Related papers: Fast Computing the Algebraic Degree of Boolean Fun…
In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function $f$ on $n=2^k$ bits defined by a complete binary tree…
Weighted Hamming distance, as a similarity measure between binary codes and binary queries, provides superior accuracy in search tasks than Hamming distance. However, how to efficiently and accurately find $K$ binary codes that have the…
We introduce the Macaulay2 package BooleanGB, which computes a Gr\"obner basis for Boolean polynomials using a binary representation rather than symbolic. We compare the runtime of several Boolean models from systems in biology and give an…
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…
We determine a connection between the weight of a Boolean function and the total weight of its first-order derivatives. The relationship established is used to study some cryptographic properties of Boolean functions. We establish a…
One of the most important steps of document image processing is binarization. The computational requirements of locally adaptive binarization techniques make them unsuitable for devices with limited computing facilities. In this paper, we…
We present a multi-step quantum algorithm for solving the $3$-bit exact cover problem, which is one of the NP-complete problems. Unlike the brute force methods have been tried before, in this algorithm, we showed that by applying the…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
We propose an algorithm for quickly evaluating polynomials. It pre-conditions a complex polynomial $P$ of degree $d$ in time $O(d\log d)$, with a low multiplicative constant independent of the precision. Subsequent evaluations of $P$…
The Boolean satisfiability (SAT) problem is a computationally challenging decision problem central to many industrial applications. For SAT problems in cryptanalysis, circuit design, and telecommunication, solutions can often be found more…
Several classes of quantum circuits have been shown to provide a quantum computational advantage under certain assumptions. The study of ever more restricted classes of quantum circuits capable of quantum advantage is motivated by possible…
We introduce the graph parameter boolean-width, related to the number of different unions of neighborhoods across a cut of a graph. Boolean-width is similar to rank-width, which is related to the number of $GF[2]$-sums (1+1=0) of…
Nonlinear boolean equation systems play an important role in a wide range of applications. Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this…
Implementing quantum algorithms on realistic hardware requires translating high-level global operations into sequences of native elementary gates, a process known as quantum compiling. Physical limitations, such as constraints in…
Weightless Neural Networks (WNNs) are a class of machine learning model which use table lookups to perform inference. This is in contrast with Deep Neural Networks (DNNs), which use multiply-accumulate operations. State-of-the-art WNN…
For fast computation of the Arnold complexity of length $2^{n}$ binary words we obtain an upper bound for the Shannon function $Sh(n)$
Allen's interval algebra is one of the most well-known calculi in qualitative temporal reasoning with numerous applications in artificial intelligence. Recently, there has been a surge of improvements in the fine-grained complexity of…
Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis, and shows that van Dam's oracle interrogation is…