Closure Properties of ContextFree languages Summer 2004 COMP
- Slides: 41
Closure Properties of Context-Free languages Summer 2004 COMP 335 1
Union Context-free languages are closed under: Union is context free Summer 2004 is context-free COMP 335 2
Example Language Grammar Union Summer 2004 COMP 335 3
In general: For context-free languages with context-free grammars and start variables The grammar of the union has new start variable and additional production Summer 2004 COMP 335 4
Concatenation Context-free languages Concatenation are closed under: is context free Summer 2004 is context-free COMP 335 5
Example Language Grammar Concatenation Summer 2004 COMP 335 6
In general: For context-free languages with context-free grammars and start variables The grammar of the concatenation has new start variable and additional production Summer 2004 COMP 335 7
Star Operation Context-free languages Star-operation are closed under: is context free Summer 2004 is context-free COMP 335 8
Example Language Grammar Star Operation Summer 2004 COMP 335 9
In general: For context-free language with context-free grammar and start variable The grammar of the star operation has new start variable and additional production Summer 2004 COMP 335 10
Negative Properties of Context-Free Languages Summer 2004 COMP 335 11
Intersection Context-free languages intersection are not closed under: is context free Summer 2004 not necessarily context-free COMP 335 12
Example Context-free: Intersection NOT context-free Summer 2004 COMP 335 13
Complement Context-free languages complement are not closed under: is context free Summer 2004 not necessarily context-free COMP 335 14
Example Context-free: Complement Summer 2004 NOT context-free COMP 335 15
Intersection of Context-free languages and Regular Languages Summer 2004 COMP 335 16
The intersection of a context-free language and a regular language is a context-free language context free regular Summer 2004 context-free COMP 335 17
Machine NPDA for DFA for regular context-free Construct a new NPDA machine that accepts simulates in parallel Summer 2004 COMP 335 and 18
NPDA DFA transition NPDA transition Summer 2004 COMP 335 19
NPDA DFA transition NPDA transition Summer 2004 COMP 335 20
NPDA DFA initial state NPDA Initial state Summer 2004 COMP 335 21
NPDA DFA final states NPDA final states Summer 2004 COMP 335 22
Example: context-free NPDA Summer 2004 COMP 335 23
regular DFA Summer 2004 COMP 335 24
context-free Automaton for: NPDA Summer 2004 COMP 335 25
In General: simulates in parallel accepts string and if and only if accepts string and accepts string Summer 2004 COMP 335 26
Therefore: is NPDA is context-free Summer 2004 COMP 335 27
Applications of Regular Closure Summer 2004 COMP 335 28
The intersection of a context-free language and a regular language is a context-free language Regular Closure context free regular Summer 2004 context-free COMP 335 29
An Application of Regular Closure Prove that: is context-free Summer 2004 COMP 335 30
We know: is context-free Summer 2004 COMP 335 31
We also know: is regular Summer 2004 COMP 335 32
context-free regular (regular closure) context-free is context-free Summer 2004 COMP 335 33
Another Application of Regular Closure Prove that: is not context-free Summer 2004 COMP 335 34
is context-free If (regular closure) Then context-free regular context-free Impossible!!! Therefore, Summer 2004 is not context free COMP 335 35
Decidable Properties of Context-Free Languages Summer 2004 COMP 335 36
Membership Question: for context-free grammar find if string Membership Algorithms: Parsers • Exhaustive search parser • CYK parsing algorithm Summer 2004 COMP 335 37
Empty Language Question: for context-free grammar find if Algorithm: 1. Remove useless variables 2. Check if start variable Summer 2004 COMP 335 is useless 38
Infinite Language Question: for context-free grammar find if is infinite Algorithm: 1. Remove useless variables 2. Remove unit and productions 3. Create dependency graph for variables 4. If there is a loop in the dependency graph then the language is infinite Summer 2004 COMP 335 39
Example: Infinite language Dependency graph Summer 2004 COMP 335 40
Summer 2004 COMP 335 41
- Closure property of cfl
- Closure and decision properties of context free languages
- Closure properties of regular languages
- Closure under intersection
- Closure property of polynomials
- Closure property of context free grammar
- Closure properties of dfa
- Np closure properties
- Decision properties of regular languages
- Decision properties of regular languages
- Decision properties of regular languages
- Decision properties of regular languages
- Decision properties of cfl
- Properties of regular languages
- Decision properties of context free languages
- Physical properties of ice cube
- Extensive properties and intensive properties
- Prep and drape
- Closure ketergantungan fungsional
- Symmetric closure examples
- Shortest paths and transitive closure in data structure
- Project closure analysis
- What is the closure of a set
- Domain testing example
- Closure of attributes
- Why fiber joints and couplers are necessary
- Project audit life cycle
- Contoh super key
- Truseal wound closure device
- Micro teaching skills
- Closure-oriented/judging vs. open/perceiving
- Watchman flx dfu
- Vena seal
- Closure property
- Floyd warshall algorithm transitive closure
- Continuous stitch
- Perpetual project closure
- Closure ketergantungan fungsional
- Wisconsin lcs
- Strong triadic closure property
- When conducting post project audits
- Floyd warshall algorithm transitive closure