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The extension of classical imperative programs with real-valued random variables and random branching gives rise to probabilistic programs. The termination problem is one of the most fundamental liveness properties for such programs. The…
Graph-based ranking methods, such as LexRank, are fundamental in Natural Language Processing (NLP) applications like text summarization, as they measure the relative importance of textual units. Building on recent advances in ranking…
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…
We present a new perspective on graph-based methods for collaborative ranking for recommender systems. Unlike user-based or item-based methods that compute a weighted average of ratings given by the nearest neighbors, or low-rank…
Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…
We consider sequential or active ranking of a set of n items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items…
Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranking} and {\em unranking} functions. Starting from a…
We consider the problems of finding the lexicographically minimal (or maximal) satisfying assignment of propositional formulae for different restricted formula classes. It turns out that for each class from our framework, the above problem…
This paper describes team LCP-RIT's submission to the SemEval-2021 Task 1: Lexical Complexity Prediction (LCP). The task organizers provided participants with an augmented version of CompLex (Shardlow et al., 2020), an English multi-domain…
We study functions that produce a ranking of $n$ individuals from $n$ such rankings and are impartial in the sense that the position of an individual in the output ranking does not depend on the input ranking submitted by that individual.…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
Refinement Modal Logic (RML), which was recently introduced by Bozzelli et al., is an extension of classical modal logic which allows one to reason about a changing model. In this paper we study computational complexity questions related to…
We consider the problem of learning the true ordering of a set of alternatives from largely incomplete and noisy rankings. We introduce a natural generalization of both the classical Mallows model of ranking distributions and the…
The Boolean satisfiability problem (SAT) holds a central place in computational complexity theory as the first shown NP-complete problem. Due to this role, SAT is often used as the benchmark for polynomial-time reductions: if a problem can…
We study the complexity of approximate counting Constraint Satisfaction Problems (#CSPs) in a bounded degree setting. Specifically, given a Boolean constraint language $\Gamma$ and a degree bound $\Delta$, we study the complexity of…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
Many important multiple-objective decision problems can be cast within the framework of ranking under constraints and solved via a weighted bipartite matching linear program. Some of these optimization problems, such as personalized content…
Size-Change Termination is an increasingly-popular technique for verifying program termination. These termination proofs are deduced from an abstract representation of the program in the form of "size-change graphs". We present algorithms…
We establish $L^p$ estimates for multilinear multipliers acting on $(n-1)$-tuples of functions on $\mathbb{R}^d$. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension $m$. The difficulty of proving…