The State Complexity of Alternating Automata

Author: Nathanaël Fijalkow

Paper Information

Title:The State Complexity of Alternating Automata
Authors:Nathanaël Fijalkow
Proceedings:LICS PDF files
Editors: Anuj Dawar and Erich Grädel
Keywords:Automata Theory, State Complexity, Lower Bounds, Alternating Automata, Hierarchy Theorem, Prime Numbers

ABSTRACT. This paper studies the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. We look at alternating automata as introduced by Chandra, Kozen and Stockmeyer: such machines run independent computations on the word and gather their answers through boolean combinations.

We devise a lower bound technique relying on boundedly generated lattices of languages, and give two applications of this technique. The first is a hierarchy theorem, stating that there are languages of arbitrarily high polynomial alternating state complexity, and the second is a linear lower bound on the alternating state complexity of the prime numbers written in binary. This second result strengthens a result of Hartmanis and Shank from 1968, which implies an exponentially worse lower bound for the same model.

Talk:Jul 09 16:40 (Session 51D)