Kojelis (2022), Completing the Picture: Complexity of the Ackermann Fragment

<h4><a href="https://figshare.com/projects/Proceedings_of_the_ESSLLI_2022_Student_Session/144189" target="_blank">Proceedings of the ESSLLI 2022 Student Session</a></h4> <h2>Completing the Picture: Complexity of the Ackermann Fragment</h2> <h3>Daumantas Kojelis</h3> <p>We give a decision procedure for the satisfiability problem of the Ackermann fragment with equality, when the number of trailing existential quantifiers is bounded by some fixed integer <em>m</em>, and thus establish an ExpTime upper-bound. Taking the work of R. Jaakkoa into account, we conclude that any Ackermann (sub-)fragment must feature at least two leading as well as an unbounded number of trailing existential quantifiers to retain NExpTime-hardness.</p>