Near Optimal Hardness of Approximating 2-Prover-1-Round Games with Small Alphabet Size
For all ε > 0, it is NP-hard to distinguish whether a 2-Prover-1-Round projection game with alphabet size q has value at least 1-δ or at most 1/q^(1-ε), establishing a nearly optimal alphabet-to-soundness tradeoff for 2-query PCPs.
The Complexity of Normalizing Planar Lambda-Terms
The complexity of normalizing planar lambda-terms is still an open problem, despite recent attempts to show it is P-complete.
A Simplified Proof of the Constraint Satisfaction Problem Dichotomy Conjecture and the Existence of XY-Symmetric Operations
This paper provides a new simplified proof of the correctness of Zhuk's algorithm for solving all tractable Constraint Satisfaction Problems (CSPs) on a finite domain, and also proves that composing a weak near-unanimity operation of an odd arity can derive an n-ary operation that is symmetric on all two-element sets.
Getting Saturated with Induction in Theorem Proving Automation
Induction in saturation-based theorem proving automates inductive reasoning for first-order properties.