arXiv subjects

Ivan Baburin

Publications and source records attributed to Ivan Baburin.

4 recordsLinked to original sources

arXiv2025

Universality Frontier for Asynchronous Cellular Automata

In this work, we investigate the computational aspects of asynchronous cellular automata (ACAs), a modification of cellular automata in which cells update independently, following an asynchronous schedule. We introduce flip automata networks (FAN), a simple modification of automata networks that remain robust under any asynchronous update schedule. We show that asynchronous automata can efficiently simulate their synchronous counterparts with a linear memory overhead, which improves upon the previously established quadratic bound. Additionally, we address the universality gap for (a)synchronous cellular automata -- the boundary separating universal and non-universal automata, which is still not fully understood. We tighten this boundary by proving that all one-way asynchronous automata lack universal computational power. Conversely, we establish the existence of a universal 6-state first-neighbor automaton in one dimension and a 3-state von Neumann automaton in two dimensions, which represent the smallest known universal constructions to date.

cs.FL↗

arXiv2024

A Close Analysis of the Subset Construction

Given a nondeterministic finite-state automaton (NFA), we aim to estimate the size of an equivalent deterministic finite-state automaton (DFA). We demonstrate that computing the state complexity of an NFA within polynomial precision is PSPACE-hard. Furthermore, we also demonstrate that it is PSPACE-hard to decide whether the classical subset construction will yield an equivalent DFA with an exponential increase in the number of states. This result implies that making any a prior estimate of the running time of the subset construction is inherently difficult. To address this, and to enable forecasting of such exponential blow-up in certain special cases, we introduce the notion of subset complexity, which provides an upper bound on the size of the DFA produced by the subset construction. We show that the subset complexity can be efficiently bounded above using the cyclicity and rank of the transition matrices of the NFA. This yields a sufficient condition for identifying NFAs that can be efficiently determinized via the subset construction.

cs.FL↗

arXiv2023

An Analysis of On-the-fly Determinization of Finite-state Automata

In this paper we establish an abstraction of on-the-fly determinization of finite-state automata using transition monoids and demonstrate how it can be applied to bound the asymptotics. We present algebraic and combinatorial properties that are sufficient for a polynomial state complexity of the deterministic automaton constructed on-the-fly. A special case of our findings is that automata with many non-deterministic transitions almost always admit a determinization of polynomial complexity. Furthermore, we extend our ideas to weighted finite-state automata.

cs.FL↗

arXiv2023

Hierarchical Block Low-rank Approximation of Cavity Radiation

In this paper we examine the use of low-rank approximations for the handling of radiation boundary conditions in a transient heat equation given a cavity radiation setting. The finite element discretization that arises from cavity radiation is well known to be dense, which poses difficulties for efficiency and scalability of solvers. Here we consider a special treatment of the cavity radiation discretization using a block low-rank approximation combined with hierarchical matrices. We provide an overview of the methodology and discusses techniques that can be used to improve efficiency within the framework of hierarchical matrices, including the usage of the approximate cross approximation (ACA) method. We provide a number of numerical results that demonstrate the accuracy and efficiency of the approach in practical problems, and demonstrate significant speedup and memory reduction compared to the more conventional "dense matrix" approach.

math.NA↗