Related papers: An Approximate Skolem Function Counter

We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…

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…

We study provably correct and efficient instantiations of Sequential Monte Carlo (SMC) inference in the context of formal operational semantics of Probabilistic Programs (PPs). We focus on universal PPs featuring sampling from arbitrary…

We study provably correct and efficient instantiations of Sequential Monte Carlo (SMC) inference in the context of formal operational semantics of Probabilistic Programs (PPs). We focus on universal PPs featuring sampling from arbitrary…

Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…

Boolean Satisfiability (SAT) is arguably the archetypical NP-complete decision problem. Progress in SAT solving algorithms has motivated an ever increasing number of practical applications in recent years. However, many practical uses of…

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…

The stochastic knapsack problem is the stochastic variant of the classical knapsack problem in which the algorithm designer is given a a knapsack with a given capacity and a collection of items where each item is associated with a profit…

The Skolem Problem asks to determine whether a given linear recurrence sequence (LRS) $\langle u_n \rangle_{n=0}^\infty$ over the integers has a zero term, that is, whether there exists $n$ such that $u_n = 0$. Decidability of the problem…

We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k >=…

Large language models (LLMs) excel at function calling, but inference scaling has been explored mainly for unstructured generation. We propose an inference-scaling framework for structured outputs that combines fine-grained beam search with…

We present an exact synthesis approach for computing Exclusive-or Sum-of-Products (ESOP) forms with a minimum number of product terms using Boolean satisfiability. Our approach finds one or more ESOP forms for a given Boolean function. The…

Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…

We propose a quantum algorithm (in the form of a quantum oracle) that estimates the closeness of a given Boolean function to one that satisfies the ``strict avalanche criterion'' (SAC). This algorithm requires $n$ queries of the Boolean…

We show that computing the strongest polynomial invariant for single-path loops with polynomial assignments is at least as hard as the Skolem problem, a famous problem whose decidability has been open for almost a century. While the…

We study the problem of multiset prediction. The goal of multiset prediction is to train a predictor that maps an input to a multiset consisting of multiple items. Unlike existing problems in supervised learning, such as classification,…

Solving systems of Boolean equations is a fundamental task in symbolic computation and algebraic cryptanalysis, with wide-ranging applications in cryptography, coding theory, and formal verification. Among existing approaches, the Boolean…

We say that a function is rare-case hard against a given class of algorithms (the adversary) if all algorithms in the class can compute the function only on an $o(1)$-fraction of instances of size $n$ for large enough $n$. Starting from any…

We propose an explainable probabilistic framework for characterizing spoofed speech by decomposing it into probabilistic attribute embeddings. Unlike raw high-dimensional countermeasure embeddings, which lack interpretability, the proposed…

A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…