The Chomsky Hierarchy

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# The Chomsky Hierarchy - PowerPoint PPT Presentation

The Chomsky Hierarchy. Linear-Bounded Automata:. Same as Turing Machines with one difference:. the input string tape space is the only tape space allowed to use. Linear Bounded Automaton (LBA). Input string. Working space in tape. Left-end marker. Right-end marker.

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### The Chomsky Hierarchy

Costas Busch - RPI

Linear-Bounded Automata:

Same as Turing Machines with one difference:

the input string tape space

is the only tape space allowed to use

Costas Busch - RPI

Linear Bounded Automaton (LBA)

Input string

Working space

in tape

Left-end

marker

Right-end

marker

All computation is done between end markers

Costas Busch - RPI

We define LBA’s as NonDeterministic

Open Problem:

NonDeterministic LBA’s

have same power as

Deterministic LBA’s ?

Costas Busch - RPI

Example languages accepted by LBAs:

LBA’s have more power than PDA’s

(pushdown automata)

LBA’s have less power than Turing Machines

Costas Busch - RPI

Unrestricted Grammars:

Productions

String of variables

and terminals

String of variables

and terminals

Costas Busch - RPI

Theorem:

A language is Turing-Acceptable

if and only if is generated by an

unrestricted grammar

Costas Busch - RPI

Context-Sensitive Grammars:

Productions

String of variables

and terminals

String of variables

and terminals

and:

Costas Busch - RPI

The language

is context-sensitive:

Costas Busch - RPI

Theorem:

A language is context sensistive

if and only if

it is accepted by a Linear-Bounded automaton

Observation:

There is a language which is context-sensitive

but not decidable

Costas Busch - RPI

The Chomsky Hierarchy

Non Turing-Acceptable

Turing-Acceptable

decidable

Context-sensitive

Context-free

Regular

Costas Busch - RPI