Note on the Lower Bounds of Bimachines

TL;DR

This paper discusses the limitations of bimachines, showing that some functional transducers with linear states require exponentially many states in any equivalent bimachine.

Contribution

It establishes a lower bound on the state complexity of bimachines for certain classes of functional transducers, highlighting a fundamental limitation.

Findings

Some functional transducers with O(n) states need Θ(2^n) states in any bimachine

Demonstrates an exponential lower bound on bimachine state complexity

Highlights a significant gap between transducer and bimachine state requirements

Abstract

This is a brief note on the lower bound of bimachines. Particularly, we report that there is a class of functional transducers with $O(n)$ states that do not admit a bimachine with fewer than $\Theta(2^n)$ states.