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Formally, the complexity class MA is the set of decision problems that can be decided in polynomial time by an Arthur – Merlin protocol where Merlin's only move precedes any computation by Arthur.

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## Some Related Sentences

Formally and complexity

__Formally__

**,**a

**decision**problem

**is**P-complete ( complete for

**the**

__complexity__

**class**P ) if it

**is**

**in**P and

**that**every problem

**in**P

**can**

**be**reduced to it

**by**using

**an**appropriate reduction

**.**

__Formally__

**,**

**the**process

**is**one

**of**progressive development

**,**divided into three stages

**of**increasingly

__complexity__

**.**

Formally and class

__Formally__

**,**this means

**that**

**the**probability density functions or probability mass functions

**in**this

__class__have

**the**form

__Formally__

**,**this sharing

**of**dynamics

**is**referred to as universality

**,**and systems with precisely

**the**same critical exponents are said to belong to

**the**same universality

__class__

**.**

__Formally__it

**is**precisely

**in**allowing quantification over

__class__variables α

**,**β

**,**etc.,

**that**we assume a range

**of**values for these variables to refer to

**.**

__Formally__

**,**it may even

**be**taken back to Marx's earliest statements about a

__class__becoming conscious

**of**itself and developing a

__class__identity

**.**

__Formally__

**,**a frieze group

**is**a

__class__

**of**infinite discrete symmetry groups for patterns on a strip ( infinitely wide rectangle ), hence a

__class__

**of**groups

**of**isometries

**of**

**the**plane

**,**or

**of**a strip

**.**

__Formally__established

**in**1921

**,**

**the**Profintern was intended to act as a counterweight to

**the**influence

**of**

**the**so-called " Amsterdam International ,"

**the**Social Democratic International Federation

**of**Trade Unions

**,**

**an**organization branded as

__class__collaborationist and

**an**impediment to revolution

**by**

**the**Comintern

**.**

__Formally__

**,**a biased graph Ω

**is**a pair ( G

**,**B )

**where**B

**is**a linear

__class__

**of**circles ; this

**by**definition

**is**a

__class__

**of**circles

**that**satisfies

**the**theta-graph property mentioned above

**.**

Formally and is

__Formally__organized vocational programs supported

**by**federal funds allow high school students to gain experience

**in**a field

**of**work which

__is__likely to lead to a full-time job on graduation

**.**

__Formally__

**,**

**the**

**set**

**of**all context-free languages

__is__identical to

**the**

**set**

**of**languages accepted

**by**pushdown automata ( PDA ).

More rigorously

**,****the**divergence**of**a vector field F at a point p__is__defined as**the**limit**of****the**net flow**of**F across**the**smooth boundary**of**a three dimensional region V divided**by****the**volume**of**V as V shrinks to p**.**__Formally__**,**__Formally__

**,**

**the**base

__is__known as Naval Support Facility Diego Garcia (

**the**US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia (

**the**UK's term ).

__Formally__

**,**there

__is__a clear distinction: " DFT " refers to a mathematical transformation or function

**,**regardless

**of**how it

__is__computed

**,**whereas " FFT " refers to a specific family

**of**algorithms for computing DFTs

**.**

__Formally__

**,**oxidation state

__is__

**the**hypothetical charge

**that**

**an**atom would have if all bonds to atoms

**of**different elements were 100 % ionic

**.**

__Formally__

**,**

**an**inner product space

__is__a vector space V over

**the**field together with

**an**inner product

**,**i

**.**e., with a map

__Formally__

**,**if M

__is__a

**set**

**,**

**the**identity function f on M

__is__defined to

**be**

**that**function with domain and codomain M which satisfies

*

__Formally__**,**when working over**the**reals**,**as here**,**this__is__accomplished**by**considering**the**limit as ε → 0 ; but**the**" infinitesimal " language generalizes directly to Lie groups over general rings**.**__Formally__

**,**a profinite group

__is__a Hausdorff

**,**compact

**,**and totally disconnected topological group:

**that**

__is__

**,**a topological group

**that**

__is__also a Stone space

**.**

__Formally__

**,**a frame

__is__defined to

**be**a lattice L

**in**which finite meets distribute over arbitrary joins

**,**i

**.**e

**.**every ( even infinite ) subset

Formally and set

__Formally__speaking

**,**a collation method typically defines a total order on a

__set__

**of**possible identifiers

**,**called sort keys

**,**which consequently produces a total preorder on

**the**

__set__

**of**items

**of**information ( items with

**the**same identifier are not placed

**in**

**any**defined order ).

__Formally__

**,**according to

**the**Constitution

**,**citizens

**of**Turkmenistan have

**the**right to

__set__up political parties and other public associations

**,**acting within

**the**framework

**of**

**the**Constitution and laws

**,**and public associations and groups

**of**citizens have

**the**right to nominate their candidates

**in**accordance with

**the**election law

**.**

__Formally__

**,**

**the**convex hull may

**be**defined as

**the**intersection

**of**all convex sets containing X or as

**the**

__set__

**of**all convex combinations

**of**points

**in**X

**.**

__Formally__

**,**

**the**discrete cosine transform

**is**a linear

**,**invertible function (

**where**denotes

**the**

__set__

**of**real numbers ), or equivalently

**an**invertible N × N square matrix

**.**

__Formally__

**,**we are given a

__set__

**of**hypotheses and a

__set__

**of**manifestations ; they are related

**by**

**the**domain knowledge

**,**represented

**by**a function

**that**takes as

**an**argument a

__set__

**of**hypotheses and gives as a result

**the**corresponding

__set__

**of**manifestations

**.**

__Formally__

**,**a function ƒ

**is**real analytic on

**an**open

__set__D

**in**

**the**real line if for

**any**x < sub > 0 </ sub >

**in**D one

**can**write

__Formally__

**,**

**the**movement

**is**a rondo

**that**acts as

**the**theme for a

__set__

**of**eight variations

**,**capped off

**by**a dramatic coda

**.**

__Formally__

**,**

**the**discrete sine transform

**is**a linear

**,**invertible function F: R < sup > N </ sup > < tt >-></ tt > R < sup > N </ sup > (

**where**R denotes

**the**

__set__

**of**real numbers ), or equivalently

**an**N × N square matrix

**.**

__Formally__

**,**

**the**discrete Hartley transform

**is**a linear

**,**invertible function H: R < sup > n </ sup > < tt >-></ tt > R < sup > n </ sup > (

**where**R denotes

**the**

__set__

**of**real numbers ).

__Formally__

**,**a constraint satisfaction problem

**is**defined as a triple

**,**

**where**

**is**a

__set__

**of**variables

**,**

**is**a domain

**of**values

**,**and

**is**a

__set__

**of**constraints

**.**

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