Complexity of Equations over Sets of Natural Numbers

Theory of Computing Systems

Volumn 48, Issue 2, 2011, Pages 319-342

  Jeż, Artur ^a   Okhotin, Alexander ^b,c  

^a UNIVERSITY OF WROC AW   (Poland)

^b UNIVERSITY OF TURKU   (Finland)

^c ACADEMY OF FINLAND   (Finland)

Author keywords

Computational complexity; Conjunctive grammars; Integer expressions; Language equations

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; MATHEMATICAL TECHNIQUES;

CONJUNCTIVE GRAMMARS; EXPTIME; INTEGER EXPRESSIONS; LANGUAGE EQUATIONS; LEAST SOLUTIONS; MEMBERSHIP PROBLEM; NATURAL NUMBER; SYSTEMS OF EQUATIONS;

FORMAL LANGUAGES;

EID: 80051665679     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-009-9246-y     Document Type: Article

References (26)

1. Brent, R. P., Goldschlager, L. M.: A parallel algorithm for context-free parsing. Aust. Comput. Sci. Commun. 6(7), 7. 1-7. 10 (1984).
2. Breunig, H.-G.: The complexity of membership problems for circuits over sets of positive numbers. In: Fundamentals of Computation Theory, FCT 2007, Budapest, Hungary, August 27-30, 2007. LNCS, vol. 4639, pp. 125-136. Springer, Berlin (2007).
3. Cai, J.-Y., Sivakumar, D.: Sparse hard sets for P: resolution of a conjecture of Hartmanis. J. Comput. Syst. Sci. 58(2), 280-296 (1999).
4. Chandra, A. K., Kozen, D. C., Stockmeyer, L. J.: Alternation. J. ACM 28(1), 114-133 (1981).
5. Ginsburg, S., Rice, H. G.: Two families of languages related to ALGOL. J. ACM, 9, 350-371 (1962).
6. Glaßer, C., Herr, K., Reitwießner, C., Travers, S. D., Waldherr, M.: Equivalence problems for circuits over sets of natural numbers. In: Computer Science in Russia, CSR 2007, Ekaterinburg, Russia, September 3-7, 2007. LNCS, vol. 4649, pp. 127-138. Springer, Berlin (2007).
7. Huynh, D. T.: Commutative grammars: the complexity of uniform word problems. Inf. Control 57(1), 21-39 (1983).
8. Jeż, A.: Conjunctive grammars can generate non-regular unary languages. Int. J. Found. Comput. Sci. 19(3), 597-615 (2008).
9. Jeż, A., Okhotin, A.: Conjunctive grammars over a unary alphabet: undecidability and unbounded growth. Theory Comput. Syst. 46(1), 27-58 (2010).
10. Jones, N. D., Laaser, W. T.: Complete problems for deterministic polynomial time. Theor. Comput. Sci. 3(1), 105-117 (1976).
11. Kunc, M.: The power of commuting with finite sets of words. Theory Comput. Syst. 40(4), 521-551 (2007).
12. Kunc, M.: What do we know about language equations? In: Developments in Language Theory, DLT 2007, Turku, Finland, July 3-6, 2007. LNCS, vol. 4588, pp. 23-27. Springer, Berlin (2007).
13. Lohrey, M.: Word problems and membership problems on compressed words. SIAM J. Comput. 35(5), 1210-1240 (2006).
14. Markey, N., Schnoebelen, Ph.: A PTIME-complete matching problem for SLP-compressed words. Inf. Process. Lett. 90(1), 3-6 (2004).
15. McKenzie, P., Wagner, K.: The complexity of membership problems for circuits over sets of natural numbers. Comput. Complex. 16(3), 211-244 (2007).
16. Ogihara, M.: Sparse hard sets for P yield space-efficient algorithms. Chic. J. Theor. Comput. Sci. (1996), article 2.
17. Okhotin, A.: Conjunctive grammars. J. Autom. Lang. Comb. 6(4), 519-535 (2001).
18. Okhotin, A.: A recognition and parsing algorithm for arbitrary conjunctive grammars. Theor. Comput. Sci. 302, 365-399 (2003).
19. Okhotin, A.: The hardest linear conjunctive language. Inf. Process. Lett. 86(5), 247-253 (2003).
20. Okhotin, A.: Unresolved systems of language equations: expressive power and decision problems. Theor. Comput. Sci. 349(3), 283-308 (2005).
21. Okhotin, A.: Decision problems for language equations. J. Comput. Syst. Sci. 76 (2010), to appear.
22. Plandowski, W., Rytter, W.: Complexity of language recognition problems for compressed words. In: Karhumäki, J., Maurer, H. A., Pǎun, G., Rozenberg, G. (eds.) Jewels are Forever, pp. 262-272. Springer, Berlin (1999).
23. Rytter, W.: On the recognition of context-free languages. In: Fundamentals of Computation Theory, FCT 1985, Cottbus, Germany. LNCS, vol. 208, pp. 315-322. Springer, Berlin (1985).
24. Stockmeyer, L. J., Meyer, A. R.: Word problems requiring exponential time. In: 5th Annual ACM Symposium on Theory of Computing, STOC 1973, Austin, USA, April 30-May 2, 1973, pp. 1-9 (1973).
25. Travers, S. D.: The complexity of membership problems for circuits over sets of integers. Theor. Comput. Sci. 369(1-3), 211-229 (2006).
26. Yang, K.: Integer circuit evaluation is PSPACE-complete. J. Comput. Syst. Sci. 63(2), 288-303 (2001).