6 papers
Universal Design and Physical Applications of Non-Uniform Cellular Automata on Translationally Invariant Lattices
Xiang-You Huang, Jie-Yu Zhang, Peng Ye
Motivated by recent theoretical and experimental advances, hyperbolic lattices have emerged as a paradigmatic setting in which geometry becomes an active organizing principle of qu…
Computing Real Numbers with Large-Population Protocols Having a Continuum of Equilibria
Xiang Huang, Rachel N. Huls
Bournez, Fraigniaud, and Koegler defined a number in [0,1] as computable by their Large-Population Protocol (LPP) model, if the proportion of agents in a set of marked states conve…
Asymptotic Divergences and Strong Dichotomy
Xiang Huang, Jack H. Lutz, Elvira Mayordomo +1
The Schnorr-Stimm dichotomy theorem concerns finite-state gamblers that bet on infinite sequences of symbols taken from a finite alphabet . In this paper we use the Kullback-Lei…
Algorithmic Randomness in Continuous-Time Markov Chains
Xiang Huang, Jack H. Lutz, Neil Lutz +1
In this paper we develop the elements of the theory of algorithmic randomness in continuous-time Markov chains (CTMCs). Our main contribution is a rigorous, useful notion of what i…
Real-Time Computability of Real Numbers by Chemical Reaction Networks
Xiang Huang, Titus H. Klinge, James I. Lathrop +2
We explore the class of real numbers that are computed in real time by deterministic chemical reaction networks that are integral in the sense that all their reaction rate constant…
Polynomial Space Randomness in Analysis
Xiang Huang, D. M. Stull
We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko's framework for polynomial…