Constant Width Planar Computation Characterizes ACC0

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.

[1]  A BarringtonDavid Bounded-width polynomial-size branching programs recognize exactly those languages in NC1 , 1989 .

[2]  Robert E. Tarjan,et al.  Applications of a planar separator theorem , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[3]  David A. Mix Barrington,et al.  Bounded-width polynomial-size branching programs recognize exactly those languages in NC1 , 1986, STOC '86.

[4]  Hans Dietmar Gröger A New Partition Lemma for Planar Graphs and Its Application to Circuit Complexity , 1991, FCT.

[5]  Andrew Chi-Chih Yao,et al.  ON ACC and threshold circuits , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[6]  Peter Bro Miltersen,et al.  Searching Constant Width Mazes Captures the AC0 Hierarchy , 1997, STACS.

[7]  Roberto Tamassia,et al.  A unified approach to visibility representations of planar graphs , 1986, Discret. Comput. Geom..

[8]  Peter Bro Miltersen,et al.  On monotone planar circuits , 1999, Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317).

[9]  Roberto Tamassia,et al.  Algorithms for Plane Representations of Acyclic Digraphs , 1988, Theor. Comput. Sci..

[10]  György Turán On Restricted Boolean Circuits , 1989, FCT.

[11]  Ioannis G. Tollis,et al.  Representations of Graphs on a Cylinder , 1991, SIAM J. Discret. Math..

[12]  Peter Bro Miltersen,et al.  Searching constant width mazes captures the AC 0 hierarchy , 1997 .

[13]  J. Hammersley,et al.  Graphs, Groups and Surfaces. , 1975 .

[14]  David Kelly Fundamentals of planar ordered sets , 1987, Discret. Math..

[15]  Kristoffer Arnsfelt Hansen,et al.  Circuits on cylinders , 2006, computational complexity.

[16]  V. Vinay Hierarchies of circuit classes that are closed under complement , 1996, Proceedings of Computational Complexity (Formerly Structure in Complexity Theory).