Finite automata, digraph connectivity, and regular expression size: (Extended abstract)

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

Volumn 5126 LNCS, Issue PART 2, 2008, Pages 39-50

  Gruber, Hermann ^a   Holzer, Markus ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; BASIC (PROGRAMMING LANGUAGE); CHLORINE COMPOUNDS; CONTROL THEORY; GRAPH THEORY; LINGUISTICS; QUERY LANGUAGES; ROBOTS; TRANSLATION (LANGUAGES);

DEGREE OF CONNECTIVITY; DETERMINISTIC FINITE AUTOMATA; DIRECTED GRAPHS; LOWER BOUNDS; PRESENTED EXAMPLES; REGULAR EXPRESSIONS; STAR HEIGHT; STRUCTURAL COMPLEXITY; TRANSITION STRUCTURE;

FINITE AUTOMATA;

EID: 49049088135     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-70583-3_4     Document Type: Conference Paper

References (26)

1. Berwanger, D., Dawar, A., Hunter, P., Kreutzer, S.: Dag-width and parity games. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 524-536. Springer, Heidelberg (2006)
2. Berwanger, D., Grädel, E.: Entanglement - A measure for the complexity of directed graphs with applications to logic and games. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 209-223. Springer, Heidelberg (2005)
3. Björklund, A., Husfeldt, T., Khanna, S.: Approximating longest directed paths and cycles. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 222-233. Springer, Heidelberg (2004)
4. Book, R.V., Chandra, A.K.: Inherently nonplanar automata. Acta Informatica 6, 89-94 (1976)
5. Eggan, L.C.: Transition graphs and the star height of regular events. Michigan Mathematical Journal 10, 385-397 (1963)
6. Ehrenfeucht, A., Zeiger, H.P.: Complexity measures for regular expressions. Journal of Computer and System Sciences 12(2), 134-146 (1976)
7. Ellul, K., Krawetz, B., Shallit, J., Wang, M.: Regular expressions: New results and open problems. Journal of Automata, Languages and Combinatorics 10(4), 407-437 (2005)
8. Gelade, W., Neven, F.: Succinctness of the complement and intersection of regular expressions. In: Albers, S., Weil, P. (eds.) Symposium on Theoretical Aspects of Computer Science. Dagstuhl Seminar Proceedings, vol. 08001, pp. 325-336. IBFI (2008)
9. Gruber, H., Holzer, M.: Finite automata, digraph connectivity and regular expression size. Technical report, Technische Universität München (December 2007)
10. Gruber, H., Johannsen, J.: Optimal lower bounds on regular expression size using communication complexity. In: Amadio, R. (ed.) Foundations of Software Science and Computation Structures. LNCS, vol. 4962, pp. 273-286. Springer, Heidelberg (2008)
11. Hashiguchi, K.: Algorithms for determining relative star height and star height. Information and Computation 78(2), 124-169 (1988)
12. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Reading (1979)
13. Ilie, L., Yu, S.: Follow automata. Information and Computation 186(1), 140-162 (2003)
14. Johnson, T., Robertson, N., Seymour, P.D., Thomas, R.: Directed tree-width. Journal of Combinatorial Theory, Series B 82(1), 138-154 (2001)
15. Kirsten, D.: Distance desert automata and the star height problem. RAIRO - Theoretical Informatics and Applications 39(3), 455-509 (2005)
16. Kleene, S.C.: Representation of events in nerve nets and finite automata. In: Shannon, C.E., McCarthy, J. (eds.) Automata Studies. Annals of Mathematics Studies, pp. 3-42. Princeton University Press, Princeton (1956)
17. Mayer, A.J., Stockmeyer, L.J.: Word problems - This time with interleaving. Information and Computation 115(2), 293-311 (1994)
18. McNaughton, R.: The loop complexity of pure-group events. Information and Control 11(1/2), 167-176 (1967)
19. McNaughton, R.: The loop complexity of regular events. Information Sciences 1, 305-328 (1969)
20. Morris, P.H., Gray, R.A., Filman, R.E.: Goto removal based on regular expressions. Journal of Software Maintenance 9(1), 47-66 (1997)
21. Nešetřil, J., de Mendez, P.O.: Tree-depth, subgraph coloring and homomorphism bounds. European Journal of Combinatorics 27(6), 1022-1041 (2006)
22. Obdržálek, J.: Dag-width: Connectivity measure for directed graphs. In: ACMSIAM Symposium on Discrete Algorithms, pp. 814-821. ACM Press, New York (2006)
23. Pinsker, M.S.: On the complexity of a concentrator. In: Annual Teletraffic Conference, pp. 318/1-318/4 (1973)
24. Robertson, N., Seymour, P.D.: Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms 7(3), 309-322 (1986)
25. Sakarovitch, J.: The language, the expression, and the (small) automaton. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 15-30. Springer, Heidelberg (2006)
26. Schnitger, G.: Regular expressions and NFAs without ε-transitions. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 432-443. Springer, Heidelberg (2006)