Separating Words from Every Start State with Horner Automata

TL;DR

This paper demonstrates how a specific family of deterministic finite automata can distinguish between binary strings of the same length from any start state, providing bounds that improve previous results.

Contribution

It introduces a novel application of Horner automata to separate strings from every start state and establishes tight bounds on the automata's size.

Findings

Established almost matching bounds on automata size

Improved the upper bound for DFA separation capabilities

Showed the effectiveness of Horner automata in string separation

Abstract

We show that a well-known family of deterministic finite automata can be used to distinguish distinct binary strings of the same length from every start state. Further, we establish almost matching lower and upper bounds on the number of states of such automata necessary to achieve this type of separation. Our result improves the currently best known linear upper bound for arbitrary DFA.