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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.

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## Some Related Sentences

Formally and decision

__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

**.**

__Formally__system networks correspond

**to**type lattices

**in**formal lattice theory

**,**although they are occasionally erroneously mistaken

**for**flowcharts or directed

__decision__trees

**.**

__Formally__

**,**

**the**power

**to**appoint members of

**the**Vorstand lies with

**the**Aufsichtsrat

**,**which

**can**appoint members with

**a**two-thirds majority vote of approval

**,**or

**a**simple majority

**if**multiple rounds of voting are required

**in**order

**to**reach

**a**

__decision__

**.**

Formally and problem

__Formally__

**,**

**a**transductive support vector machine

**is**defined

**by**

**the**following primal optimization

__problem__:

__Formally__

**,**

**the**

__problem__of supervised pattern recognition

**can**

**be**stated as follows: Given

**an**unknown function

**(**

**the**ground truth

**)**

**that**maps input instances

**to**output labels

**,**along with training data assumed

**to**represent accurate examples of

**the**mapping

**,**produce

**a**function

**that**approximates as closely as possible

**the**correct mapping

**.**

__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

**.**

__Formally__

**,**

**the**

__problem__

**can**

**be**stated as follows: given

**a**desired property

**,**expressed as

**a**temporal logic formula p

**,**

**and**

**a**structure M with initial state s

**,**decide

**if**

**.**

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__

**,**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__

**,**

**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 complete

__Formally__

**,**

**if**T

**is**

**a**

__complete__sufficient statistic

**for**θ

**and**E

**(**g

**(**T )) = τ

**(**θ

**)**then g

**(**T

**)**

**is**

**the**minimum-variance unbiased estimator

**(**MVUE

**)**of τ

**(**θ ).

__Formally__

**,**

**an**iterated function system

**is**

**a**finite set of contraction mappings on

**a**

__complete__metric space

**.**

__Formally__

**,**

**a**partially ordered set

**(**

**P**

**,**≤)

**is**bounded

__complete__

**if**

**the**following holds

**for**any subset S of

**P**:

__Formally__

**,**

**a**market

**is**

__complete__with respect

**to**

**a**trading strategy

**,**

**,**

**if**there exists

**a**self-financing trading strategy

**,**such

**that**at any time

**,**

**the**returns of

**the**two strategies

**,**

**and**are equal

**.**

Formally and for

__Formally__neutral

**and**reluctant

**to**become involved with

**the**great powers except as

**a**last resort

**,**Kuwait turned

**to**

**the**United States

**,**

**the**Soviet Union

**and**Britain

__for__naval protection of its tanker fleet after twenty-one ships were attacked

**in**

**the**gulf since late 1986

**.**

*

**,**see On__Formally__Undecidable Propositions of Principia Mathematica**and**Related Systems__for__details on English translations**.**__Formally__named " United Press Associations "

__for__incorporation

**and**legal purposes

**,**but publicly known

**and**identified as United Press or UP

**,**

**it**was created

**by**

**the**1907 uniting of three smaller news syndicates

**by**

**the**Midwest newspaper publisher E

**.**W

**.**Scripps

**.**

__Formally__stated

**,**

**the**FFT

**is**

**a**method

__for__computing

**the**discrete Fourier transform of

**a**sampled signal

**.**

__Formally__

**,**collective noun forms such as “

**a**group of people ” are represented

**by**second-order variables

**,**or

**by**first-order variables standing

__for__sets

**(**which are well-defined objects

**in**mathematics

**and**logic ).

__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**

**.**

If R

**is****a**ring**,**let R denote**the**ring of polynomials**in****the**indeterminate X over R**.**Hilbert proved**that****if**R**is**" not too large ",**in****the**sense**that****if**R**is**Noetherian**,****the**same must**be**true__for__R**.**__Formally__**,**__Formally__

**,**

**the**sequence of partial sums of some infinite summation converges

**if**

__for__

**every**fixed power of X

**the**coefficient stabilizes: there

**is**

**a**point beyond which all further partial sums have

**the**same coefficient

**.**

__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__

**,**

**an**elliptic function

**is**

**a**function meromorphic on

__for__which there exist two non-zero complex numbers

**and**with

**(**

**in**other words

**,**not parallel ), such

**that**

**and**

__for__all

**.**

__Formally__

**,**

**if**

**is**

**an**open subset of

**the**complex plane

**,**

**a**point of

**,**

**and**

**is**

**a**holomorphic function

**,**then

**is**called

**a**removable singularity

__for__

**if**there exists

**a**holomorphic function which coincides with on

**.**

__Formally__

**,**we have

__for__

**the**approximation

**to**

**the**full solution A

**,**

**a**series

**in**

**the**small parameter

**(**here called ), like

**the**following:

In late 1900s

**the**day**that**of**the**City was founded**is**Jakin School**is****a**Private School**is**__Formally__Part of Jakin School Board was Grades One through Twelve there**is**no Football field on this school**.**In 1966 When Jakin School was Closed were Sent**to**Blakely-Union Elementary**,**Junior High**,****and**High School**(**which later Became Early County High**,**Middle**,****and**Elementary School ). while Carver school was built__for__African-American students grades One through Twelve**.**although late 1960s when Carver school was closed along with Kestler School was based**in**Damascus were sent**to**Washington High & Elementary at Blakely**.**In addition**to**small farm agriculture**,**Jakin's early economic growth resulted from turpentine**.**__Formally__

**,**cl

**(**S

**)**denotes

**the**smallest subset Y of M

**that**contains S such

**that**

__for__each reaction

**(**A

**,**B

**)**

__Formally__

**,**

**it**

**is**

**a**coalition of U

**.**S

**.**

**and**European CEOs

**,**largely from transnational corporations

**,**launched at

**the**urging of former United States Secretary of Commerce Ron Brown

**in**Seville

**(**Spain

**)**

**in**late 1995 at

**a**conference attended

**by**CEOs from more than 100 U

**.**S

**.**

**and**EU companies

**and**

**by**top government representatives led

**by**

**the**Commissioners

__for__Trade

**and**Industry

**and**

**by**

**the**U

**.**S

**.**Secretary of Commerce

**.**

__Formally__

**,**

**a**government would lay out its reasons

__for__going

**to**war

**,**as well as its intentions

**in**prosecuting

**it**

**and**

**the**steps

**that**might

**be**taken

**to**avert

**it**

**.**

__Formally__

**,**

**the**movement

**is**

**a**rondo

**that**acts as

**the**theme

__for__

**a**set of eight variations

**,**capped off

**by**

**a**dramatic coda

**.**

**(**

__Formally__speaking

**,**this then satisfies

**the**premises of

**an**axiom of well-founded induction

**,**which asserts

**that**these two conditions are sufficient

__for__

**the**proposition

**to**hold

__for__all x

**.**

__Formally__

**,**

**the**motion merely calls on parliament

**to**thank

**the**monarch or viceroy

__for__

**the**speech via

**an**Address

**in**Reply

**.**

; Electronics:

__Formally__**a**fixture**in**radio shacks**,**now used__for__assembly**and**repair of all sorts of electronic equipment including communication**,**computer**,****and**home entertainment items**.**
It has been leased from

**the**National Trust since 1974**by****the**Somerset Wildlife Trust**(**__Formally__Somerset Trust__for__Nature Conservation**)****and****is**run as**a**nature reserve**and**visitor centre**.**0.193 seconds.