#### TWO ALGORITHMIC PROBLEMS IN LATTICE THEORY

John Harding

Dept. of Mathematical Sciences, NMSU

jharding@nmsu.edu
It is easy to determine whether an equation such as x^2 yx = y x^3 must hold in all abelian groups --- if each symbol occurs the same number of times on the left as the right,
then it must always hold, otherwise it doesn't. This is called a solution to the free word problem for abelian groups.
For any kind of algebra, one may ask whether there is an efficient algorithm to decide the free word problem,
or even whether the free word problem is decidable at all.
We discuss the free word problem for lattices and two problems that arise in this area.
One problem asks for an algorithm, the other asks a question whose solution may be gained by application of existing algorithms (perhaps in novel way).