Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Genetic programming II: automatic discovery of reusable programs
Genetic programming II: automatic discovery of reusable programs
Genetic programming: an introduction: on the automatic evolution of computer programs and its applications
Logic in computer science: modelling and reasoning about systems
Logic in computer science: modelling and reasoning about systems
Machine Learning
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
A Representation for the Adaptive Generation of Simple Sequential Programs
Proceedings of the 1st International Conference on Genetic Algorithms
Proceedings of the European Conference on Genetic Programming
Finding Needles in Haystacks Is Not Hard with Neutrality
EuroGP '02 Proceedings of the 5th European Conference on Genetic Programming
Algorithm evolution with internal reinforcement for signal understanding
Algorithm evolution with internal reinforcement for signal understanding
Scaling of program fitness spaces
Evolutionary Computation
Toward simulated evolution of machine-language iteration
GECCO '96 Proceedings of the 1st annual conference on Genetic and evolutionary computation
Theoretical results in genetic programming: the next ten years?
Genetic Programming and Evolvable Machines
Genetic Programming and Evolvable Machines
Dilemmas in knowledge-based evolutionary computation for financial investing
Intelligent Decision Technologies
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Search spaces sampled by the process of Genetic Programming often consist of programs which can represent a function in many different ways. Thus, when the space is examined it is highly likely that different programs may be tested which represent the same function, which is an undesirable waste of resources. It is argued that, if a search space can be constructed where only unique representations of a function are permitted, then this will be more successful than employing multiple representations. When the search space consists of canonical representations it is called a canonical search space, and when Genetic Programming is applied to this search space, it is called Canonical Representation Genetic Programming. The challenge lies in constructing these search spaces. With some function sets this is a trivial task, and with some function sets this is impossible to achieve. With other function sets it is not clear how the goal can be achieved. In this paper, we specically examine the search space dened by the function set f+;À; _; =g and the terminal set fx; 1g. Drawing inspiration from the fundamental theorem of arithmetic, and results regarding the fundamental theorem of algebra, we construct a representation where each function that can be constructed with this primitive set has a unique representation. Abbreviations: Genetic Programming (GP), Genetic Algorithm (GA) , The No Free Lunch Theorem (NFL) Keywords: canonical representation, standard form, evolutionary computation, genetic programming, no free lunch, bias, symmetric functions, inverse functions, complementary functions, isomorphic representations.