5 papers
Mastering NIM and Impartial Games with Weak Neural Networks: An AlphaZero-inspired Multi-Frame Approach
Søren Riis
We study impartial games under fixed-latency, fixed-scale quantised inference (FSQI). In this fixed-scale, bounded-range regime, we prove that inference is simulable by constant-de…
Term Coding and Dispersion: A Perfect-vs-Rate Complexity Dichotomy for Information Flow
Søren Riis
We introduce a new framework term coding for extremal problems in discrete mathematics and information flow, where one chooses interpretations of function symbols so as to maximise…
Term Coding: An Entropic Framework for Extremal Combinatorics and the Guessing--Number Sandwich Theorem
Søren Riis
Term Coding asks: given a finite system of term identities in variables, how large can its solution set be on an --element alphabet, when we are free to choose the inte…
Coin flipping and waiting times paradoxes: Why fair coins are exceptional
Søren Riis, Mike Paterson
Penney's Ante exhibits non-transitivity when two target strings race to appear in a shared stream of coin tosses. We study instead independent string races, where each player obser…
Term Coding for Extremal Combinatorics: Dispersion and Complexity Dichotomies
Søren Riis
We introduce \emph{Term Coding}, a novel framework for analysing extremal problems in discrete mathematics by encoding them as finite systems of \emph{term equations} (and, optiona…