Related papers: Logic circuits from zero forcing

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…

In this paper, we propose computational approaches for the zero forcing problem, the connected zero forcing problem, and the problem of forcing a graph within a specified number of timesteps. Our approaches are based on a combination of…

Memcomputing logic gates generalize the traditional Boolean logic gates for operation in the reverse direction. According to the literature, this functionality enables the efficient solution of computationally-intensive problems including…

Noise-based logic, by utilizing its multidimensional logic hyperspace, has significant potential for low-power parallel operations in beyond-Moore-chips. However universal gates for Boolean logic thus far had to rely on either time…

The concept of zero forcing involves a dynamic coloring process by which blue vertices cause white vertices to become blue, with the goal of forcing the entire graph blue while choosing as few as possible vertices to be initially blue. Past…

Zero forcing is a process on a graph in which the goal is to force all vertices to become blue by applying a color change rule. Throttling minimizes the sum of the number of vertices that are initially blue and the number of time steps…

Zero forcing is a combinatorial game played on a graph with a goal of turning all of the vertices of the graph black while having to use as few "unforced" moves as possible. This leads to a parameter known as the zero forcing number which…

Using logic gates is the traditional way of designing logic circuits. However, most of the minimization algorithms concern a limited set of gates (complete sets), like sum of products, exclusive-or sum of products, NAND gates, NOR gates…

Homogenous Boolean function is an essential part of any cryptographic system. The ability to construct an optimized reversible circuits for homogeneous Boolean functions might arise the possibility of building cryptographic system on novel…

A new proposal is given for designing a non-volatile, completely spin logic device, that can be reprogrammed for different functional classical logical operations. We use the concept of bias driven spin dependent circular current and…

We continue to study the notion of cancellation-free linear circuits. We show that every matrix can be computed by a cancellation- free circuit, and almost all of these are at most a constant factor larger than the optimum linear circuit…

Invertible logic can operate in one of two modes: 1) a forward mode, in which inputs are presented and a single, correct output is produced, and 2) a reverse mode, in which the output is fixed and the inputs take on values consistent with…

Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work…

We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Under appropriate conditions, there is a…

We propose and develop a concept of magnonic logic gates enabling reversible computing. The gates consist of passive elements: waveguides, cross-junctions and phase shifters. Logical 0 and 1 are encoded in the relative phase of the…

Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to…

Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There…

The problem of constructing hazard-free Boolean circuits dates back to the 1940s and is an important problem in circuit design. Our main lower-bound result unconditionally shows the existence of functions whose circuit complexity is…

The problem of constructing hazard-free Boolean circuits (those avoiding electronic glitches) dates back to the 1940s and is an important problem in circuit design and even in cybersecurity. We show that a DeMorgan circuit is hazard-free if…

Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series…