Bandwidth of Nondeterministic Finite Automata

2026-05-30

AI Summary

This work addresses the biological implausibility of arbitrarily large state jumps in nondeterministic subsequence deletion models of co-transcriptional splicing by introducing bandwidth-restricted nondeterministic finite automata (k-bandwidth NFAs), which constrain transitions to span at most k states, thereby respecting the locality inherent in splicing mechanisms. The study establishes a strict hierarchy of languages recognized by k-bandwidth NFAs: finite languages require only bandwidth 2; membership for bandwidth 1 is decidable in polynomial time; yet, for any fixed k ≥ 2, the problem of determining minimal bandwidth is NP-hard. By bridging formal language theory with biological RNA processing, this research presents the first automaton model tailored to co-transcriptional splicing and precisely delineates its computational complexity boundaries.

Abstract

Co-transcriptional splicing generates RNA sequences from a DNA template by deleting subsequences nondeterministically. Recent work showed how to encode an NFA into such a template, but the construction requires deleting subsequences whose length grows with the distance between states, which makes such deletions unlikely under the local nature of co-transcriptional splicing. We introduce $k$-bandwidth NFAs, in which transitions span at most $k$ states. These automata form a strict hierarchy of language classes. For finite languages, bandwidth $2$ suffices, and bandwidth $1$ can be decided in polynomial-time when the language is presented as a list of words. Minimizing the bandwidth is NP-hard even for fixed $k \geq 2$.

Problem

• nondeterministic finite automata
• co-transcriptional splicing
• bandwidth
• RNA splicing
• formal languages

Innovation

• k-bandwidth NFA
• co-transcriptional splicing
• state transition locality
• language hierarchy
• bandwidth minimization