium on Principles of Database Systems, 2001, pp. 82-92.
20. M. Grohe, T. Schwentick, L. Segoufin, When is the evaluation of conjunctive queries tractable, in: Proceedings of the 33rd ACM Symposium on Theory of Computing, 2001, pp. 657-666.
21. N. Immerman, Relational queries computable in polynomial time, Inform. Control 68 (1986) 86-104.
22. N. Immerman, Languages that capture complexity classes, SIAM J. Comput. 16 (1987) 760-778.
23. N. Immerman, Descriptive Complexity, Springer, Berlin, 1999.
24. C.H. Papadimitriou, M. Yannakakis, On the complexity of database queries, in: Proceedings of the 17th ACM Symposium on Principles of Database Systems, 1997, pp. 12-19.
25. C.H. Papadimitriou, Computational Complexity, Addison-Wesley, 1994.
26. U. Stege, Resolving conflicts in problems from computational biology. PhD thesis, ETH Zuerich, 2000. PhD thesis No.13364.
27. L.J. Stockmeyer, The complexity of decision problems in automata theory. PhD thesis, Department of Electrical Engineering, MTT, 1974.
28. M.Y. Vardi, The complexity of relational query languages, in: Proceedings of the 14th ACM Symposium on Theory of Computing, 1982, pp. 137-146.