Related papers: Pebble Games and Algebraic Proof Systems
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of…
The Unique Games Conjecture (UGC) constitutes a highly dynamic subarea within computational complexity theory, intricately linked to the outstanding P versus NP problem. Despite multiple insightful results in the past few years, a proof for…
A pebbling move on a graph removes two pebbles from a vertex and adds one pebble to an adjacent vertex. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using pebbling moves. The optimal…
We prove the following strong hardness result for learning: Given a distribution of labeled examples from the hypercube such that there exists a monomial consistent with $(1-\eps)$ of the examples, it is NP-hard to find a halfspace that is…
A pebbling move refers to the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The goal of graph pebbling is: Given an initial distribution of pebbles, use pebbling moves to reach a specified goal…
The pebbling number of a graph $G$, $f(G)$, is the least $p$ such that, however $p$ pebbles are placed on the vertices of $G$, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and…
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege---yielding a semantic way to define a…
We prove that for every 3-player game with binary questions and answers and value $<1$, the value of the $n$-fold parallel repetition of the game decays polynomially fast to 0. That is, for every such game, there exists a constant $c>0$,…
We consider one-round games between a classical verifier and two provers who share entanglement. We show that when the constraints enforced by the verifier are `unique' constraints (i.e., permutations), the value of the game can be well…
We study zero-sum games, a variant of the classical combinatorial Subtraction games (studied for example in the monumental work "Winning Ways", by Berlekamp, Conway and Guy), called Cumulative Subtraction (CS). Two players alternate in…
Two selection games from the literature, $G_c(\mathcal O,\mathcal O)$ and $G_1(\mathcal O_{zd},\mathcal O)$, are known to characterize countable dimension among certain spaces. This paper studies their perfect- and limited-information…
Some variants of the (block) Gauss--Seidel iteration for the solution of linear systems with $M$-matrices in (block) Hessenberg form are discussed. Comparison results for the asymptotic convergence rate of some regular splittings are…
Counting logics with a bounded number of variables form one of the central concepts in descriptive complexity theory. Although they restrict the number of variables that a formula can contain, the variables can be nested within scopes of…
We study the refutation complexity of graph isomorphism in the tree-like resolution calculus. Tor\'an and W\"orz (TOCL 2023) showed that there is a resolution refutation of narrow width $k$ for two graphs if and only if they can be…
For current state-of-the-art DPLL SAT-solvers the two main bottlenecks are the amounts of time and memory used. In proof complexity, these resources correspond to the length and space of resolution proofs. There has been a long line of…
The foundations of classical Algebraic Geometry and Real Algebraic Geometry are the Nullstellensatz and Positivstellensatz. Over the last two decades the basic analogous theorems for matrix and operator theory (noncommutative variables)…
We reduce the problem of proving a "Boolean Unique Games Conjecture" (with gap 1-delta vs. 1-C*delta, for any C> 1, and sufficiently small delta>0) to the problem of proving a PCP Theorem for a certain non-unique game. In a previous work,…
Our objective in this project is three-fold, the first two covered in this paper. In tropical mathematics, as well as other mathematical theories involving semirings, when trying to formulate the tropical versions of classical algebraic…
The framework of graded semantics uses graded monads to capture behavioural equivalences of varying granularity, for example as found on the linear-time/branching-time spectrum, over general system types. We describe a generic…
Let $\mathcal{G}$ be a $k$-player game with value $<1$, whose query distribution is such that no marginal on $k-1$ players admits a non-trivial Abelian embedding. We show that for every $n\geq N$, the value of the $n$-fold parallel…