Computer Explorations of Fractals, Chaos,Complex Systems, and Adaptation

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 Glossary - P

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# P

Parallel/Parallelism     Many things happening at once.

Pattern Classification     A task that neural networks are often trained to do. Given some input pattern, the task is to make an accurate class assignment to the input. For example, classifying many images of letters to one of the twenty-six letters of the alphabet is a pattern classification task.

Payoff     In game theory, the amount that a player wins, given the player's and his opponent's actions.

Peano Curve     A fractal space-filling curve that can fill a plane even though it is a line of infinite length. Oddly enough, it has an integer fractal dimension of 2.

Perceptron     The simplest type of feedforward neural network. It has only inputs and outputs, i.e., no hidden layers.

Periodic     Refers to motion that goes through a finite number of regions, returns to a previous state, and repeats the same fixed pattern forever.

Perturbation     A slight nudge.

Phase Space     In this book, another name for state space. In the scientific literature, ``phase space'' is used to denote the space of motion in a dynamical system that moves in continuous time, while state space is often used for discrete time systems.

Phase Transition     In physics, a change from one state of matter to another. In dynamical systems theory, a change from one mode of behavior to another.

Planning     In computer science, and particularly in artificial intelligence, the task of determining a stepwise plan to accomplish a very specific task.

Polynomial     A function in which the output is the sum of terms that are the products of constant values and the input raised to some integer power. The polynomial of a polynomial is another polynomial. From a time complexity point of view, polynomials are well-behaved.

Post Production System     A model of computation that resembles a collection of ``if ... then'' rules and is capable of universal computation.

Predator-Prey System     An ecosystem in which one portion of the population consumes another. With three or more species, simple predator-prey interactions can lead to chaos and biological arms races. See also Lotka-Volterra system.

Prime Number     A natural number that can be evenly divided only by itself and 1.

Prisoner's Dilemma     A non-zero-sum game in which both players have incentive not to cooperate under any circumstances. Thus, the optimal game theory strategy of always defect has the paradoxical property that both players would have a higher payoff if they ignored the advice of game theory.

Probability     The likelihood that a random event will occur.

Program     An algorithm that is written in a programming language for execution on a physical computer.

Proof     A sequence of statements in which each subsequent statement is derivable from one of the previous statements or from an axiom of a formal system. The final statement of a proof is usually the theorem that one has set out to prove.

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