CS 345 Lecture 1: Introduction and Math Review
This content encompasses the introduction and mathematical review covered in CS 345 lecture 1, including topics such as sets, sequences, logarithms, logical equivalences, and proofs. It delves into sets theory, mathematical operations, deductive reasoning, and examples like the conjecture of even nu
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Additive Combinatorics Approach to Log-Rank Conjecture in Communication Complexity
This research explores an additive combinatorics approach to the log-rank conjecture in communication complexity, addressing the maximum total bits sent on worst-case inputs and known bounds. It discusses the Polynomial Freiman-Ruzsa Conjecture and Approximate Duality, highlighting technical contrib
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Insights into Graph Colorings, Chromatic Polynomials, and Conjectures in Discrete Geometry
Delve into the fascinating world of graph colorings, chromatic polynomials, and notable conjectures in discrete geometry. Explore the impact of June Huh in bringing Hodge theory to combinatorics and his proof of various mathematical conjectures. Uncover the significance of the four-color theorem, co
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Approximability and Proof Complexity in Constraint Satisfaction Problems
Explore the realm of constraint satisfaction problems, from Max-Cut to Unique Games, delving into approximation algorithms and NP-hardness. Dive into open questions surrounding the Unique Games Conjecture, the hardness of Max-Cut approximations, and the quest to approximate the Balanced Separator pr
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MathCheck: A Math Assistant Combining SAT with Computer Algebra Systems
MathCheck is a project focused on incorporating algorithms from Computer Algebra Systems (CAS) with SAT solvers to enhance problem-solving capabilities in math, such as counterexample construction and bug finding. The goal is to design an easily extensible system with a current focus on graph theory
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Understanding Daubert Standard in Expert Testimony: A Legal Analysis
Explore the Daubert standard for expert testimony, focusing on the rules of admissibility, qualifications, reliability, and methodology. Learn how judges act as gatekeepers to prevent conjecture and speculation in court. Discover the importance of scientific foundation and peer review in expert opin
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Black-Box Separations in Quantum Commitment Protocols
Protocol analysis of non-interactive commitments in classical and quantum settings, including discussions on OWF, NIC, PRS, and quantum communication implications. The results based on the Polynomial Compatibility Conjecture showcase advancements in post-quantum OWF and NIC scenarios.
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Middle Levels Gray Codes: Loopless Generation Algorithms and Conjecture
Combinatorial Gray codes involve generating combinatorial objects with minimal differences between consecutive objects. The Middle Levels Conjecture focuses on cyclically generating ground set subsets with specific characteristics. This conjecture has led to significant theoretical and experimental
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Understanding Complexity Measures of Boolean Functions
This work delves into the intricate world of complexity measures for Boolean functions, exploring concepts such as certificate complexity, decision tree depth, sensitivity, block sensitivity, PRAM complexity, and more. It sheds light on the relationships among different complexity measures and provi
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Addenda to Casas-Alvero Conjecture: Polynomial Derivatives and Common Roots.
In this research work, the Casas-Alvero conjecture is explored, focusing on polynomials and their derivatives, and the common roots they share. The study delves into the normalization of roots under various transformations, using p-adic methods and Gröbner bases. Noteworthy findings include implica
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Orthogonal Vectors Conjecture and Sparse Graph Properties Workshop
Exploring the computational complexity of low-polynomial-time problems, this workshop delves into the Orthogonal Vectors Problem and its conjectures. It introduces concepts like the Sparse OV Problem, first-order graph properties, and model checking in graphs. Discussing the hardness of problems rel
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Insights on Linear Programming and Pivoting Rules in Optimization
Linear programming involves maximizing a linear objective function within a set of linear constraints to find the optimal point in a polytope. The simplex algorithm, introduced by Dantzig in 1947, navigates through vertices to reach the optimal solution. Deterministic and randomized pivoting rules,
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Implementing Goldbach's Conjecture in Programming: A Practical Guide
Exploring the famous Goldbach's Conjecture in programming, this content provides a step-by-step approach to implementing a checker for the theorem. From outlining the necessary parts to structuring code and iterating through prime numbers, this guide offers a hands-on perspective on tackling this ma
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