Related papers: Logic circuits from zero forcing
We consider the problem of computing a binary linear transformation using unreliable components when all circuit components are unreliable. Two noise models of unreliable components are considered: probabilistic errors and permanent errors.…
Recent work has shown that the input-output behavior of some machine learning systems can be captured symbolically using Boolean expressions or tractable Boolean circuits, which facilitates reasoning about the behavior of these systems.…
A logical zonotope, which is a new set representation for binary vectors, is introduced in this paper. A logical zonotope is constructed by XOR-ing a binary vector with a combination of other binary vectors called generators. Such a…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
The zero forcing number was introduced as a combinatorial bound on the maximum nullity taken over the set of real symmetric matrices that respect the pattern of an underlying graph. The $Z_q$-forcing game is an analog to the standard zero…
In this study, we construct the quantum reversible counterparts of the logical AND, OR, XOR, NOR, and NAND gates. We utilize a quantum Fourier transform (QFT)-based adder circuit that replicates the functionality of a digital half-adder,…
Zero forcing is a graph coloring process that is used to model spreading phenomena in real-world scenarios. It can also be viewed as a single-player combinatorial game on a graph, where the player's goal is to select a subset of vertices of…
Probabilistic zero forcing is a graph coloring process in which blue vertices "infect" (color blue) white vertices with a probability proportional to the number of neighboring blue vertices. We introduce reversion probabilistic zero forcing…
Basic arithmetic is the cornerstone of mathematics and computer sciences. In arithmetic, 'division by zero' is an undefined operation and any attempt at extending logic for algebraic division to incorporate division by zero has resulted in…
The end of Moore's law for CMOS technology has prompted the search for low-power computing alternatives, resulting in several promising proposals based on magnetic logic[1-8]. One approach aims at tailoring arrays of nanomagnetic islands in…
Reversible computation is one of the most promising emerging technologies of the future. The usage of reversible circuits in computing devices can lead to a significantly lower power consumption. In this paper we study reversible logic…
We introduce a cyclic proof system for the two-way alternation-free modal $\mu$-calculus. The system manipulates one-sided Gentzen sequents and locally deals with the backwards modalities by allowing analytic applications of the cut rule.…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…
In Boolean algebra, it is known that the logical function that corresponds to the negation of the conjunction --NAND-- is universal in the sense that any other logical function can be built based on it. This property makes it essential to…
We present fully polynomial-time (deterministic or randomised) approximation schemes for Holant problems, defined by a non-negative constraint function satisfying a generalised second order recurrence modulo a couple of exceptional cases.…
We study the computational expressivity of proof systems with fixed point operators, within the 'proofs-as-programs' paradigm. We start with a calculus muLJ (due to Clairambault) that extends intuitionistic logic by least and greatest…
Following the success of Moore's predictions, we are approaching a limit in the miniaturization of semiconductors for computing materials. This has led to the exploration of various research paths to develop alternative computing paradigms,…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
Over the past decade, a number of quantum processes have been proposed which are logically consistent, yet feature a cyclic causal structure. However, there is no general formal method to construct a process with an exotic causal structure…
Physical implementations of digital computers began in the latter half of the 1930's and were first constructed from various forms of logic gates. Based on the prime numbers, we introduce prime clocks and prime clock sums, where the clocks…