Unification as defined by Robinson [Rob65] is one of two dual concepts, the
other is called anti-unification. These concepts are presented in terms of
category theory and concepts from algebra.
The unification algorithm from [Rob65] is presented and I argue that it has
a worst-case exponential runtime. Modifying this algorithm, I remove one
source of exponential runtime. Paterson & Wegman showed in [PW78] that
a linear unification algorithm exists. I present this algorithm and compare
actual runtimes for all algorithms.
I then present an algorithm for anti-unification by Plotkin [Plo69] and
Reynolds [Rey69]. This algorithm has O(n2) runtime. Two new linear algorithms,
based on the same principle as the linear Paterson & Wegman
unification algorithm, are presented. Finally a parallel anti-unification algorithm
from [KMPP88] is presented.
This report investigates various ways of doing nonlinear optimization with
constraints. Methods used include the penalty method, the simplex method,
pattern search, Newton-Raphson, and Hestenes-Powell.
Testing each method an optimal linear least squares problem is used. Programs in Pascal are
provided. In addition parts of the mathematics involved is presented.
I live in Denmark. I write programs for websites and computers. 1 wife, 2 kids, no rabbit, 3 cats.