- author = "John R. Woodward",
- title = "Invariance of Function Complexity under Primitive Recursive Functions",
- editor = "Pierre Collet and Marco Tomassini and Marc Ebner and Steven Gustafson and Anik\'o Ek\'art",
- booktitle = "Proceedings of the 9th European Conference on Genetic Programming",
- publisher = "Springer",
- series = "Lecture Notes in Computer Science",
- volume = "3905",
- year = "2006",
- address = "Budapest, Hungary",
- month = "10 - 12 " # apr,
- organisation = "EvoNet",
- keywords = "genetic algorithms, genetic programming",
- ISBN = "3-540-33143-3",
- pages = "310--319",
-
DOI = "
doi:10.1007/11729976_28",
- bibsource = "DBLP, http://dblp.uni-trier.de",
-
abstract = "Genetic Programming (GP) \cite{banzhaf:1997:book}
often uses a tree form of a graph to represent
solutions. An extension to this representation,
Automatically Defined Functions (ADFs) is to allow the
ability to express modules. In Woodward we proved that
the complexity of a function is independent of the
primitive set (function set and terminal set) if the
representation has the ability to express modules. This
is essentially due to the fact that if a representation
can express modules, then it can effectively define its
own primitives at a constant cost. This is reminiscent
of the result that the complexity of a bit string is
independent of the choice of Universal Turing Machine
(UTM) (within an additive constant), the constant
depending on the UTM but not on the function.
The representations typically used in GP are not capable of expressing recursion, however a few researchers have introduced recursion into their representations. These representations are then capable of expressing a wider classes of functions, for example the primitive recursive functions (PRFs). We prove that given two representations which express the PRFs (and only the PRFs), the complexity of a function with respect to either of these representations is invariant within an additive constant. This is in the same vein as the proof of the invariants of Kolmogorov complexity and the proof in Woodward.",
- notes = "Part of \cite{collet:2006:GP} EuroGP'2006 held in conjunction with EvoCOP2006 and EvoWorkshops2006",
