By:video.edhole.com

Fall 2006 2Costas Busch - RPI

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Fall 2006Costas Busch - RPI3

Same as Turing Machines with one difference:

the input string tape spaceis the only tape space allowed to use

Linear-Bounded Automata:

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Fall 2006Costas Busch - RPI4

[ ]a b c d e

Left-endmarker

Input string

Right-endmarker

Working space in tape

All computation is done between end markers

Linear Bounded Automaton (LBA)

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Fall 2006Costas Busch - RPI5

We define LBA’s as NonDeterministic

Open Problem:

NonDeterministic LBA’shave same power asDeterministic LBA’s ?

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Fall 2006Costas Busch - RPI6

Example languages accepted by LBAs:

}{ nnn cbaL }{ !naL

LBA’s have more power than PDA’s (pushdown automata)

LBA’s have less power than Turing Machines

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Fall 2006Costas Busch - RPI7

Unrestricted Grammars:

Productionsvu

String of variablesand terminals

String of variablesand terminals

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Fall 2006Costas Busch - RPI8

Example unrestricted grammar:

dAc

cAaB

aBcS

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Fall 2006Costas Busch - RPI9

A language is Turing-Acceptableif and only if is generated by anunrestricted grammar

LL

Theorem:

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Fall 2006Costas Busch - RPI10

Context-Sensitive Grammars:

and: |||| vu

Productionsvu

String of variablesand terminals

String of variablesand terminals

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Fall 2006Costas Busch - RPI11

The language }{ nnn cba

is context-sensitive:

aaAaaaB

BbbB

BbccAc

bAAb

aAbcabcS

|

|

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Fall 2006Costas Busch - RPI12

A language is context sensistive if and only ifit is accepted by a Linear-Bounded automaton

LTheorem:

There is a language which is context-sensitivebut not decidable

Observation:

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Fall 2006Costas Busch - RPI13

Non Turing-Acceptable

Turing-Acceptable

decidable

Context-sensitive

Context-free

Regular

The Chomsky Hierarchy

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