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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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## Some Related Sentences

Formally and satisfaction

**a**< sub > i </ sub >,

**a**< sub > i + 1 </ sub >,..., which

**is**

**a**suffix

**of**w

**.**

__Formally__

**,**the

__satisfaction__relation between

**a**word

**and**an LTL formula

**is**

**defined**

**as**follows:

__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 problem

__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__

**,**

**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__

**,**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 defined

__Formally__

**,**

**as**per the 2002 Memorandum

**of**Understanding between the BSI

**and**the United Kingdom Government

**,**British Standards are

__defined__

**as**:

__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__

**,**these reside in

**a**complex separable Hilbert space-variously called the " state space " or the " associated Hilbert space "

**of**the system-that

**is**well

__defined__up to

**a**complex number

**of**norm 1 ( the phase factor ).

Limits

**and**colimits in**a**category C are__defined__by means**of**diagrams in C**.**__Formally__**,****a**diagram**of**type J in C**is****a**functor from J to C:__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__

**,**

**a**unique factorization

**domain**

**is**

__defined__to be an integral

**domain**R in which every non-zero

**and**non-unit x

**of**R can be written

**as**

**a**product ( including an empty product )

**of**irreducible elements p < sub > i </ sub >

**of**R

**and**

**a**unit u:

__Formally__

**,**bending modulus

**is**

__defined__

**as**the energy required to deform

**a**membrane from its intrinsic curvature to some other curvature

**.**

__Formally__

**,**the case

**where**only

**a**subset

**of**parameters

**is**

__defined__

**is**still

**a**composite hypothesis ; nonetheless

**,**the term point hypothesis

**is**often applied in such cases

**,**particularly

**where**the hypothesis test can be structured in such

**a**way that the distribution

**of**the test statistic ( the distribution under the null hypothesis ) does not depend on the parameters whose

**values**have not been specified under the point null hypothesis

**.**

__Formally__

**,**the index

**of**H in G

**is**

__defined__

**as**the number

**of**cosets

**of**H in G

**.**( The number

**of**left cosets

**of**H in G

**is**always equal to the number

**of**right cosets

**.**

__Formally__

**,**it

**is**

**a**norm

__defined__on the space

**of**bounded linear operators between two given normed vector spaces

**.**

__Formally__

**,**

**a**cardinal κ

**is**

__defined__to be weakly compact if it

**is**uncountable

**and**for every function f: < sup > 2 </ sup > →

__Formally__

**,**the sets

**of**free

**and**bound names

**of**

**a**process in π – calculus are

__defined__inductively

**as**follows

**.**

__Formally__

**,**an absolute coequalizer

**of**

**a**pair in

**a**category C

**is**

**a**coequalizer

**as**

__defined__above but with the added property that given any functor F ( Q ) together with F ( q )

**is**the coequalizer

**of**F ( f )

**and**F ( g ) in the category D

**.**Split coequalizers are examples

**of**absolute coequalizers

**.**

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