Related papers: All Superlinear Inverse Schemes are coNP-Hard
We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition. We follow the approach of untrusted certificates,…
We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants…
In the field of machine unlearning, certified unlearning has been extensively studied in convex machine learning models due to its high efficiency and strong theoretical guarantees. However, its application to deep neural networks (DNNs),…
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
The authors discuss how general regularization schemes, in particular linear regularization schemes and projection schemes, can be used to design tests for signal detection in statistical inverse problems. It is shown that such tests can…
Recently it was proved that the group of rough paths modulo tree-like equivalence is isomorphic to the corresponding signature group through the signature map S (a generalized notion of taking iterated path integrals). However, the proof of…
Recent cognitive experiments have shown that the negative impact of an edge crossing on the human understanding of a graph drawing, tends to be eliminated in the case where the crossing angles are greater than 70 degrees. This motivated the…
Assuming that the Permanent polynomial requires algebraic circuits of exponential size, we show that the class VNP does not have efficiently computable equations. In other words, any nonzero polynomial that vanishes on the coefficient…
IV-matching is a generalization of perfect bipartite matching. The complexity of finding IV-matching in a graph was posted as an open problem at the ICALP 2014 conference. In this note, we resolve the question and prove that, contrary to…
We show that the problem of deciding whether the vertex set of a graph can be covered with at most two bicliques is in NP$\cap$coNP. We thus almost determine the computational complexity of a problem whose status has remained open for quite…
Hardware reverse engineering is a universal tool for both legitimate and illegitimate purposes. On the one hand, it supports confirmation of IP infringement and detection of circuit malicious manipulations, on the other hand it provides…
Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework…
In the pinwheel problem, one is given an $m$-tuple of positive integers $(a_1, \ldots, a_m)$ and asked whether the integers can be partitioned into $m$ color classes $C_1,\ldots,C_m$ such that every interval of length $a_i$ has non-empty…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
A real symmetric n times n matrix is called copositive if the corresponding quadratic form is non-negative on the closed first orthant. If the matrix fails to be copositive there exists some non-negative certificate for which the quadratic…
This paper describes the formal verification of NP-hardness reduction functions of two key problems relevant in algebraic lattice theory: the closest vector problem and the shortest vector problem, both in the infinity norm. The…
We prove that checking if a partial matrix is partial totally positive is co-NP-complete. This contrasts with checking a conventional matrix for total positivity, for which we provide a cubic time algorithm. Checking partial sign regularity…
Verification is one of the central tasks during circuit design. While most of the approaches have exponential worst-case behaviour, in the following techniques are discussed for proving polynomial circuit verification based on Binary…
We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization…
Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…