Related papers: Subtropical Satisfiability
One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are `flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct)…
We study the learnability of symbolic finite state automata (SFA), a model shown useful in many applications in software verification. The state-of-the-art literature on this topic follows the query learning paradigm, and so far all…
Artificial Neural Networks (ANNs) are being deployed for an increasing number of safety-critical applications, including autonomous cars and medical diagnosis. However, concerns about their reliability have been raised due to their…
Fault tree (FT) analysis is a prominent risk assessment method in industrial systems. Unreliability is one of the key safety metrics in quantitative FT analysis. Existing algorithms for unreliability analysis are based on binary decision…
Given a formula $F$ of satisfiability modulo theory (SMT), the classical SMT solver tries to (1) abstract $F$ as a Boolean formula $F_B$, (2) find a Boolean solution to $F_B$, and (3) check whether the Boolean solution is consistent with…
Smale's alpha-theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to a square polynomial system. The program alphaCertified implements…
This paper argues that the method of least squares has significant unfulfilled potential in modern machine learning, far beyond merely being a tool for fitting linear models. To release its potential, we derive custom gradients that…
We show that a collection of three-sorted set-theoretic formulae, denoted TLQSR and which admits a restricted form of quantification over individual and set variables, has a solvable satisfiability problem by proving that it enjoys a small…
Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and $L_2$-norm.…
We present a general simplification of quantified SMT formulas using variable elimination. The simplification is based on an analysis of the ground terms occurring as arguments in function applications. We use this information to generate a…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
In the quadratic minimum spanning tree problem (QMSTP) one wants to find the minimizer of a quadratic function over all possible spanning trees of a graph. We present a formulation of the QMSTP as a mixed-integer semidefinite program…
In this paper, we study the problem of computing by relaxation hierarchies the infimum of a real polynomial function f on a closed basic semialgebraic set and the points where this infimum is reached, if they exist. We show that when the…
Focusing on Stable Roommates (SR) instances, we contribute to the toolbox for conducting experiments for stable matching problems. We introduce a polynomial-time computable pseudometric to measure the similarity of SR instances, analyze its…
We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…
Many procedures for SAT and SAT-related problems -- in particular for those requiring the complete enumeration of satisfying truth assignments -- rely their efficiency on the detection of partial assignments satisfying an input formula. In…
This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…
Propositional model counting} (#SAT), i.e., counting the number of satisfying assignments of a propositional formula, is a problem of significant theoretical and practical interest. Due to the inherent complexity of the problem, approximate…
Efficient solutions for satisfiability modulo theories (SMT) are integral in industrial applications such as hardware verification and design automation. Existing approaches are predominantly based on conflict-driven clause learning, which…
This paper develops a parallel computational solver for computing all satifying assignments of a Boolean system of equations defined by Boolean functions of several variables. While there are we known solvers for satisfiability of Boolean…