The most nonelementary theory

Information and Computation

Volumn 190, Issue 2, 2004, Pages 196-219

  Vorobyov, Sergei ^a  

^a UPPSALA UNIVERSITY   (Sweden)

Author keywords

Generic reduction; Inductive definition; Lower complexity bound; Nonelementary theory; Reduction via length order

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; FORMAL LOGIC; SET THEORY; TECHNICAL PRESENTATIONS;

GENERIC REDUCTION; INDUCTIVE DEFINITION; LOWER COMPLEXITY BOUND; NONELEMENTARY THEORY; REDUCTION VIA LENGTH ORDER;

THEOREM PROVING;

EID: 2342486133     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ic.2004.02.002     Document Type: Article

References (18)

1. K.J. Compton, C.W. Henson, A uniform method for proving lower bounds on the computational complexity of logical theories, Ann. Pure Appl. Logic 48 (1990) 1-79.
2. J. Ferrante, C. W. Rackoff, The computational complexity of logical theories,in: Lect. Notes Math., vol. 718, Springer-Verlag, Berlin, 1979.
3. L. Henkin, A theory of prepositional types, Fundamenta Mathematics 52 (1963) 323-344.
4. J. Hopcroft, J. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, Reading, MA, 1979.
5. R. Hull, J. Su, On the expressive power of database queries with intermediate types, J. Comput. Syst. Sci. 43 (1991) 219-267.
6. G. Kuper, M. Vardi, On the complexity of queries in the logical data model, Theor. Comput. Sci. 116 (1993) 33-57.
7. H.R. Lewis, Complexity results for classes of quantificational formulas, J. Comput. Syst. Sci. 21 (1980) 317-353.
8. H. Mairson, A simple proof of a theorem of Statman, Theor. Comput. Sci. 103 (1992) 387-394.
9. A.R. Meyer, The inherent computational complexity of theories of ordered sets, in: International Congress of Mathematicians, Vancouver, 1974, pp. 477-482.
10. A.R. Meyer, Weak monadic second-order theory of successor is not elementary-recursive, in: R. Parikh (Ed.), Logic Colloquium: Symposium on Logic Held at Boston, 1972-1973, Vol. 453 of Lect. Notes Math., Springer-Verlag, 1975, pp. 132-154.
11. R. Statman, The typed λ-calculus is not elementary recursive, Theor. Comput. Sci. 9 (1979) 73-81.
12. L.J. Stockmeyer, A.R. Meyer, Word problems requiring exponential time: preliminary report, in: 5th Symposium on Theory of Computing, 1973, pp. 1-9.
13. L.J. Stockmeyer, The complexity of decision problems in automata theory and logic, PhD thesis, MIT Lab for Computer Science, 1974 (Also/MIT/LCS Tech Rep 133).
14. L.J. Stockmeyer, The polynomial-time hierarchy, Theor. Comput. Sci. 3 (1977) 1-22.
15. L.J. Stockmeyer, Classifying the computational complexity of problems, J. Symb. Logic 52 (1) (1987) 1-43.
16. A. Urquhart, The complexity of decision procedures in relevance logic, in: J.M. Dunn, A. Gupta (Eds.), Truth or Consequences: Essays in Honor of Nuel Belnap, Kluwer, 1990, pp. 61-76.
17. S. Vorobyov, The "hardest" natural decidable theory, in: G. Winskel (Ed.), 12th Annual IEEE Symp. on Logic in Computer Science (LICS'97), 1997, pp. 294-305.
18. S. Vorobyov, A. Voronkov, Complexity of nonrecursive logic programs with complex values, in: J. Paredaens, L. Colby (Eds.), Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS'98), 1998, pp. 244-253.