Difference in Concept of Lumped Constant Circuit and Distributed Constant Circuit

Arithmetic Constant-Depth Circuit Complexity Classes

The boolean circuit complexity classes AC ⊆ AC[m] ⊆ TC ⊆ NC have been studied intensely. Other than NC, they are defined by constant-depth circuits of polynomial size and unbounded fan-in over some set of allowed gates. One reason for interest in these classes is that they contain the boundary marking the limits of current lower bound technology: such technology exists for AC and some of the cl...

Circuit Complexity of Properties of Graphs with Constant Planar Cutwidth

We study the complexity of several of the classical graph decision problems in the setting of bounded cutwidth and how imposing planarity affects the complexity. We show that for 2-coloring, for bipartite perfect matching, and for several variants of disjoint paths the straightforward NC1 upper bound may be improved to AC0[2], ACC0, and AC0 respectively for bounded planar cutwidth graphs. We ob...

Arithmetic Versions of Constant Depth Circuit Complexity Classes

The boolean circuit complexity classes AC ⊆ AC[m] ⊆ TC ⊆ NC have been studied intensely. Other than NC, they are defined by constant-depth circuits of polynomial size and unbounded fan-in over some set of allowed gates. One reason for interest in these classes is that they contain the boundary marking the limits of current lower bound technology: such technology exists for AC and some of the cl...

Bifurcation from a 3-D hysteresis piecewise-constant circuit

We propose a 3-D hysteresis piecewise-constant circuit. The circuit consists of linear capacitors and nonlinear voltage controlled current sources. This circuit is extremely simple, but exhibits interesting bifurcation phenomena. The righthand side of the state equation is piecewise-constant, hence the system dynamics can be simplified into a piecewiselinear return map. Using the return map, th...

Difference between combinational circuit and sequential circuit pdf