TL;DR
This paper introduces a novel algorithm for the star height problem by reducing it to a Gale-Stewart game with an -regular winning condition, advancing automata theory and decision procedures.
Contribution
It presents a new approach to the limitedness problem by formulating it as a Gale-Stewart game, offering a different algorithm for automata with counters.
Findings
The new algorithm effectively decides the star height problem.
Reduction to Gale-Stewart games simplifies the limitedness problem.
The approach connects automata theory with game-theoretic methods.
Abstract
This paper proposes a new algorithm deciding the star height problem. As shown by Kirsten, the star height problem reduces to a problem concerning automata with counters, called limitedness. The new contribution is a different algorithm for the limitedness problem, which reduces it to solving a Gale-Stewart game with an {\omega}-regular winning condition.
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Taxonomy
Topicssemigroups and automata theory · Logic, programming, and type systems · Formal Methods in Verification