Even harder pseudovariety membership problem

2026-06-19

AI Summary

This study investigates lower bounds on the computational complexity of the membership problem for pseudovarieties of finite semigroups. By integrating techniques from computational complexity theory and algebraic semigroup theory, the authors construct a specific finite semigroup whose pseudovariety membership problem is shown for the first time to be Difference P-hard. This result not only establishes a high level of complexity for pseudovariety membership within the Difference P hierarchy but also advances the understanding of the interplay between algebraic automata theory and computational complexity. The findings provide new theoretical evidence that enriches both fields and opens avenues for further research at their intersection.

Abstract

We present a finite semigroup whose pseudovariety has membership problem hard for the class \emph{Difference P}

Problem

• pseudovariety
• membership problem
• finite semigroup
• Difference P
• computational complexity

Innovation

• pseudovariety
• membership problem
• Difference P
• finite semigroup
• computational complexity