Mathematics and statistics

PP (complexity)

PP, or probabilistic polynomial time, is a complexity class of decision problems accepted by probabilistic polynomial-time machines with probability greater than 1/2, defined by John Gill in 1977.

PPA (complexity)

PPA, short for Polynomial Parity Argument, is a complexity class of total search problems within TFNP, introduced by Christos Papadimitriou in 1994, whose totality rests on undirected parity.

Practical number

A practical number is a positive integer such that every integer up to n is a sum of distinct divisors of n; 12 is the classic example.

Precalculus, also known as pre-calc or Advanced Algebra and Trigonometry, is the secondary and early college mathematics course covering algebra, trigonometry, and function theory, typically ending with limits, to prepare students for calculus.

Precision and recall

Precision and recall are two paired measures of the performance of a binary classifier or retrieval system, often combined into the F1 score and generally trading off against each other.

Preconditioner

A preconditioner is a matrix, or any linear operator, applied to a linear system to give it better spectral properties so iterative methods converge faster.

Predicate abstraction

Predicate abstraction is a formal verification technique that converts infinite-state programs into finite Boolean models over chosen predicates, underpinning software model checkers such as SLAM, Blast, and CPAchecker.

Predictable process

A predictable process is a stochastic process whose value is known just before each time: it is measurable with respect to information available strictly before that time.

Prediction interval

A prediction interval is a statistical interval estimate that brackets a single future observation with a stated probability, and is wider than a confidence interval.

Prediction of stochastic processes

Prediction of stochastic processes is the estimation of a random process's future values from its observed past under a mean-square-error criterion, initiated independently by Kolmogorov and Wiener.

Prediction-powered inference

Prediction-powered inference (PPI) is a statistical framework that combines machine-learning predictions on a large unlabeled dataset with a small gold-standard labeled set, yielding valid confidence intervals and p-values.

Predictive maintenance

Predictive maintenance (PdM) is a maintenance strategy that uses condition monitoring and data analysis to predict failures, so maintenance happens just in time rather than on a fixed schedule.

Predictive modelling

Predictive modeling, also called predictive models, applies statistical models or data-mining algorithms to data to predict new or future observations, unlike explanatory modeling, which targets causal relationships.

Predictor–corrector method

A predictor–corrector method is a numerical method for solving ordinary differential equations: an explicit formula predicts the next step, and a more accurate implicit formula corrects it.

Predual and ultraweak topology of von Neumann algebras

The predual of a von Neumann algebra is the Banach space whose dual it is, unique up to isometric isomorphism; it determines the ultraweak topology and normal maps.

Preference elicitation

Preference elicitation is the set of methods for turning a person's choices and trade-offs into a formal preference representation, such as utility-function parameters or attribute weights.

Preferential attachment

Preferential attachment is a network growth rule where new links attach to already well-connected vertices, explaining the scale-free structure of citation networks and the web.

Prefix code

A prefix code, also called a prefix-free or instantaneous code, is a variable-length code in which no codeword is a prefix of another, allowing unambiguous decoding without separators.

Pregeometry (model theory)

In model theory, a pregeometry, known in combinatorics as a matroid, is a set with a finitary closure operator satisfying the Steinitz exchange property, abstracting linear span and algebraic closure.

Prenex normal form

Prenex normal form (PNF), also called prenex form, is a standard form for first-order logic formulas in which all quantifiers are gathered at the front, before a quantifier-free matrix.

Preorder

A preorder, also called a quasiorder, is a binary relation on a set that is reflexive and transitive, and a partial order if also antisymmetric.

Presburger arithmetic

Presburger arithmetic is the first-order theory of the integers with addition and order, omitting multiplication; Mojżesz Presburger proved it decidable in 1929, while adding multiplication yields undecidability.

Presheaf with transfers

A presheaf with transfers is a contravariant additive functor from smooth schemes with finite correspondences to abelian groups, used by Voevodsky to build motivic cohomology.

Primality test

A primality test (prime testing) is an algorithm deciding whether an integer is prime or composite; Miller–Rabin is the practical workhorse, and AKS proved in 2002 a deterministic polynomial-time test exists.

Primary decomposition

Primary decomposition represents an ideal of a commutative ring as an intersection of primary ideals, generalizing prime factorization of integers; it was proved for Noetherian rings by Emmy Noether.

Primary endpoint

A primary endpoint is the main outcome of a clinical trial, chosen in advance, on which its hypothesis is tested and regulatory approval is judged.

Primary ideal

A primary ideal is a proper ideal of a commutative ring such that a product in it forces one factor, or a power of the other, into it.

Prime (symbol)

The prime (′), also called the prime mark, is a typographic symbol marking minutes of arc, feet, and the derivative in calculus, attributed to Lagrange.

Prime and irreducible elements

Prime and irreducible elements are related notions in ring theory: every prime element of an integral domain is irreducible, while the converse fails, as in Z[√−5].