Download presentation

Presentation is loading. Please wait.

Published byAyana Herlan Modified over 2 years ago

1
Fall 2003Costas Busch - RPI1 Properties of Context-Free languages

2
Fall 2003Costas Busch - RPI2 Context-free languages are closed under: Union is context free is context-free Union

3
Fall 2003Costas Busch - RPI3 Example Union LanguageGrammar

4
Fall 2003Costas Busch - RPI4 In general: The grammar of the union has new start variable and additional production For context-free languages with context-free grammars and start variables

5
Fall 2003Costas Busch - RPI5 Context-free languages are closed under: Concatenation is context free is context-free Concatenation

6
Fall 2003Costas Busch - RPI6 Example Concatenation LanguageGrammar

7
Fall 2003Costas Busch - RPI7 In general: The grammar of the concatenation has new start variable and additional production For context-free languages with context-free grammars and start variables

8
Fall 2003Costas Busch - RPI8 Context-free languages are closed under: Star-operation is context freeis context-free Star Operation

9
Fall 2003Costas Busch - RPI9 Example Language Grammar Star Operation

10
Fall 2003Costas Busch - RPI10 In general: The grammar of the star operation has new start variable and additional production For context-free language with context-free grammar and start variable

11
Fall 2003Costas Busch - RPI11 Negative Properties of Context-Free Languages

12
Fall 2003Costas Busch - RPI12 Context-free languages are not closed under: intersection is context free not necessarily context-free Intersection

13
Fall 2003Costas Busch - RPI13 Example Context-free: NOT context-free Intersection

14
Fall 2003Costas Busch - RPI14 Context-free languages are not closed under: complement is context freenot necessarily context-free Complement

15
Fall 2003Costas Busch - RPI15 NOT context-free Example Context-free: Complement

16
Fall 2003Costas Busch - RPI16 Intersection of Context-free languages and Regular Languages

17
Fall 2003Costas Busch - RPI17 The intersection of a context-free language and a regular language is a context-free language context free regular context-free

18
Fall 2003Costas Busch - RPI18 for NPDA DFA Construct a new NPDA machine that accepts Machine context-free regular simulates in parallel and

19
Fall 2003Costas Busch - RPI19 transition NPDADFA transition NPDA

20
Fall 2003Costas Busch - RPI20 transition NPDADFA transition NPDA

21
Fall 2003Costas Busch - RPI21 initial state NPDADFA Initial state NPDA

22
Fall 2003Costas Busch - RPI22 final state final states NPDADFA final states NPDA

23
Fall 2003Costas Busch - RPI23 Example: NPDA context-free

24
Fall 2003Costas Busch - RPI24 DFA regular

25
Fall 2003Costas Busch - RPI25 Automaton for: NPDA context-free

26
Fall 2003Costas Busch - RPI26 simulates in parallel and accepts stringif and only if accepts string and accepts string In General:

27
Fall 2003Costas Busch - RPI27 Therefore: is NPDA is context-free

28
Fall 2003Costas Busch - RPI28 Applications of Regular Closure

29
Fall 2003Costas Busch - RPI29 The intersection of a context-free language and a regular language is a context-free language context free regular context-free Regular Closure

30
Fall 2003Costas Busch - RPI30 An Application of Regular Closure Prove that: is context-free

31
Fall 2003Costas Busch - RPI31 We know: is context-free

32
Fall 2003Costas Busch - RPI32 is regular We also know:

33
Fall 2003Costas Busch - RPI33 regularcontext-free is context-free (regular closure)

34
Fall 2003Costas Busch - RPI34 Another Application of Regular Closure Prove that: is not context-free

35
Fall 2003Costas Busch - RPI35 context-freeregularcontext-free If is context-free Then Impossible!!! Therefore, is not context free (regular closure)

Similar presentations

OK

Fall 2006Costas Busch - RPI1 Reductions. Fall 2006Costas Busch - RPI2 Problem is reduced to problem If we can solve problem then we can solve problem.

Fall 2006Costas Busch - RPI1 Reductions. Fall 2006Costas Busch - RPI2 Problem is reduced to problem If we can solve problem then we can solve problem.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on rainwater harvesting structures Ppt on business model of hul Ppt on web 2.0 Ppt on hotel industry in india Ppt on role of individual in conservation of natural resources Ppt on time division switching pdf Ppt on as 14 amalgamation synonyms Ppt on sanskritization in india Ppt on chemical and magnetic effect of electric current Ppt on ashoka the great emperor