Descriptive complexity, lower bounds and linear time

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

Volumn 1584, Issue , 1999, Pages 9-28

  Schwentick, Thomas ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER CIRCUITS;

DESCRIPTIVE COMPLEXITY; EXISTENTIAL SECOND-ORDER LOGIC; EXPRESSIBILITY; LINEAR TIME; LINEAR TIME COMPLEXITY; LOGICAL CHARACTERIZATION; LOWER BOUNDS; PAPER SURVEYS;

TEMPORAL LOGIC;

EID: 0038337278     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/10703163_2     Document Type: Conference Paper

References (53)

1. 1 formulae on finite structures. Ann. of Pure and Applied Logic, 24:1-48, 1983. 24
2. M. Ajtai and R. Fagin. Reachability is harder for directed than for undirected finite graphs. Journal of Symbolic Logic, 55(1):113-150, 1990. 14, 23
3. M. Ajtai, R. Fagin, and L. Stockmeyer. The closure of monadic NP. IBM Research Report RJ 10092, 1997. 24
4. Sanjeev Arora and Ronald Fagin. On winning strategies in Ehrenfeucht-Fraïsse games. Theoretical Computer Science, 174(1-2):97-121, 1997. 24
5. Theodore Baker, John Gill, and Robert Solovay. Relativizations of the P =? NP question. SIAM Journal on Computing, 4(4):431-442, December 1975. 9
6. Ronald V. Book and Sheila A. Greibach. Quasi-realtime languages. Mathematical System Theory, 4(2):97-111, 1970. 20
7. R. Buchi. Weak second-order arithmetic and finite automata. Z. Math. Logik Grundlagen Math., 6:66-92, 1960. 22
8. Stephen A. Cook. A hierarchy for nondeterministic time complexity. Journal of Computer and System Sciences, 7(4):343-353, August 1973. 9
9. S. Cosmadakis. Logical reducibility and monadic NP. In Proc. 34th, IEEE Symp. on Foundations of Computer Science, pages 52-61, 1993. 23
10. M. de Rougemont. Second-order and inductive definability on finite structures. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, 33:47-63, 1987. 22
11. Arnaud Durand, Ron Fagin, and Bernd Loescher. Spectra with only unary function symbols. In 11th Annual Conference of the EACSL, CSL '97, pages 189-202, 1997. 24
12. Arnaud Durand, Clemens Lautemann, and Thomas Schwentick. Subclasses of binary NP. Journal of Logic and Computation, 8(2):189-207, April 1998. 24
13. Arnaud Durand and Solomampionona Ranaivoson. First-order spectra with one binary predicate. Theoretical Computer Science, 160(1-2):305-320, 10 June 1996. 19
14. H.-D. Ebbinghaus and J. Flum. Finite Model Theory. Springer-Verlag, 1995. 10, 14
15. A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fund. Math., 49:129-141, 1961. 13
16. Thomas Eiter, Georg Gottlob, and Yuri Gurevich. Existential second-order logic over strings. LICS '98, 1998. 21
17. R. Fagin. Generalized first-order spectra and polynomial-time recognizable sets. In R. M. Karp, editor, Complexity of Computation, SIAM-AMS Proceedings, Vol. 7, pages 43-73, 1974. 10
18. R. Fagin. Monadic generalized spectra. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, 21:89-96, 1975. 10, 14
19. R. Fagin. Easier ways to win logical games. In Proceedings of the DIMACS Workshop on Finite Models and Descriptive Complexity. American Mathematical Society, 1997. 24
20. R. Fagin, L. Stockmeyer, and M. Vardi. On monadic NP vs. monadic co-NP. Information and Computation, 120:78-92, 1995. Preliminary version appeared in 1993 IEEE Conference on Structure in Complexity Theory, pp. 19-30. 15, 15, 22, 24
21. R. Fraïsse. Sur quelques classifications des systemes de relations. Publ. Sci. Univ. Alger. Sér. A, 1:35-182, 1954. 13
22. E. Grädel. On the notion of linear time computability. Int. J. Found. Comput. Sci., 1:295-307, 1990. 16
23. E. Grandjean. A natural NP-complete problem with a nontrivial lower bound. SIAM Journal of Computing, 17:786-809, 1988. 19
24. E. Grandjean. Invariance properties of RAMs and linear time. Computational Complexity, 4:62-106, 1994. 16
25. E. Grandjean. Linear time algorithms and NP-complete problems. SIAM Journal of Computing, 23:573-597, 1994. 16, 19, 19, 21
26. E. Grandjean. Sorting, linear time and the satisfiability problem. Annals of Mathematics and Artificial Intelligence, 16:183-236, 1996. 16, 17
27. E. Grandjean and F. Olive. Monadic logical definability of NP-complete problems. In Proc. 1994 of the Annual Conference of the EACSL, pages 190-204, 1994. Extended version submitted. 18, 19, 22, 23
28. Etienne Grandjean and Thomas Schwentick. Machine-independent characterizations and complete problems for deterministic linear time. In preparation, 1998. 19
29. Y. Gurevich and S. Shelah. Nearly linear time. In A. Meyer and M. Taitslin, editors, Logic at Botik '89, Lecture Notes in Computer Science 363, pages 108-118. Springer Verlag, 1989. 16
30. J. Hartmanis and R. E. Stearns. On the computational complexity of algorithms. Transactions of the AMS, 117:285-306, 1965. 9
31. John Hopcroft, Wolfgang Paul, and Leslie Valiant. On time versus space. Journal of the ACM, 24(2):332-337, April 1977. 9
32. Neil Immerman. Descriptive Complexity. Graduate Texts in Computer Science. Springer-verlag, New York, 1998. 10
33. M. Kreidler and D. Seese. Monadic NP and built-in trees. In Proceedings CSL 96, volume 1258 of LNCS, pages 260-274. Springer-Verlag, 1997. 22, 22
34. Martin Kreidler and Detlef Seese. Monadic NP and graph minors. CSL '98, 1998. 22, 22
35. Clemens Lautemann, Nicole Schweikardt, and Thomas Schwentick. A logical characterization of nondeterministic linear time on Turing machines. to be presented at STACS 99, 1998. 20, 20
36. J. F. Lynch. Complexity classes and theories of finite models. Mathematical System Theory, 15:127-144, 1982. 19
37. J. F. Lynch. On sets of relations definable by addition. Journal of Symbolic Logic, 47:659-668, 1982. 24
38. J. F. Lynch. The quantifier structure of sentences that characterize nondetermin- istic time complexity. Computational Complexity, 2:40-66, 1992. 19
39. Wolfgang Maass, Georg Schnitger, Endre Szemeredi, and Gyorgy Turán. Two tapes versus one for off-line turing machines. Computational Complexity, 3(4):392-401, 1993. 21
40. F. Olive. A conjunctive logical characterization of nondeterministic linear time. In 11th Annual Conference of the EACSL, CSL '97, pages 360-372, 1997. 19
41. Wolfgang J. Paul, Nicholas Pippenger, Endre Szemeredi, and William T. Trotter. On determinism versus non-determinism and related problems (preliminary version). In 24th Annual Symposium on Foundations of Computer Science, pages 429-438, Tucson, Arizona, 7-9 November 1983. IEEE. 9, 19
42. K. Regan. Machine models and linear time complexity. SIGACT News, 24:4, Fall 1993. 16
43. Matthias Ruhl. Counting and addition cannot express deterministic transitive closure. 1998. 24
44. C. P. Schnorr. Satisfiability is quasilinear complete in NQL. Journal of the ACM, 25:136-145, 1978. 16
45. T. Schwentick. Graph connectivity and monadic NP. In Proc. 35th IEEE Symp. on Foundations of Computer Science, pages 614-622, 1994. 22, 24
46. T. Schwentick. On winning Ehrenfeucht games and monadic NP. Doktorarbeit, Universität Mainz, 1994. 23
47. T. Schwentick. Graph connectivity, monadic NP and built-in relations of moderate degree. In Proc. 22nd International Colloq. on Automata, Languages, and Programming, pages 405-416, 1995. 22
48. T. Schwentick. On winning Ehrenfeucht games and monadic NP. Annals of Pure and Applied Logic, 79:61-92, 1996. 15
49. T. Schwentick. Algebraic and logical characterizations of deterministic linear time classes. In Proc. 14th Symposium on Theoretical Aspects of Computer Science STACS 97, pages 463-474, 1997. 19
50. T. Schwentick. Padding and the expressive power of existential second-order logics. In 11th Annual Conference of the EACSL, CSL '97, pages 461-477, 1997. 23
51. T. Schwentick and K. Barthelmann. Local normal forms for first-order logic with applications to games and automata. In Proc. 15th Symposium on Theoretical Aspects of Computer Science STACS 98, pages 444-454, 1998. 24
52. J. I. Seiferas, M. J. Fischer, and A. R. Meyer. Refinements of the nondeterministic time and space hierarchies. In 14th Annual Symposium on Switching and Automata Theory, pages 130-137, The University of Iowa, 15-17 October 1973. IEEE. 9
53. R. E. Stearns, J. Hartmanis, and P. M. Lewis II. Hierarchies of memory limited computations. In Proceedings of the Sixth Annual Symposium on Switching Circuit Theory and Logical Design, pages 179-190. IEEE, 1965. 9