Abstract
We obtain a characterization of ACC 0 in terms of a natural class of constant width circuits, namely in terms of constant width polynomial size planar circuits. This is shown via a characterization of the class of acyclic digraphs which can be embedded on a cylinder surface in such a way that all arcs flow along the same direction of the axis of the cylinder.
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.
References
Barrington, D.A.: Bounded-width polynomial-size branching programs recognize exactly those languages in NC1. J. Comput. System Sci. 38(1), 150–164 (1989)
Mix Barrington, D.A., Lu, C.-J., Miltersen, P.B., Skyum, S.: Searching constant width mazes captures the AC0 hierarchy. In: Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science, pp. 73–83 (1998)
Mix Barrington, D.A., Lu, C.-J., Miltersen, P.B., Skyum, S.: On monotone planar circuits. In: 14th Annual IEEE Conference on Computational Complexity, pp. 24–31. IEEE Computer Society Press, Los Alamitos (1999)
Mix Barrington, D.A., Thérien, D.: Finite monoids and the fine structure of NC1. Journal of the ACM (JACM) 35, 941–952 (1988)
Di Battista, G., Tamassia, R.: Algorithms for plane representations of acyclic digraphs. Theoretical Computer Science 61(2-3), 175–198 (1988)
Edmonds, D.: A combinatorial representation for polyhedral surfaces. Notices Amer. Math. Soc. 7, 646 (1960)
Gröger, H.D.: A new partition lemma for planar graphs and its application to circuit complexity. In: Budach, L. (ed.) FCT 1991. LNCS, vol. 529, pp. 220–229. Springer, Heidelberg (1991)
Hansen, K.A., Miltersen, P.B., Vinay, V.: Circuits on cylinders. In: Lingas, A., Nilsson, B.J. (eds.) FCT 2003. LNCS, vol. 2751, pp. 171–182. Springer, Heidelberg (2003)
Kelly, D.: Fundamentals of planar ordered sets. Discrete Mathematics 63(2,3), 197–216 (1987)
Lipton, R.J., Tarjan, R.E.: Applications of a planar separator theorem. SIAM Journal on Computing 9(3), 615–627 (1980)
Tamassia, R., Tollis, I.G.: A unified approach to visibility representations of planar graphs. Discrete & Computational Geometry 1(1), 312–341 (1986)
Tamassia, R., Tollis, I.G.: Tessellation representations of planar graphs. In: Proceedings 27th Annual Allerton Conference on Communications, Control and Computing, September 1989, University of Illinois at Urbana-Champaign, pp. 48–57 (1989)
Turán, G.: On restricted boolean circuits. In: Csirik, J.A., Demetrovics, J., Gecseg, F. (eds.) FCT 1989. LNCS, vol. 380, pp. 460–469. Springer, Heidelberg (1989)
Vinay, V.: Hierarchies of circuit classes that are closed under complement. In: 11th Annual IEEE Conference on Computational Complexity, pp. 108–117. IEEE Computer Society, Los Alamitos (1996)
White, A.T.: Graphs, Groups and Surfaces. Elsevier Science Publishers B.V., Amsterdam (1984)
Yao, C.-C.: On ACC0 and threshold circuits. In: Proceedings 31st Annual Symposium on Foundations of Computer Science, pp. 619–627. IEEE Computer Society Press, Los Alamitos (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hansen, K.A. (2004). Constant Width Planar Computation Characterizes ACC0 . In: Diekert, V., Habib, M. (eds) STACS 2004. STACS 2004. Lecture Notes in Computer Science, vol 2996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24749-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-24749-4_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21236-2
Online ISBN: 978-3-540-24749-4
eBook Packages: Springer Book Archive