The Role of Monotonicity in Descriptive Complexity Theory
It is well-known that monotonicity, in a variety of guises, plays an essential role in descriptive complexity theory and finite model theory. In this paper, we highlight existing well-known roles and also explain two other not so well-known roles of monotonicity. The first arises due to an anomaly in logically characterizing NP using operators corresponding to traditional NP-complete problems; and the second arises due to the consideration of the logical characterization of complexity classes defined with respect to “monotone” models of computation.
KeywordsHamiltonian Path Relation Symbol Constant Symbol Projective Formula Oracle Query
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- 1.F. Afrati and S.S. Cosmadakis and M. Yannakakis, On Datalog vs. polynomial time, Proc. 10th ACM Ann. Symp. on Principles of Database Systems (1991) 13–23Google Scholar
- 4.J.L. Balcâzar and J. Diaz and J. Gabarró, Structural Complexity Theory I, Springer-Verlag, Berlin (1988)Google Scholar
- 6.A. Dawar and I.A. Stewart, manuscriptGoogle Scholar
- 7.R. Fagin, Generalized first-order spectra and polynomial-time recognizable sets, Complexity of Computation, SIAM-AMS Proceedings, Vol. 7 (ed. R.M. Karp ) (1974) 43–73Google Scholar
- 12.P.G. Kolaitis and J.A. Väänänen, Generalised quantifiers and pebble games on finite structures, J. Pure App. Logic,to appearGoogle Scholar
- 13.A.A. Razborov, A lower bound on the monotone network complexity of the logical permanent, Mat. Zametki 41 (1987) 598–607 (in Russian; English translation in: Math. Notes,41 (1987), 333–338)Google Scholar
- 23.J.D. Ullman, Database and Knowledge-Base Systems, Computer Science Press (1989)Google Scholar
- 24.M. Vardi, Complexity of relational query languages, Proc. 14th ACM Ann. Symp. on Theory of Computing (1982) 137–146Google Scholar