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Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…
We study the problem of conditional expectations in free random variables and provide closed formulas for the conditional expectation of resolvents of arbitrary non-commutative polynomials in free random variables onto the subalgebra of an…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…
Polynomial quantified entailments with existentially and universally quantified variables arise in many problems of verification and program analysis. We present PolyQEnt which is a tool for solving polynomial quantified entailments in…
In this paper we investigate the problem of quantifying the contribution of each variable to the satisfying assignments of a Boolean function based on the Shapley value. Our main result is a polynomial-time equivalence between computing…
In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an…
Quantifier-free nonlinear arithmetic (QF_NRA) appears in many applications of satisfiability modulo theories solving (SMT). Accordingly, efficient reasoning for corresponding constraints in SMT theory solvers is highly relevant. We propose…
A delta-model is a satisfying assignment of a Boolean formula for which any small alteration, such as a single bit flip, can be repaired by flips to some small number of other bits, yielding a new satisfying assignment. These satisfying…
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…
We introduce power term polynomial algebra, a representation language for Boolean formulae designed to bridge conjunctive normal form (CNF) and algebraic normal form (ANF). The language is motivated by the tiling mismatch between these…
An algorithm for computing the nonlinearity of a Boolean function from its algebraic normal form (ANF) is proposed. By generalizing the expression of the weight of a Boolean function in terms of its ANF coefficients, a formulation of the…
Given a relational specification R(X, Y), where X and Y are sequences of input and output variables, we wish to synthesize each output as a function of the inputs such that the specification holds. This is called the Boolean functional…
In recent years, machine learning has begun automating decision making in fields as varied as college admissions, credit lending, and criminal sentencing. The socially sensitive nature of some of these applications together with increasing…
How to handle division in systems that compute with logical formulas involving what would otherwise be polynomial constraints over the real numbers is a surprisingly difficult question. This paper argues that existing approaches from both…
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
We present a multi-step quantum algorithm for solving the $3$-bit exact cover problem, which is one of the NP-complete problems. Unlike the brute force methods have been tried before, in this algorithm, we showed that by applying the…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We present novel algorithms for design and design space exploration. The designs discovered by these algorithms are compositions of function types specified in component libraries. Our algorithms reduce the design problem to quantified…
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…