Research
Research
Research
Research
56+ open-access research outputs.
We present a tractable, incremental framework for topological dialogue semantics based on finite, discrete semantic spaces. Building on the intuition that utterances correspond to open sets and their …
While theoretical computer science primarily works with discrete models of computation, like the Turing machine and the wordRAM, there are many scenarios in which introducing real computation models i…
Decision trees are a classic model for summarizing and classifying data. To enhance interpretability and generalization properties, it has been proposed to favor small decision trees. Accordingly, in …
In the algebraic metacomplexity framework we prove that the decomposition of metapolynomials into their isotypic components can be implemented efficiently, namely with only a quasipolynomial blowup in…
People with disabilities that affect their speech may use speech-generating devices (SGD), commonly referred to as Augmentative and Alternative Communication (AAC) technology. This technology enables …
In August 2023, Scott Aaronson and I reported the results of testing GPT4 with the Wolfram Alpha and Code Interpreter plug-ins over a collection of 105 original high-school level and college-level sci…
We present LinApart, a routine designed for efficiently performing the univariate partial fraction decomposition of large symbolic expressions. Our method is based on an explicit closed formula for th…
Zero-knowledge proofs (zk-Proofs) are communication protocols by which a prover can demonstrate to a verifier that it possesses a solution to a given public problem without revealing the content of th…
In the rapidly evolving landscape of education, digital technologies have repeatedly disrupted traditional pedagogical methods. This paper explores the latest of these disruptions: the potential integ…
The past decade highlighted the usefulness of social network simulations that run on k-regular, n-size, connected graphs. These can be seen as small-scale models of human social networks of large soci…
The increasing number of questions on Question Answering (QA) platforms like Math Stack Exchange (MSE) signifies a growing information need to answer math-related questions. However, there is currentl…
In combinatory logic it is known that the set of two combinators K and S are universal; in the sense that any other combinator can be expressed in terms of these two. K combinator can not be expressed…
As it is known, universal codes, which estimate the entropy rate consistently, exist for stationary ergodic sources over finite alphabets but not over countably infinite ones. We generalize universal …
A set $S\subseteq V$ of vertices is an offensive alliance in an undirected graph $G=(V,E)$ if each $v\in N(S)$ has at least as many neighbours in $S$ as it has neighbours (including itself) not in $S$…
This paper provides an analytical solution to the Wolfram Alpha Rule 30 Problem 1. In this paper we discuss whether the central column of the Rule 30 structure is purely random and aperiodic.…
In this article, we create a system called AI-EVL. This is an annotated-based learning system. We extend AI to learning experience. If a user from the main YouTube page browses YouTube videos and a us…
The area method is a decision procedure for geometry developed by Chou et al. in the 1990's. The method aims to reduce the specified hypothesis to an algebraically verifiable form by applying eliminat…
The Bose-Chaudhuri-Hocquenghem (BCH) codes are a well-studied subclass of cyclic codes that have found numerous applications in error correction and notably in quantum information processing. A subcla…
Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Instit…
This paper presents a formally verified quantifier elimination (QE) algorithm for first-order real arithmetic by linear and quadratic virtual substitution (VS) in Isabelle/HOL. The Tarski-Seidenberg t…
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