Alejandro Guillen’s PhD defense

When:
May 1, 2018 @ 1:00 pm – May 1, 2018 @ 3:00 pm
2018-05-01T13:00:00-10:00
2018-05-01T15:00:00-10:00

Keller Hall 403

Dissertation draft (department only)

Alejandro Guillen, PhD defense, Tuesday, May 1, 2018, 12 noon,
        Title:  On the Generalized Word Problem for Finitely Presented Lattices”

        Abstract: The generalized word problem for a lattice L in a variety V asks if, given a finite
        subset Y of L and an element d in L, there is an algorithm to determine if d is in the subalgebra 
        of L generated by Y. Freese and Nation showed that the generalized word problem for finitely 
        presented lattices is solvable. This algorithm, though effective, is potentially exponential. We 
        present a polynomial time algorithm for the generalized word problem for free lattices, but 
        explain the complications which can arise when trying to adapt this algorithm to the generalized 
        word problem for finitely presented lattices. Though some of the results for free lattices are 
        shown to transfer over for finitely presented lattices, we give a potential syntactic algorithm 
        for the generalized word problem for finitely presented lattices. Finally, we give a new proof 
        that the generalized word problem for finitely presented lattices is solvable, relying on the 
        partial completion, PC(P), of a partially defined lattice P.