aarjaneiro/planetmath huggingface dataset:
Boolean valued model

Boolean valued model

A traditional model of a

language

makes every

formula

of that language either true or false. A

Boolean valued model

is a

generalization

in which formulas take on any value in a

Boolean algebra

.

Specifically, a Boolean valued model of a

signature

Σ

over the language

ℒ

is a set

𝒜

together with a Boolean algebra

ℬ

. Then the objects of the model are the

functions

𝒜

ℬ

=

ℬ

→

𝒜

.

For any formula

ϕ

, we can assign a value

∥

ϕ

∥

from the Boolean algebra. For example, if

ℒ

is the language of

first order logic

, a typical recursive definition of

∥

ϕ

∥

might look something like this:

•

∥

f

=

g

∥

=

⋁

f

⁢

(

b

)

=

g

⁢

(

b

)

b

•

∥

¬

⁢

ϕ

∥

=

∥

ϕ

∥

′

•

∥

ϕ

∨

ψ

∥

=

∥

ϕ

∥

∨

∥

ψ

∥

•

∥

∃

x

⁢

ϕ

⁢

(

x

)

∥

=

⋁

f

∈

𝒜

ℬ

∥

ϕ

⁢

(

f

)

∥

Title

Boolean valued model

Canonical name

BooleanValuedModel

Date of creation

2013-03-22 12:51:08

Last modified on

2013-03-22 12:51:08

Owner

Henry (455)

Last modified by

Henry (455)

Numerical id

8

Author

Henry (455)

Entry type

Definition

Classification

msc 03C90

Classification

msc 03E40

Defines

Boolean-valued model

Generated on Thu Feb 8 19:56:43 2018 by

LaTeXML
model

model

Let

τ

be a

signature

and

φ

be a

sentence

over

τ

. A

structure

(

http://planetmath.org/Structure

)

ℳ

for

τ

is called a

model

of

φ

if

ℳ

⊧

φ

,

where

⊧

is the

satisfaction relation

. When

ℳ

⊧

φ

, we says that

φ

satisfies

ℳ

, or that

ℳ

is

satisfied by

φ

.

More generally, we say that a

τ

-structure

ℳ

is a

model

of a theory

T

over

τ

, if

ℳ

⊧

φ

for every

φ

∈

T

. When

ℳ

is a model of

T

, we say that

T

satisfies

ℳ

, or that

ℳ

is satisfied by

T

, and is written

ℳ

⊧

T

.

Example

. Let

τ

=

{

⋅

}

, where

⋅

is a

binary operation

symbol. Let

x

,

y

,

z

be

variables

and

T

=

{

∀

x

∀

y

∀

z

(

(

x

⋅

y

)

⋅

z

=

x

⋅

(

y

⋅

z

)

)

}

.

Then it is easy to see that any model of

T

is a

semigroup

, and vice versa.

Next, let

τ

′

=

τ

∪

{

e

}

, where

e

is a constant symbol, and

T

′

=

T

∪

{

∀

x

(

x

⋅

e

=

x

)

,

∀

x

∃

y

(

x

⋅

y

=

e

)

}

.

Then

G

is a model of

T

′

iff

G

is a group. Clearly any group is a model of

T

′

. To see the

converse

, let

G

be a model of

T

′

and let

1

∈

G

be the

interpretation

of

e

∈

τ

′

and

⋅

:

G

×

G

→

G

be the interpretation of

⋅

∈

τ

′

. Let us write

x

⁢

y

for the

product

x

⋅

y

. For any

x

∈

G

, let

y

∈

G

such that

x

⁢

y

=

1

and

z

∈

G

such that

y

⁢

z

=

1

. Then

1

⁢

z

=

(

x

⁢

y

)

⁢

z

=

x

⁢

(

y

⁢

z

)

=

x

⁢

1

=

x

, so that

1

⁢

x

=

1

⁢

(

1

⁢

z

)

=

(

1

⋅

1

)

⁢

z

=

1

⁢

z

=

x

. This shows that

1

is the

identity

of

G

with respect to

⋅

. In particular,

x

=

1

⁢

z

=

z

, which implies

1

=

y

⁢

z

=

y

⁢

x

, or that

y

is a

inverse

of

x

with respect to

⋅

.

Remark

. Let

T

be a theory. A class of

τ

-structures is said to be

axiomatized by

T

if it is the class of all models of

T

.

T

is said to be the

set of axioms

for this class. This class is necessarily unique, and is denoted by

Mod

⁡

(

T

)

. When

T

consists of a single sentence

φ

, we write

Mod

⁡

(

φ

)

.

Title

model

Canonical name

Model

Date of creation

2013-03-22 13:00:14

Last modified on

2013-03-22 13:00:14

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

33

Author

CWoo (3771)

Entry type

Definition

Classification

msc 03C95

Related topic

Structure

Related topic

SatisfactionRelation

Related topic

AlgebraicSystem

Related topic

RelationalSystem

Defines

model

Generated on Thu Feb 8 19:56:49 2018 by

LaTeXML
atomic formula

atomic formula

Let

Σ

be a

signature

and

T

⁢

(

Σ

)

the set of terms over

Σ

. The set

S

of symbols for

T

⁢

(

Σ

)

is the

disjoint union

of

Σ

and

V

, a

countably infinite

set whose

elements

are called

variables

. Now, adjoin

S

the set

{

=

,

(

,

)

}

, assumed to be

disjoint

from

S

. An

atomic formula

φ

over

Σ

is any one of the following:

1.

either

(

t

1

=

t

2

)

, where

t

1

and

t

2

are terms in

T

⁢

(

Σ

)

,

2.

or

(

R

⁢

(

t

1

,

…

,

t

n

)

)

, where

R

∈

Σ

is an

n

-ary relation symbol, and

t

i

∈

T

⁢

(

Σ

)

.

Remarks

.

1.

Using atomic formulas, one can inductively build

formulas

using the

logical connectives

∨

,

¬

,

∃

, etc… In this sense, atomic formulas are formulas that can not be broken down into simpler formulas; they are the building blocks of formulas.

2.

A

literal

is a formula that is either atomic or of the form

¬

⁢

φ

where

φ

is atomic. If a literal is atomic, it is called a

positive literal

. Otherwise, it is a

negative literal

.

3.

A finite

disjunction

of literals is called a

clause

. In other words, a clause is a formula of the form

φ

1

∨

φ

2

∨

⋯

∨

φ

n

, where each

φ

i

is a literal.

4.

A

qunatifier-free formula

is a formula that does not contain the symbols

∃

or

∀

.

5.

If we identify a formula

φ

with its

double negation

¬

⁡

(

¬

⁢

φ

)

, then it can be shown that any quantifier-free formula can be identified with a formula that is in

conjunctive normal form

, that is, a finite

conjunction

of clauses. For a proof, see this link (

http://planetmath.org/EveryPropositionIsEquivalentToAPropositionInDNF

)

Title

atomic formula

Canonical

name

AtomicFormula

Date of creation

2013-03-22 12:42:54

Last modified on

2013-03-22 12:42:54

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

10

Author

CWoo (3771)

Entry type

Definition

Classification

msc 03C99

Classification

msc 03B10

Synonym

quantifier free formula

Related topic

TermsAndFormulas

Related topic

CNF

Related topic

DNF

Defines

literal

Defines

clause

Defines

quantifier-free formula

Defines

positive literal

Defines

negative literal

Generated on Thu Feb 8 19:57:01 2018 by

LaTeXML
axiom of foundation

axiom of foundation

The

axiom of foundation

(also called the

axiom of regularity

) is an axiom of ZF

set theory

prohibiting circular sets and sets with

infinite

levels of containment. Intuitively, it that every set can be built up from the

empty set

. There are several

equivalent

formulations, for

instance

:

For any

nonempty set

X

there is some

y

∈

X

such that

y

∩

X

=

∅

.

For any set

X

, there is no

function

f

from

ω

to the

transitive closure

of

X

such that for every

n

,

f

⁢

(

n

+

1

)

∈

f

⁢

(

n

)

.

For any

formula

ϕ

, if there is any set

x

such that

ϕ

⁢

(

x

)

then there is some

X

such that

ϕ

⁢

(

X

)

but there is no

y

∈

X

such that

ϕ

⁢

(

y

)

.

Sets which

satisfy

this axiom are called

artinian

. It is known that, if ZF without this axiom is

consistent

, then this axiom does not add any inconsistencies.

One important

consequence

of this property is that no set can contain itself. For instance, if there were a set

X

such that

X

∈

X

then we could define a function

f

⁢

(

n

)

=

X

for all

n

, which would then have the property that

f

⁢

(

n

+

1

)

∈

f

⁢

(

n

)

for all

n

.

Title

axiom of foundation

Canonical name

AxiomOfFoundation

Date of creation

2013-03-22 13:04:31

Last modified on

2013-03-22 13:04:31

Owner

Henry (455)

Last modified by

Henry (455)

Numerical id

10

Author

Henry (455)

Entry type

Definition

Classification

msc 03C99

Synonym

foundation

Synonym

regularity

Synonym

axiom of regularity

Defines

artinian

Defines

artinian set

Defines

artinian sets

Generated on Thu Feb 8 19:57:03 2018 by

LaTeXML
elementarily equivalent

elementarily equivalent

Conventions

All

structures

share a common

signature

; the

first-order
language

L

is the

language

determined by that signature.

Definition

The

theory

of a structure

M

⁢

,

⁢

Th

⁡

(

M

)

⁢

,

is the set of all

sentences

of

L

that are true in

M

.

Definition

Structures

M

and

N

are

elementarily equivalent

,
(in symbols:

M

≡

N

)

if and only if

Th

⁡

(

M

)

=

Th

⁡

(

N

)

.

Title

elementarily equivalent

Canonical name

ElementarilyEquivalent

Date of creation

2013-03-22 13:00:26

Last modified on

2013-03-22 13:00:26

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

8

Author

CWoo (3771)

Entry type

Definition

Classification

msc 03C99

Defines

theory

Generated on Thu Feb 8 19:57:05 2018 by

LaTeXML
elementary embedding

elementary embedding

Let

τ

be a

signature

and

𝒜

and

ℬ

be two

structures

for

τ

such that

f

:

𝒜

→

ℬ

is an

embedding

. Then

f

is said to be

elementary

if for every first-order

formula

ϕ

∈

F

⁢

(

τ

)

, we have

𝒜

⊨

ϕ

iff

ℬ

⊨

ϕ

.

In the expression above,

𝒜

⊨

ϕ

means: if we write

ϕ

=

ϕ

⁢

(

x

1

,

…

,

x

n

)

where the

free variables

of

ϕ

are all in

{

x

1

,

…

,

x

n

}

, then

ϕ

⁢

(

a

1

,

…

,

a

n

)

holds in

𝒜

for any

a

i

∈

𝒜

(the underlying

universe

of

𝒜

).

If

𝒜

is a

substructure

of

ℬ

such that the

inclusion

homomorphism

is an

elementary embedding

, then we say that

𝒜

is an

elementary substructure

of

ℬ

, or that

ℬ

is an elementary extension of

𝒜

.

Remark

. A chain

𝒜

1

⊆

𝒜

2

⊆

⋯

⊆

𝒜

n

⊆

⋯

of

τ

-structures is called an

elementary chain

if

𝒜

i

is an elementary substructure of

𝒜

i

+

1

for each

i

=

1

,

2

,

…

. It can be shown (Tarski and Vaught) that

⋃

i

<

ω

𝒜

i

is a

τ

-structure that is an elementary extension of

𝒜

i

for every

i

.

Title

elementary embedding

Canonical name

ElementaryEmbedding

Date of creation

2013-03-22 13:00:29

Last modified on

2013-03-22 13:00:29

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

5

Author

CWoo (3771)

Entry type

Definition

Classification

msc 03C99

Synonym

elementary monomorphism

Defines

elementary substructure

Defines

elementary extension

Defines

elementary chain

Generated on Thu Feb 8 19:57:07 2018 by

LaTeXML
proof equivalence of formulation of foundation

proof equivalence of formulation of foundation

We show that each of the three formulations of the

axiom of foundation

given are

equivalent

.

1

⇒

2

Let

X

be a set and consider any

function

f

:

ω

→

tc

⁡

(

X

)

. Consider

Y

=

{

f

⁢

(

n

)

∣

n

<

ω

}

. By

assumption

, there is some

f

⁢

(

n

)

∈

Y

such that

f

⁢

(

n

)

∩

Y

=

∅

, hence

f

⁢

(

n

+

1

)

∉

f

⁢

(

n

)

.

2

⇒

3

Let

ϕ

be some

formula

such that

ϕ

⁢

(

x

)

is true and for every

X

such that

ϕ

⁢

(

X

)

, there is some

y

∈

X

such that

ϕ

⁢

(

y

)

. Then define

f

⁢

(

0

)

=

x

and

f

⁢

(

n

+

1

)

is some

y

∈

f

⁢

(

n

)

such that

ϕ

⁢

(

y

)

. This would construct a function violating the assumption, so there is no such

ϕ

.

3

⇒

1

Let

X

be a

nonempty set

and define

ϕ

⁢

(

x

)

≡

x

∈

X

. Then

ϕ

is true for some

X

, and by assumption, there is some

y

such that

ϕ

⁢

(

y

)

but there is no

z

∈

y

such that

ϕ

⁢

(

z

)

. Hence

y

∈

X

but

y

∩

X

=

∅

.

Title

proof equivalence of formulation of foundation

Canonical name

ProofEquivalenceOfFormulationOfFoundation

Date of creation

2013-03-22 13:04:37

Last modified on

2013-03-22 13:04:37

Owner

Henry (455)

Last modified by

Henry (455)

Numerical id

6

Author

Henry (455)

Entry type

Proof

Classification

msc 03C99

Generated on Thu Feb 8 19:57:11 2018 by

LaTeXML
term algebra

term algebra

Let

Σ

be a

signature

and

V

a set of

variables

. Consider the set of all terms of

T

:=

T

⁢

(

Σ

)

over

V

. Define the following:

•

For each constant symbol

c

∈

Σ

,

c

T

is the

element

c

in

T

.

•

For each

n

and each

n

-ary function symbol

f

∈

Σ

,

f

T

is an

n

-ary

operation

on

T

given by

f

T

⁢

(

t

1

,

…

,

t

n

)

=

f

⁢

(

t

1

,

…

,

t

n

)

,

meaning that the evaluation of

f

T

at

(

t

1

,

…

,

t

n

)

is the term

f

⁢

(

t

1

,

…

,

t

n

)

∈

T

.

•

For each relational symbol

R

∈

Σ

,

R

T

=

∅

.

Then

T

, together with the set of

constants

and

n

-ary operations defined above is an

Σ

-

structure

(

http://planetmath.org/Structure

). Since there are no

relations

defined on it,

T

is an algebraic system whose signature

Σ

′

is the subset of

Σ

consisting of all but the relation symbols of

Σ

. The

algebra

T

is aptly called the

term algebra

of the signature

Σ

(over

V

).

The prototypical example of a term algebra is the set of all

well-formed formulas

over a set

V

of

propositional variables

in classical

propositional logic

. The signature

Σ

is just the set of

logical connectives

. For each

n

-ary logical connective

#

, there is an associated

n

-ary operation

[

#

]

on

V

, given by

[

#

]

⁢

(

p

1

,

…

,

p

n

)

=

#

⁢

p

1

⁢

⋯

⁢

p

n

.

Remark

. The term algebra

T

of a signature

Σ

over a set

V

of variables can be thought of as a

free structure

in the following sense: if

A

is any

Σ

-structure, then any

function

ϕ

:

V

→

A

can be extended to a unique

structure homomorphism

ϕ

′

:

T

→

A

. In this regard,

V

can be viewed as a free basis for the algebra

T

. As such,

T

is also called the

absolutely free

Σ

-structure with basis

V

.

Title

term algebra

Canonical

name

TermAlgebra

Date of creation

2013-03-22 17:35:24

Last modified on

2013-03-22 17:35:24

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

9

Author

CWoo (3771)

Entry type

Definition

Classification

msc 03C99

Classification

msc 03C60

Synonym

word algebra

Related topic

PolynomialsInAlgebraicSystems

Related topic

FreeAlgebra

Generated on Thu Feb 8 19:57:21 2018 by

LaTeXML
artificial intelligence

artificial intelligence

Artificial intelligence

aims to mimic the ‘

operation

’ of the human mind using

sequential machines

,

automata

, robots, or computers. Indeed there are two different claims on how far AI can go in exhibiting human behaviors, and especially in emulating the actions of the human mind:

•

Strong AI thesis

, or

http://en.wikipedia.org/wiki/Artificial_intelligence

‘general intelligence’,
is a very long term aim of AI research in Computer Science that might not be achievable
within the bounds of Boolean logic if it does aim to match human intelligence that often operates
beyond chrysippian, formal or even symbolic two-value logic, and indeed as it remains currently undefined (or undefinable ?) in terms of either

Boolean

or symbolic, two-value logic.

•

Weak AI thesis

:

(a)

Knowledge-based AI

(b)

Symbolic computation

AI

(c)

Sub-symbolic AI

(d)

Computational ‘Intelligence’ and ‘Neural’ Networks or Nets

Remarks:

1.

A

http://etd.library.pitt.edu/ETD/available/etd-03102008-120235/unrestricted/ColinIhrig-ms-3-18-08.pdf

Super-complex Computer System Architecture may give one the illusion of ‘strong AI’ in spite of its
Boolean logic limitations, as there are no stringent tests defined so far that are capable of correctly ‘measuring’ intelligence either in humans or in computers. Until a satisfactory

definition

of ‘human intelligence’ is arrived at, it will not
be possible to design acceptable means or tests to ‘measure’ such intelligence, and therefore one could not establish
if the ‘strong AI’ thesis is valid or not. It may indeed remain an

undecidable

issue on a chrysippian logic basis.

2.

An

universal Turing machine

(

A

⁢

U

⁢

T

⁢

M

) was shown to be able to simulate any other sequential machine, automaton, robot, or computer by employing steps that humans do not consider to require ‘intelligence’ (i.e.,
human intelligence).

Title

artificial intelligence

Canonical

name

ArtificialIntelligence

Date of creation

2013-03-22 15:31:51

Last modified on

2013-03-22 15:31:51

Owner

aplant (12431)

Last modified by

aplant (12431)

Numerical id

15

Author

aplant (12431)

Entry type

Topic

Classification

msc 03D05

Classification

msc 18B20

Classification

msc 68T40

Classification

msc 68T27

Classification

msc 68-00

Classification

msc 68T01

Synonym

computer programmimg

Synonym

symbolic computation

Synonym

computer simulation

Synonym

sub-symbolic computation

Synonym

super-complex systems

Synonym

universal Turing machines

Related topic

CategoryOfAutomata

Related topic

Automaton

Related topic

CategoryOfMRSystems3

Related topic

StateMachine

Related topic

UniversalTuringMachine

Related topic

StrongAIThesis

Related topic

Supercomputers2

Generated on Thu Feb 8 19:57:33 2018 by

LaTeXML
automatic presentation

automatic presentation

Let

S

be a

relational structure

(for example, a graph).

S

has an

automatic presentation

if (for some

alphabet

Σ

) there is a

language

L

⊆

Σ

*

and a surjective map

f

from

L

onto the ) of

S

such that

•

L

can be checked by a finite automaton (

http://planetmath.org/DeterministicFiniteAutomaton

) (Membership)

•

The language of all convolutions of

x

,

y

∈

L

where

f

⁢

(

x

)

=

f

⁢

(

y

)

can be checked by a (Equality)

•

For all

n

-ary

relations

(

http://planetmath.org/Relation

)

R

i

in

S

, the language of all convolutions of

x

1

,

x

2

,

…

,

x

n

∈

L

where

R

i

⁢

(

f

⁢

(

x

1

)

,

f

⁢

(

x

2

)

,

…

,

f

⁢

(

x

n

)

)

can be checked by a ()

The class of languages accepted by finite

automata

, i.e. regular languages, is

closed under

operations

like union,

intersection

,

complementation

etc, and it is

decidable

whether or not a finite accepts the empty language. This allows any

first order

sentence

over the

structure

to be decided - using union for ’and’, complementation for ’not’ etc., and emptiness for dealing with ’there exists’. As such, the

first order theory

of any structure with an automatic presentation is decidable.

Note that wrt group this is inspired by, but not to, the definition of

automatic groups

.

Title

automatic presentation

Canonical name

AutomaticPresentation

Date of creation

2013-03-22 14:16:57

Last modified on

2013-03-22 14:16:57

Owner

mathcam (2727)

Last modified by

mathcam (2727)

Numerical id

8

Author

mathcam (2727)

Entry type

Definition

Classification

msc 03D05

Classification

msc 03C57

Synonym

automatic structure

Synonym

FA presentation

Related topic

AutomaticGroup

Generated on Thu Feb 8 19:57:35 2018 by

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automaton

automaton

An

automaton

is a

semiautomaton

with two types of special states: starting states, and final states. Specifically, an automaton

A

is is a five-tuple

(

S

,

Σ

,

δ

,

I

,

F

)

, where

1.

(

S

,

Σ

,

δ

)

is a semiautomaton,

2.

a non-empty set

I

⊆

S

of

starting states

, and

3.

a set

F

⊆

S

of

final states

or

terminating states

.

A triple

(

s

,

a

,

t

)

is called a

transition

if

t

∈

δ

⁢

(

s

,

a

)

, and is written

s

⟶

a

t

. The set

δ

⁢

(

s

,

a

)

may contain more than one

element

(or none at all), which is why an automaton is also said to be

non-deterministic

. If on the other hand

δ

⁢

(

s

,

a

)

is a

singleton

for every

(

s

,

a

)

, and

I

is a singleton, then

A

is said to be

deterministic

. In a deterministic automaton,

δ

can be viewed as a

function

from

S

×

Σ

to

S

.

If

S

and

Σ

are both finite, then

A

is called a

finite-state automaton

, or

FSA

for short.

The

state diagram

G

A

of a finite-state automaton

A

is constructed as if

A

is being treated as a semiautomaton. In

addition

, a vertex corresponding to a starting state has an incoming arrow without a source, and a vertex corresponding to a final state has an outgoing arrow without a destination (alternatively, it may be represented by a double circle). This is illustrated in the following example:

Let

A

be given by

S

=

{

σ

,

s

,

t

}

, where

σ

is the starting state, and

t

the final state,

Σ

=

{

a

,

b

}

, with the transition function given by the following table

Title

automaton

Canonical

name

Automaton

Date of creation

2013-03-22 12:26:34

Last modified on

2013-03-22 12:26:34

Owner

CWoo (3771)

Last modified by

CWoo (3771)

Numerical id

42

Author

CWoo (3771)

Entry type

Definition

Classification

msc 03D05

Classification

msc 68Q45

Synonym

next-state function

Synonym

terminating state

Synonym

FSA

Synonym

start state

Synonym

recognizer

Related topic

DeterministicFiniteAutomaton

Related topic

NonDeterministicFiniteAutomaton

Related topic

PushdownAutomaton

Related topic

Semiautomaton

Defines

finite-state automaton

Defines

transition function

Defines

starting state

Defines

final state

Defines

configuration

Defines

acceptor

Defines

automata

Defines

deterministic automaton

\@unrecurse

Generated on Thu Feb 8 19:57:38 2018 by

LaTeXML
Turing computable

Turing computable

A

function

is

Turing computable

if the function’s value can be
computed with a

Turing machine

.

More specifically, let

D

be a set of words in a given

alphabet

and
let

f

be a function which maps elements of

D

to words on the
same alphabet. We say that

f

is

Turing computable

if there
exists a Turing machine such that

•

If one starts the Turing machine with a word

w

∈

D

as the
initial content of the tape, the

computation

will halt.

•

When the computation halts, the tape will read

f

⁢

(

w

)

.

Formally, let

Σ

be an alphabet and

f

:

Σ

*

→

Σ

*

on words over

Σ

. Then

f

is said to be Turing-computable if there is a Turing machine

T

over

Σ

(its input alphabet), as defined in this entry (

http://planetmath.org/FormalDefinitionOfATuringMachine

), such that for any

w

∈

Σ

*

,

(

s

,

τ

w

,

1

)

→

*

(

h

,

τ

f

⁢

(

w

)

,

m

)

for some

m

. Here,

h

is a halt state (either an accept or a reject state), and

τ

w

for any word

w

is defined as the tape description such that the content of the

i

-th square is the

i

-th letter of

w

, and blank everywhere else.

Because of the fact that all types of Turing machines (

deterministic

,
non-deterministic, single head, multiple head, etc.) all have the same
computational power, it does not matter which type of Turing machine
one uses in the definition.

It is not hard to find examples of Turing computable functions —
because Turing machines provide an idealized model for the

operation

of the digital computer, any function which can be evaluated by a
computer provides an example.

Title

Turing computable

Canonical name

TuringComputable

Date of creation

2013-03-22 12:33:16

Last modified on

2013-03-22 12:33:16

Owner

rspuzio (6075)

Last modified by

rspuzio (6075)

Numerical id

9

Author

rspuzio (6075)

Entry type

Definition

Classification

msc 03D10

Classification

msc 68Q05

Synonym

Turing-computable

Related topic

RecursivelyEnumerable

Related topic

FormalDefinitionOfATuringMachine

Generated on Thu Feb 8 20:01:42 2018 by

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