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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…
The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which…
Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an…
In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast…
We propose a novel, fully explainable neural approach to synthesis of combinatorial logic circuits from input-output examples. The carrying advantage of our method is that it readily extends to inductive scenarios, where the set of examples…
Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum…
Despite the rapid development of quantum computing these years, state-of-the-art quantum devices still contain only a very limited number of qubits. One possible way to execute more realistic algorithms in near-term quantum devices is to…
The synthesis approaches for quantum circuits typically aim at minimizing the number of lines or gates. Given the tight restrictions on those logical resources in physical implementations, we propose to view the problem fundamentally…
We establish a lower bound for deciding the satisfiability of the conjunction of any two Boolean formulas from a set called a full representation of Boolean functions of $n$ variables - a set containing a Boolean formula to represent each…
A notorious open question in circuit complexity is whether Boolean operations of arbitrary arity can efficiently be expressed using modular counting gates only. H{\aa}stad's celebrated switching lemma yields exponential lower bounds for the…
String matching is a fundamental problem in computer science, with critical applications in text retrieval, bioinformatics, and data analysis. Among the numerous solutions that have emerged for this problem in recent decades,…
This work identifies a necessary condition for any variational quantum approach to reach the exact ground state. Briefly, the norms of the projections of the input and the ground state onto each group module must match, implying that module…
In the last decades, great achievements have been made in the development of computing machines. However, due to exponential growth of transistor density and in particular due to tremendously increasing power consumption, researchers expect…
In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the…
Ensuring large language model (LLM) reliability requires distinguishing objective unsolvability (inherent contradictions) from subjective capability limitations (tasks exceeding model competence). Current LLMs often conflate these…
We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier Hierarchy, the lowest…
The minimum number of NOT gates in a Boolean circuit computing a Boolean function is called the inversion complexity of the function. In 1957, A. A. Markov determined the inversion complexity of every Boolean function and proved that…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
This paper proposes a new logic optimization paradigm based on circuit simulation, which reduces the need for Boolean computations such as SAT-solving or constructing BDDs. The paper develops a Boolean resubstitution framework to…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…