Related papers: Monotonic and Non-Monotonic Solution Concepts for …
We present faster approximation algorithms for generalized network flow problems. A generalized flow is one in which the flow out of an edge differs from the flow into the edge by a constant factor. We limit ourselves to the lossy case,…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
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…
We present the notion of monotone solution of mean field games master equations in the case of a continuous state space. We establish the existence, uniqueness and stability of such solutions under standard assumptions. This notion allows…
We formulate and discuss generalized bootstrap equations in nonabelian gauge theories. They are shown to hold in the leading logarithmic approximation. Since their validity is related to the self-consistency of the Steinmann relations for…
In arXiv:1710.08163 a generalization of Boolean circuits to arbitrary finite algebras had been introduced and applied to sketch P versus NP-complete borderline for circuits satisfiability over algebras from congruence modular varieties.…
In this paper we present a generalized analytical solution to the generalized state equations of coupled second-order non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of…
Quantified constraints and Quantified Boolean Formulae are typically much more difficult to reason with than classical constraints, because quantifier alternation makes the usual notion of solution inappropriate. As a consequence, basic…
For Boolean satisfiability problems, the structure of the solution space is characterized by the solution graph, where the vertices are the solutions, and two solutions are connected iff they differ in exactly one variable. In 2006, Gopalan…
Bosonic mean-field theories can approximate the dynamics of systems of $n$ bosons provided that $n \gg 1$. We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions…
Towards better understanding of gate elimination, the only method known that can prove complexity lower bounds for explicit functions against unrestricted Boolean circuits, this work contributes: (1) formalizing circuit simplifications as a…
This paper develops a general approach to nonlinear circuit modelling aimed at preserving the intrinsic symmetry of electrical circuits when formulating reduced models. The goal is to provide a framework accommodating such reductions in a…
The standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant…
We study the asymptotic behaviour of solutions to Dirichlet problems in perforated domains for nonlinear elliptic equations associated with monotone operators. The main difference with respect to the previous papers on this subject is that…
Typical properties of computing circuits composed of noisy logical gates are studied using the statistical physics methodology. A growth model that gives rise to typical random Boolean functions is mapped onto a layered Ising spin system,…
Computational asymmetry, i.e., the discrepancy between the complexity of transformations and the complexity of their inverses, is at the core of one-way transformations. We introduce a computational asymmetry function that measures the…
The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…
We prove that weighted circuit satisfiability for monotone or antimonotone circuits has no fixed-parameter tractable approximation algorithm with any approximation ratio function $\rho$, unless $FPT\neq W[1]$. In particular, not having such…
We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices…
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…