Abstract
The effect of severely tightening the uniformity of Boolean circuit families is investigated. The impact on NC1 and its subclasses is shown to depend on the characterization chosen for the class, while classes such as P appear to be more robust. Tightly uniform subclasses of NC1 whose separation may be within reach of current techniques emerge.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Allender, E.: P-uniform circuit complexity. J. ACM 36(4), 912–928 (1989)
Mix Barrington, D.A.: Bounded-width polynomial-size branching programs recognize exactly those languages in NC1. J. Comput. Syst. Sci. 38(1), 150–164 (1989)
Buss, S.R., Cook, S., Gupta, A., Ramachandran, V.: An optimal parallel algorithm for formula evaluation. SIAM J. Comput. 21(4), 755–780 (1992)
Mix Barrington, D.A., Immerman, N., Straubing, H.: On Uniformity within NC1. J. Comput. Syst. Sci. 41(3), 274–306 (1990)
Behle, C., Lange, K.-J.: FO[<]-Uniformity. In: IEEE Conference on Computational Complexity, pp. 183–189 (2006)
Borodin, A.: On relating time and space to size and depth. SIAM J. Comput. 6(4), 733–744 (1977)
Buss, S.R.: The boolean formula value problem is in alogtime. In: STOC, pp. 123–131. ACM (1987)
Cook, S.A.: Deterministic CFL’s are accepted simultaneously in polynomial time and log squared space. In: STOC, pp. 338–345. ACM (1979)
Goldschlager, L.M.: A unified approach to models of synchronous parallel machines. In: STOC, pp. 89–94 (1978)
Immerman, N.: Languages that capture complexity classes. SIAM J. Comput. 16(4), 760–778 (1987)
Krebs, A., Sreejith, V.: Non-definability of languages by generalized first-order formulas over (ℕ,+). In: LICS (to appear, 2012)
Lautemann, C., McKenzie, P., Schwentick, T., Vollmer, H.: The descriptive complexity approach to LOGCFL. J. Comput. Syst. Sci. 62(4), 629–652 (2001)
McNaughton, R., Papert, S.: Counter-free automata. With an appendix by William Henneman. In: Research Monograph No. 65, vol. XIX, 163 p. The M. I. T. Press, Cambridge (1971)
McKenzie, P., Thomas, M., Vollmer, H.: Extensional uniformity for boolean circuits. SIAM J. Comput. 39(7), 3186–3206 (2010)
Roy, A., Straubing, H.: Definability of languages by generalized first-order formulas over N + . SIAM J. Comput. 37(2), 502–521 (2007)
Ruzzo, W.L.: On uniform circuit complexity. J. Comput. Syst. Sci. 22(3), 365–383 (1981)
Straubing, H.: Finite Automata, Formal Logic, and Circuit Complexity. Birkhäuser, Boston (1994)
Thomas, W.: The theory of successor with an extra predicate. Math. Annalen 237, 121–132 (1978)
Vollmer, H.: Introduction to Circuit Complexity. Springer (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Behle, C., Krebs, A., Lange, KJ., McKenzie, P. (2012). The Lower Reaches of Circuit Uniformity. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_52
Download citation
DOI: https://doi.org/10.1007/978-3-642-32589-2_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32588-5
Online ISBN: 978-3-642-32589-2
eBook Packages: Computer ScienceComputer Science (R0)