**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.