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Formally, the set of all context-free languages is identical to the set of languages accepted by pushdown automata ( PDA ).

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## Some Related Sentences

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__

**,**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__

**,**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.

Formally and all

__Formally__

**,**oxidation state

**is**

**the**hypothetical charge that an atom would have if

__all__bonds

**to**atoms

**of**different elements were 100 % ionic.

__Formally__given

**to**bishop Philip

**of**Senj

**,**

**the**permission

**to**use

**the**Glagolitic liturgy

**(**

**the**Roman Rite conducted in Slavic language instead

**of**Latin

**,**not

**the**Byzantine rite ), actually extended

**to**

__all__Croatian lands

**,**mostly along

**the**Adriatic coast.

__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__

**,**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__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.

; 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.__Formally__

**,**a ring

**is**an Abelian group

**(**R

**,**+), together with a second binary operation * such that for

__all__a

**,**b and c in R

**,**

__Formally__speaking

**,**

**the**opportunity was extended

**to**

__all__classes

**to**join China's project on its Leninist terms.

__Formally__

**,**

__all__

**of**them are entitled El Camarón de la Isla con la colaboración especial de Paco de Lucía with

**the**exception

**of**Canastera.

__Formally__

**,**Liouville numbers and elementary numbers contain

**the**algebraic numbers

**,**and they include some but not

__all__transcendental numbers.

__Formally__titled ' An Act

**to**protect

__all__Persons in

**the**United States in their Civil Rights

**,**and furnish

**the**Means

**of**their vindication

**,**

**the**Act declared that people born in

**the**United States and not subject

**to**any foreign power are entitled

**to**be citizens

**,**without regard

**to**race

**,**color

**,**or previous condition

**of**slavery or involuntary servitude.

__Formally__

**,**

**the**game

**(**coalitional game ) consists

**of**a finite

**set**

**of**players

**,**called

**the**grand coalition

**,**and a characteristic function denotes

**the**power

**set**

**of**.</ ref > from

**the**

**set**

**of**

__all__possible coalitions

**of**players

**to**a

**set**

**of**payments that satisfies.

__Formally__

**,**rotational symmetry

**is**symmetry with respect

**to**some or

__all__rotations in m-dimensional Euclidean space.

__Formally__

**,**given two partially ordered sets

**(**S

**,**≤) and

**(**T

**,**≤), a function f: S → T

**is**an order-embedding if f

**is**both order-preserving and order-reflecting

**,**i. e. for

__all__x and y in S

**,**one has

__Formally__

**,**it

**is**

**the**solid figure formed

**by**

**the**locus

**of**

__all__straight line segments that join

**the**apex

**to**

**the**base.

__Formally__

**,**a cardinal number κ

**is**λ-unfoldable if and only if for every transitive model M

**of**cardinality κ

**of**ZFC-minus-power

**set**such that κ

**is**in M and M contains

__all__its sequences

**of**length less than κ

**,**there

**is**a non-trivial elementary embedding j

**of**M into a transitive model with

**the**critical point

**of**j being κ and j

**(**κ ) ≥ λ.

__Formally__

**,**given a finite

**set**X

**,**a collection C

**of**subsets

**of**X

**,**

__all__

**of**size n

**,**has Property B if we can partition X into two disjoint subsets Y and Z such that every

**set**in C meets both Y and Z.

__Formally__

**,**

__all__members

**of**

**the**Ghelani family are Hindu Leuva Patel

**,**although some have since chosen other religious beliefs.

__Formally__

**,**

**the**semantic

**of**influence diagram

**is**based on sequential construction

**of**nodes and arcs

**,**which implies a specification

**of**

__all__conditional independencies in

**the**diagram.

__Formally__

**,**a redistribution

**of**

__all__agents ’ initial endowments

**of**goods among

__all__agents in

**the**system

**is**a core allocation if no group

**of**agents can redistribute their own initial endowments among themselves so as

**to**improve

**the**satisfaction

**of**someone in

**the**group without impairing that

**of**any other in

**the**group.

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.

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__

**,**an inner product space

__is__a vector space V over

**the**field together with an inner product

**,**i. e., with a map

*

__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

0.159 seconds.