Courcelle's theorem-A game-theoretic approach

Discrete Optimization

Volumn 8, Issue 4, 2011, Pages 568-594

  Kneis, Joachim ^a   Langer, Alexander ^a   Rossmanith, Peter ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Model checking; Monadic Second Order logic; Parameterized algorithms; Treewidth

Indexed keywords

AUTOMATA-THEORETIC APPROACH; BOUNDED TREEWIDTH; DIRECT APPROACH; LINEAR TIME; MONADIC SECOND-ORDER LOGIC; PARAMETERIZED ALGORITHMS; POWER SET; TREE AUTOMATA; TREE DECOMPOSITION; TREE-WIDTH;

GAME THEORY; MODEL CHECKING; PLANT EXTRACTS; PROBLEM SOLVING;

AUTOMATA THEORY;

EID: 80054707104     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2011.06.001     Document Type: Article

References (52)

1. B. Courcelle The monadic second order theory of graphs I: recognisable sets of finite graphs Inform. Comput. 85 1990 12 75 (Pubitemid 20680563)
2. M. Frick, and M. Grohe The complexity of first-order and monadic second-order logic revisited Ann. Pure Appl. Logic 130 13 2004 3 31 (Pubitemid 40393343)
3. S. Arnborg, J. Lagergren, and D. Seese Easy problems for tree-decomposable graphs J. Algorithms 12 2 1991 308 340
4. B. Courcelle, and M. Mosbah Monadic second-order evaluations on tree-decomposable graphs Theoret. Comput. Sci. 109 12 1993 49 82 (Pubitemid 23639489)
5. B. Courcelle Graph rewriting: an algebraic and logic approach Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics (B) 1990 Elsevier 193 242
6. R.G. Downey, and M.R. Fellows Parameterized Complexity 1999 Springer-Verlag
7. J. Flum, M. Frick, and M. Grohe Query evaluation via tree-decompositions J. ACM 49 6 2002 716 752
8. J. Flum, and M. Grohe Parameterized Complexity Theory 2006 Springer-Verlag
9. M. Weyer, Modifizierte parametrische Komplexittstheorie, Ph.D. Thesis, Universitt Freiburg, 2008.
10. B. Courcelle, J. Engelfriet, Graph Structure and Monadic Second-Order Logic, A Language Theoretic Approach, Cambridge University Press, 2011 (submitted for publication).
11. S. Feferman, and R. Vaught The first order properties of algebraic systems Fund. Math. 47 1959 57 103
12. Y. Gurevich Modest theory of short chains. I J. Symbolic Logic 44 4 1979 481 490
13. M. Frick, Easy instances for model checking, Ph.D. Thesis, Universitt Freiburg, 2001.
14. J.A. Makowsky Algorithmic uses of the FefermanVaught theorem Ann. Pure Appl. Logic 126 13 2004 159 213
15. M. Grohe Logic, graphs, and algorithms J. Flum, E. Grdel, T. Wilke, Logic and Automata: History and Perspectives 2007 Amsterdam University Press Amsterdam 357 422
16. N. Klarlund, A. Møller, MONA version 1.4 user manual, BRICS, Dept. of Comp. Sc., University of Aarhus, Available from: http://www.brics.dk/mona/ (January 2001).
17. N. Klarlund, A. Møller, and M.I. Schwartzbach MONA implementation secrets Proc. of CIAA00 2001 Springer-Verlag 182 194 (Pubitemid 33329027)
18. D. Soguet, Génération automatique d'algorithmes linéaires, Doctoral Dissertation, University Paris-Sud, 2008.
19. B. Courcelle, J.A. Makowsky, and U. Rotics Linear time solvable optimization problems on graphs of bounded clique width Theory Comput. Syst. 33 2000 125 150
20. B. Courcelle Graph structure and monadic second-order logic: language theoretical aspects Proceedings of the 35th International Colloquium on Automata, Languages, and Programming ICALP Lecture Notes in Computer Science vol. 5125 2008 Springer 1 13
21. G. Gottlob, R. Pichler, and F. Wei Abduction with bounded treewidth: from theoretical tractability to practically efficient computation Proc. of 23rd AAAI 2008 AAAI Press 1541 1546
22. G. Gottlob, R. Pichler, and F. Wei Monadic datalog over finite structures of bounded treewidth ACM Trans. Comput. Log. 12 1 2010 3:1 3:48
23. B. Courcelle, I.A. Durand, Verifying monadic second-order graph properties with tree automata, in: C. Rhodes (Ed.), 3rd European Lisp Symposium, Informal Proceedings, 2010, pp. 721.
24. B. Courcelle, I.A. Durand, Tractable constructions of finite automata from monadic second-order formulas, presented at Logical Approaches to Barriers in Computing and Complexity, Greifswald, Germany, 2010.
25. B. Courcelle Special tree-width and the verification of monadic second-order graph properties Proceedings of the 30th Conference on Foundations of Software Technology and Theoretical Computer Science FSTTCS Leibniz International Proceedings in Informatics, LIPIcs vol. 8 2010 Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl Germany 13 29
26. J. Hintikka Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic 1973 Clarendon Press
27. E. Grdel Finite model theory and descriptive complexity Finite Model Theory and its Applications 2007 Springer 125 230
28. E. Grdel Back and forth between logics and games K.R. Apt, E. Grdel, Lectures in Game Theory for Computer Scientists 2011 Cambridge University Press 99 145
29. K.A. Abrahamson, and M.R. Fellows Finite automata, bounded treewidth, and well-quasiordering Graph Structure Theory Contemporary Mathematics vol. 147 1993 American Mathematical Society 539 564
30. J.W. Thatcher, and J.B. Wright Generalized finite automata theory with an application to a decision problem of second-order logic Math. Syst. Theory 2 1 1968 57 81
31. J. Doner Tree acceptors and some of their applications J. Comput. System Sci. 4 1970 406 451
32. T. Ganzow, and. Kaiser New algorithm for weak monadic second-order logic on inductive structures Proceedings of the 24th International Workshop on Computer Science Logic CSL Lecture Notes in Computer Science vol. 6247 2010 Springer 366 380
33. P.B. Miltersen, J. Radhakrishnan, and I. Wegener On converting CNF to DNF Theoret. Comput. Sci. 347 12 2005 325 335 (Pubitemid 41650223)
34. B. Courcelle, On the model-checking of monadic second-order formulas with edge set quantifications, Discrete Appl. Math. (in press).
35. K.L. McMillan A technique of state space search based on unfolding Form. Methods Syst. Des. 6 1995 45 65
36. H.-D. Ebbinghaus, and J. Flum Finite Model Theory 1999 Springer
37. R. Ganian, and P. Hlinn On parse trees and MyhillNerode-type tools for handling graphs of bounded rank-width Discrete Appl. Math. 158 7 2010 851 867
38. N. Robertson, and P.D. Seymour Graph minors. II. Algorithmic aspects of tree-width J. Algorithms 7 1986 309 322
39. R. Diestel Graph Theory 4th ed. 2010 Springer-Verlag Heidelberg
40. S. Arnborg, D.G. Corneil, and A. Proskurowski Complexity of finding embeddings in a k-tree SIAM J. Algebr. Discrete Methods 8 1987 277 284
41. H.L. Bodlaender A linear time algorithm for finding tree-decompositions of small treewidth SIAM J. Comput. 25 1996 1305 1317 (Pubitemid 126584672)
42. H. Bodlaender, and A.M.C.A. Koster Treewidth computations I. Upper bounds Inform. Comput. 208 3 2010 259 275
43. H.L. Bodlaender, and A.M.C.A. Koster Treewidth computations II. Lower bounds Inform. Comput. 209 7 2011 1103 1119
44. H.L. Bodlaender A tourist guide through treewidth Acta Cybernet. 11 1993 1 21
45. H.L. Bodlaender A partial k-arboretum of graphs with bounded treewidth Theoret. Comput. Sci. 209 1998 1 45 (Pubitemid 128450429)
46. A. Tarski The semantic conception of truth Philos. Phenomenolog. Res. 4 1944 13 47
47. C. Baier, and J.-P. Katoen Principles of Model Checking Representation and Mind Series 2008 The MIT Press
48. J.A. Telle, and A. Proskurowski Algorithms for vertex partitioning problems on partial k-trees SIAM J. Discrete Math. 10 4 1997 529 550 (Pubitemid 127642991)
49. J.M.M. van Rooij, H.L. Bodlaender, and P. Rossmanith Dynamic programming on tree decompositions using generalised fast subset convolution ESA Lecture Notes in Computer Science vol. 5757 2009 Springer 566 577
50. D. Lokshtanov, D. Marx, S. Saurabh, Known algorithms on graphs on bounded treewidth are probably optimal, in: Proceedings of the 22th ACM-SIAM Symposium on Discrete Algorithms, SODA, 2011, pp. 777789.
51. J. Alber, and R. Niedermeier Improved tree decomposition based algorithms for domination-like problems Proceedings of the 5th Symposium on Latin American Theoretical Informatics LATIN Lecture Notes in Computer Science vol. 2286 2002 Springer Cancun, Mexico 613 627
52. H.L. Bodlaender Necessary edges in k-chordalisations of graphs J. Comb. Optim. 7 3 2003 283 290