treeProbability

<code>treeProbability()</code> returns the path
 probability of generating the derivation tree <code>tree</code> 
 by the context-free grammar <code>G</code>. 
 The probability is exact, if the grammar is not ambiguous and
 if the grammar does not contain redundant rules.

Derivation tree operations are needed for implementing
grammar-based genetic programming and grammatical evolution:
Generating a random derivation trees of a context-free grammar
of bounded depth, decoding a derivation tree,
choosing a random node in a derivation tree,
extracting a tree whose root is a specified node, and
inserting a subtree into a derivation tree at a specified node.
These operations are necessary for the initialization and
for decoders of a random population of programs,
as well as for implementing crossover and mutation operators.
Depth-bounds are guaranteed by switching to a grammar
without recursive production rules.
For executing the examples, the package 'BNF' is needed.
The basic tree operations for generating, extracting, and
inserting derivation trees as well as the conditions
for guaranteeing complete derivation trees have been
presented in Geyer-Schulz (1997, ISBN:978-3-7908-0830-X).
The use of random integer vectors for the generation
of derivation trees has been introduced in
Ryan, C., Collins, J. J., and O'Neill, M. (1998)
<doi:10.1007/BFb0055930> for grammatical evolution.

Andreas Geyer-Schulz

xegaDerivationTrees

Generating and Manipulating Derivation Trees

treeProbability function

<dl><dt>tree</dt>
<dd>Derivation tree.</dd>
<dt>G</dt>
<dd>A context-free grammar.</dd></dl>

Arguments

The (path) probability of generating tree by grammar G. — treeProbability

<dl>

<dt>tree</dt>
<dd>Derivation tree.</dd>


<dt>G</dt>
<dd>A context-free grammar.</dd>

</dl>

treeProbability: The (path) probability of generating `tree` by grammar `G`.

Description

Usage

Value

Arguments

See Also

Examples