Operational State Complexity of Block Languages

TL;DR

This paper investigates the state complexity of operations on block languages, a subclass of finite languages, using bitmap representations to analyze minimal automata and identify tighter bounds.

Contribution

It provides new, smaller bounds for the state complexity of operations on block languages, enhancing understanding beyond existing finite language results.

Findings

Smaller upper bounds for state complexity of block language operations.

Bitmap representations effectively analyze minimal automata.

Enhanced bounds improve automata design for block languages.

Abstract

In this paper we consider block languages, namely sets of words having the same length, and study the deterministic and nondeterministic state complexity of several operations on these languages. Being a subclass of finite languages, the upper bounds of operational state complexity known for finite languages apply for block languages as well. However, in several cases, smaller values were found. Block languages can be represented as bitmaps, which are a good tool to study their minimal finite automata and their operations, as we illustrate here.