The monadic quantifier alternation hierarchy over grids and pictures

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

Volumn 1414, Issue , 1998, Pages 441-460

  Schweikardt, Nicole ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FORMAL LOGIC; GAME THEORY; RECONFIGURABLE HARDWARE;

EXPRESSIVE POWER; MONADIC QUANTIFIER; MONADIC SECOND-ORDER LOGIC; QUANTIFIER-ALTERNATION HIERARCHY; SECOND ORDERS; TWO-DIMENSIONAL GRIDS;

COMPUTER CIRCUITS;

EID: 0000416481     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/BFb0028030     Document Type: Conference Paper

References (20)

1. M. Ajtai, R. Fagin, L. Stockmeyer. The Closure of Monadic NP. IBM Research Report RJ 10092, November 1997.
2. J. R. Biichi. Weak second-order arithmetic and finite automata. Z. Math. Logik Grundl. Math. 6 (1960), 66-92.
3. J. Doner. Tree acceptors and some of their applications. J. Comput. System Sci. 4 (1970), 405-451.
4. H. Ebbinghaus, J. Flum. Finite Model Theory. Springer-Verlag, New York, 1995.
5. A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fund. Math. 49 (1961), 129-141.
6. C. Elgot. Decision problems of finite automata design and related arithmetics. Trans. Amer. Math. Soc., page 21, 1961.
7. R. Fagin. Generalized first-order spectra and polynomial-time recognizable sets. Complexity of Computation (R.M. Karp, Ed.), SIAM-AMS Proceedings 7 (1974), 43-73.
8. R. Fagin. Monadic generalized spectra. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 21 (1975), 89-96.
9. R. Fagin. Problem proposed in Oberwolfach Meeting 1994; published in: Collection of open problems in finite model theory, see http://speedy.informatik.rwth-aachen.de/WWW/FMT.html
10. R. Frai'sse. Sur quelques classification des systemes de relations (english summary). Universite d’Alger, Publications Scientifiques, Serie A, 1, 35182, 1954.
11. R. Fagin, L. Stockmeyer, M. Vardi. On monadic NP vs. monadic co-NP. Information and Computation 120 (1995), 78-92.
12. D. Giammarresi, A. Restivo, S. Seibert, W. Thomas. Monadic second-order logic and recognizability by tiling systems. Information and Computation 125 (1996), 32-45.
13. J. Makowsky, Y. Pnueli. Arity vs Alternation in Second Order Logic. Logical Foundations of Computer Science. Lecture Notes in Computer Science, Vol. 813, pages 240-252, Springer-Verlag, 1994.
14. O. Matz and W. Thomas. The monadic quantifier alternation hierarchy over graphs is infinite. Proceedings of the 12th IEEE Symposium on Logic in Computer Science (1997), to appear.
15. M. Otto. Note on the number of monadic quantifiers in monadic S. Information Processing Letters 53 (1995), 337-339.
16. N. Schweikardt. The Monadic Second-Order Quantifier Alternation Hierarchy over Grids and Pictures. Diploma thesis, Johannes Gutenberg-Universitat Mainz, 1997.
17. T. Schwentick. On winning Ehrenfeucht games and monadic NP. Annals of Pure and Applied Logic 79 (1996), 61-92.
18. L. Stockmeyer. The Polynomial Time Hierarchy. Theoretical Computer Science 3 (1977), 1-22.
19. W. Thomas. Classifying regular events in symbolic logic. Journal of Computer and System Sciences 25 (1982), 360-376.
20. J. W. Thatcher, J. B. Wright. Generalized finite automata with an application to a decision problem of second order logic. Math. Syst. Theory 2 (1968), 57-82.