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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