Related papers: A proof algorithm associated with the dipole split…
We investigate a difference-of-convex (DC) formulation where the second term is allowed to be weakly convex. We examine the precise behavior of a single iteration of the difference-of-convex algorithm (DCA), providing a tight…
Because of several technological limitations of traditional silicon based computing, for past few years a paradigm shift, from silicon to carbon, is occurring in computational world. DNA computing has been considered to be quite promising…
The problem of joint direction-of-arrival estimation and distorted sensor detection has received a lot of attention in recent decades. Most state-of-the-art work formulated such a problem via low-rank and row-sparse decomposition, where the…
Constrained quadratic programs and Euclidean projections are ubiquitous in engineering, arising in machine learning, estimation, control, and signal processing. Dykstra's algorithm is an iterative scheme for computing the Euclidean…
The Distributional Principal Autoencoder (DPA) combines distributionally correct reconstruction with principal-component-like interpretability of the encodings. In this work, we provide exact theoretical guarantees on both fronts. First, we…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
The verification of systems combining hard timing constraints with concurrency is challenging. This challenge becomes even harder when some timing constants are missing or unknown. Parametric timed formalisms, such as parametric timed…
We present a polynomial time algorithm that constructs a deterministic parity automaton (DPA) from a given set of positive and negative ultimately periodic example words. We show that this algorithm is complete for the class of…
We use the Sum of Squares method to develop new efficient algorithms for learning well-separated mixtures of Gaussians and robust mean estimation, both in high dimensions, that substantially improve upon the statistical guarantees achieved…
We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical…
We develop a new semi-algebraic proof system called Stabbing Planes which formalizes modern branch-and-cut algorithms for integer programming and is in the style of DPLL-based modern SAT solvers. As with DPLL there is only a single rule:…
We prove a complexity dichotomy theorem for Holant Problems on 3-regular graphs with an arbitrary complex-valued edge function. Three new techniques are introduced: (1) higher dimensional iterations in interpolation; (2) Eigenvalue Shifted…
By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…
There is an increasing need to model plasma interaction with complex engineered surfaces, notably to verify that power deposition rates are acceptable. The SMARDDA algorithm has been developed to meet this requirement, with particular…
We propose a novel approach for the development, analysis, and verification of reductions between NP-complete problems. This method uses the URSA system, a SAT-based constraint solver and incorporates features that distinguish it from…
We consider estimation models of the form $Y=X^*+N$, where $X^*$ is some $m$-dimensional signal we wish to recover, and $N$ is symmetrically distributed noise that may be unbounded in all but a small $\alpha$ fraction of the entries. We…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a…
In \emph{Guo et al, arXiv:2005.08288}, we propose a decoupled form of the structure-preserving doubling algorithm (dSDA). The method decouples the original two to four coupled recursions, enabling it to solve large-scale algebraic Riccati…