Re: CYK & Context-Free Expressions

On May 1, 4:34 pm, Rock Brentwood <markw...@xxxxxxxxx> wrote:
On Apr 28, 12:58 pm, Tegiri Nenashi <TegiriNena...@xxxxxxxxx> wrote:
On Apr 28, 12:58 pm, Tegiri Nenashi <TegiriNena...@xxxxxxxxx> wrote:

BTW, speaking of trees, what is algebraic definition of tree
structure?

An element of a free magma.

A magma is an "algebra without axioms".

But before going to axioms, what operations are?

That is, it's an algebra
comprising a signature plus no axioms. So the magma generated freely
from a set X is the same thing as the term language over the same
signature with members of X as its indeterminates.

The archetypical example of a magma is the one which has just one
operator -- a binary operator. The elements of this magma are then
binary trees.

OK, binary tree is easy. I see that all you need is a binary operator
(say $) and binary trees as elements. Then x $ y is naturally a tree
with the first child being the tree branch x and the second y.

Can you generalize it to arbitrary tree wouthout being forced to
explode the set of operations?

.