Deterministic Bandwidth of Finite Languages

2026-08-25

AI Summary

研究通过确定性有限自动机的带宽限制探讨了有限语言的结构特性，并提出了估计最小DFA带宽的上下界方法。

Abstract

Bandwidth restricts how far transitions can move under an ordering of the states in an automaton. While every finite language admits a bandwidth-2 NFA representation, the deterministic setting is substantially more restrictive. We investigate the bandwidth of partial DFAs accepting finite languages. We show that bounded bandwidth imposes strong structural restrictions on deterministic representations. We prove that there is an infinite hierarchy of classes of finite languages defined by deterministic bandwidth. As a special case of interest, we consider finite languages accepted by bandwidth-1 partial DFAs, and show that they admit a positional characterization, which yields a polynomial-time decision algorithm. We further study how the minimum DFA bandwidth can be estimated from the structure of the minimal DFA. We derive computable upper and lower bounds based on position-unfolding, and local growth of reachable residual states. These bounds can be computed efficiently and differ by at most a linear factor in the maximum word length. We also present a simple language family where the bounds match exactly.

Problem

• bandwidth
• finite languages
• deterministic finite automata
• structural restrictions
• estimation

Innovation

• Deterministic Bandwidth
• Finite Languages
• Positional Characterization
• Polynomial-time Decision Algorithm
• Bounds on DFA Bandwidth