The Chomsky Hierarchy Chomsky Hierarchy Type0 grammars unrestricted
![The Chomsky Hierarchy The Chomsky Hierarchy](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-1.jpg)
![Chomsky Hierarchy • Type-0 grammars (unrestricted grammars) include all formal grammars. – In which Chomsky Hierarchy • Type-0 grammars (unrestricted grammars) include all formal grammars. – In which](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-2.jpg)
![The chomsky hierarchy • Type-2 grammars (context-free grammars) generate the context-free languages. • Context The chomsky hierarchy • Type-2 grammars (context-free grammars) generate the context-free languages. • Context](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-3.jpg)
![Linear-Bounded Automata: Same as Turing Machines with one difference: the input string tape space Linear-Bounded Automata: Same as Turing Machines with one difference: the input string tape space](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-4.jpg)
![Linear Bounded Automaton (LBA) Input string Left-end marker Working space in tape Right-end marker Linear Bounded Automaton (LBA) Input string Left-end marker Working space in tape Right-end marker](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-5.jpg)
![We define LBA’s as Non. Deterministic Open Problem: Non. Deterministic LBA’s have same power We define LBA’s as Non. Deterministic Open Problem: Non. Deterministic LBA’s have same power](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-6.jpg)
![Example languages accepted by LBAs: LBA’s have more power than PDA’s (pushdown automata) LBA’s Example languages accepted by LBAs: LBA’s have more power than PDA’s (pushdown automata) LBA’s](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-7.jpg)
![Unrestricted Grammars: Productions String of variables and terminals 8 Unrestricted Grammars: Productions String of variables and terminals 8](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-8.jpg)
![Type-0 grammar (Unrestricted Grammar) • They generate exactly all languages that can be recognized Type-0 grammar (Unrestricted Grammar) • They generate exactly all languages that can be recognized](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-9.jpg)
![Example unrestricted grammar: 10 Example unrestricted grammar: 10](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-10.jpg)
![Theorem: A language is Turing-Acceptable if and only if is generated by an unrestricted Theorem: A language is Turing-Acceptable if and only if is generated by an unrestricted](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-11.jpg)
![Context-Sensitive Grammars: Productions String of variables and terminals and: 12 Context-Sensitive Grammars: Productions String of variables and terminals and: 12](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-12.jpg)
![Context-Sensitive Grammars: Type-1 grammar • The rule is allowed if S does not appear Context-Sensitive Grammars: Type-1 grammar • The rule is allowed if S does not appear](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-13.jpg)
![The language is context-sensitive: 14 The language is context-sensitive: 14](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-14.jpg)
![Theorem: A language is context sensistive if and only if it is accepted by Theorem: A language is context sensistive if and only if it is accepted by](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-15.jpg)
![The Chomsky Hierarchy Turing-Acceptable decidable Context-sensitive Context-free Regular 16 The Chomsky Hierarchy Turing-Acceptable decidable Context-sensitive Context-free Regular 16](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-16.jpg)
![Summary 17 Summary 17](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-17.jpg)
- Slides: 17
![The Chomsky Hierarchy The Chomsky Hierarchy](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-1.jpg)
The Chomsky Hierarchy
![Chomsky Hierarchy Type0 grammars unrestricted grammars include all formal grammars In which Chomsky Hierarchy • Type-0 grammars (unrestricted grammars) include all formal grammars. – In which](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-2.jpg)
Chomsky Hierarchy • Type-0 grammars (unrestricted grammars) include all formal grammars. – In which no restrictions are made on the left and right sides of the grammar's productions • Type-1 grammars (context-sensitive grammars) generate the context-sensitive languages. – in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and non terminal symbols 2
![The chomsky hierarchy Type2 grammars contextfree grammars generate the contextfree languages Context The chomsky hierarchy • Type-2 grammars (context-free grammars) generate the context-free languages. • Context](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-3.jpg)
The chomsky hierarchy • Type-2 grammars (context-free grammars) generate the context-free languages. • Context free languages are theoretical basis for the syntax of most programming languages. • Type-3 grammars (regular grammars) generate the regular languages. • These languages are exactly all languages that can be decided by a finite state automaton. Additionally, this family of formal languages can be obtained by regular expressions. 3
![LinearBounded Automata Same as Turing Machines with one difference the input string tape space Linear-Bounded Automata: Same as Turing Machines with one difference: the input string tape space](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-4.jpg)
Linear-Bounded Automata: Same as Turing Machines with one difference: the input string tape space is the only tape space allowed to use 4
![Linear Bounded Automaton LBA Input string Leftend marker Working space in tape Rightend marker Linear Bounded Automaton (LBA) Input string Left-end marker Working space in tape Right-end marker](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-5.jpg)
Linear Bounded Automaton (LBA) Input string Left-end marker Working space in tape Right-end marker All computation is done between end markers 5
![We define LBAs as Non Deterministic Open Problem Non Deterministic LBAs have same power We define LBA’s as Non. Deterministic Open Problem: Non. Deterministic LBA’s have same power](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-6.jpg)
We define LBA’s as Non. Deterministic Open Problem: Non. Deterministic LBA’s have same power as Deterministic LBA’s ? 6
![Example languages accepted by LBAs LBAs have more power than PDAs pushdown automata LBAs Example languages accepted by LBAs: LBA’s have more power than PDA’s (pushdown automata) LBA’s](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-7.jpg)
Example languages accepted by LBAs: LBA’s have more power than PDA’s (pushdown automata) LBA’s have less power than Turing Machines 7
![Unrestricted Grammars Productions String of variables and terminals 8 Unrestricted Grammars: Productions String of variables and terminals 8](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-8.jpg)
Unrestricted Grammars: Productions String of variables and terminals 8
![Type0 grammar Unrestricted Grammar They generate exactly all languages that can be recognized Type-0 grammar (Unrestricted Grammar) • They generate exactly all languages that can be recognized](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-9.jpg)
Type-0 grammar (Unrestricted Grammar) • They generate exactly all languages that can be recognized by a Turing machine. • These languages are also known as the recursively enumerable languages. • This is different from the recursive languages which can be decided by an always halting Turing machine. 9
![Example unrestricted grammar 10 Example unrestricted grammar: 10](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-10.jpg)
Example unrestricted grammar: 10
![Theorem A language is TuringAcceptable if and only if is generated by an unrestricted Theorem: A language is Turing-Acceptable if and only if is generated by an unrestricted](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-11.jpg)
Theorem: A language is Turing-Acceptable if and only if is generated by an unrestricted grammar 11
![ContextSensitive Grammars Productions String of variables and terminals and 12 Context-Sensitive Grammars: Productions String of variables and terminals and: 12](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-12.jpg)
Context-Sensitive Grammars: Productions String of variables and terminals and: 12
![ContextSensitive Grammars Type1 grammar The rule is allowed if S does not appear Context-Sensitive Grammars: Type-1 grammar • The rule is allowed if S does not appear](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-13.jpg)
Context-Sensitive Grammars: Type-1 grammar • The rule is allowed if S does not appear on the right side of any rule. • The languages described by these grammars are exactly all languages that can be recognized by a non-deterministic Turing machine whose tape is bounded by a constant times the length of the input. 13
![The language is contextsensitive 14 The language is context-sensitive: 14](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-14.jpg)
The language is context-sensitive: 14
![Theorem A language is context sensistive if and only if it is accepted by Theorem: A language is context sensistive if and only if it is accepted by](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-15.jpg)
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 15
![The Chomsky Hierarchy TuringAcceptable decidable Contextsensitive Contextfree Regular 16 The Chomsky Hierarchy Turing-Acceptable decidable Context-sensitive Context-free Regular 16](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-16.jpg)
The Chomsky Hierarchy Turing-Acceptable decidable Context-sensitive Context-free Regular 16
![Summary 17 Summary 17](https://slidetodoc.com/presentation_image/08c0011f288a435b13084a127a43b5bf/image-17.jpg)
Summary 17
Unrestricted grammar is also known as
Unrestricted grammer
Conditional sentence type zero
Which grammar generates regular language?
Eliminating epsilon productions from cfg
Questions on context free grammar
Chomsky computer science
Railroad diagram
Liquid unrestricted net assets
Unrestricted narration
Contoh unrestricted grammar
Unrestricted use stock
Unrestricted simplex protocol
Unrestricted simplex protocol program in c
Selective service act of 1917
Greg szabo
Inference
German unrestricted submarine warfare