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Theory of Computation Regular Expressions & Context-Free Languages

Theory of Computation Regular Expressions & Context-Free Languages. Prof. Muhammad Saeed. Regular Expressions. Regular Expression. Regular Expressions. Regular Expressions. Precedence of Regular Expression Operators. Regular Expressions. Regular Expressions.

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Theory of Computation Regular Expressions & Context-Free Languages

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  1. Theory of Computation Regular Expressions & Context-Free Languages Prof. Muhammad Saeed

  2. Regular Expressions Regular Expression Dept. of Computer Science & IT, FUUAST Theory of Computation

  3. Regular Expressions Dept. of Computer Science & IT, FUUAST Theory of Computation

  4. Regular Expressions Precedence of Regular Expression Operators Dept. of Computer Science & IT, FUUAST Theory of Computation

  5. Regular Expressions Dept. of Computer Science & IT, FUUAST Theory of Computation

  6. Regular Expressions Represent the following sets by regular expression • {a,bc} • {1,11,111,1111,………..} • {ab, a, b, bb} • {b2 , b5 , b8 , ………….} • {a2n+1 | n≥0} Write Regular expression for the following languages d) L1 ={a2n b2m+1 | n≥0, m ≥0 } Dept. of Computer Science & IT, FUUAST Theory of Computation

  7. Regular Expressions Identities: Dept. of Computer Science & IT, FUUAST Theory of Computation

  8. Regular Expressions Dept. of Computer Science & IT, FUUAST Theory of Computation

  9. Regular Expressions Dept. of Computer Science & IT, FUUAST Theory of Computation

  10. Regular Expressions Dept. of Computer Science & IT, FUUAST Theory of Computation

  11. Regular Expressions Dept. of Computer Science & IT, FUUAST Theory of Computation

  12. Regular Expressions Converting Regular Expressions to Automata R + S L(R)⋃L(S) RS L(R)L(S) Dept. of Computer Science & IT, FUUAST Theory of Computation

  13. Regular Expressions R* L(R*) Regular Expression to an є-NFA Dept. of Computer Science & IT, FUUAST Theory of Computation

  14. Regular Expressions a) Regular Expression to an є-NFA b) Dept. of Computer Science & IT, FUUAST Theory of Computation

  15. Regular Expressions c) Dept. of Computer Science & IT, FUUAST Theory of Computation

  16. Regular Expressions Closure properties of Regular Languages: Dept. of Computer Science & IT, FUUAST Theory of Computation

  17. Regular Expressions Dept. of Computer Science & IT, FUUAST Theory of Computation

  18. Regular Expressions Dept. of Computer Science & IT, FUUAST Theory of Computation

  19. Regular Expressions Dept. of Computer Science & IT, FUUAST Theory of Computation

  20. Context-Free Languages ( CFL ) Dept. of Computer Science & IT, FUUAST Theory of Computation

  21. Context-Free Languages ( CFG ) Dept. of Computer Science & IT, FUUAST Theory of Computation

  22. Context-Free Languages Dept. of Computer Science & IT, FUUAST Theory of Computation

  23. Context-Free Languages Dept. of Computer Science & IT, FUUAST Theory of Computation

  24. Context-Free Languages Dept. of Computer Science & IT, FUUAST Theory of Computation

  25. Context-Free Languages Rules: Productions: Derivation Symbols Dept. of Computer Science & IT, FUUAST Theory of Computation

  26. Context-Free Languages Dept. of Computer Science & IT, FUUAST Theory of Computation

  27. Context-Free Languages Derivation Symbols Dept. of Computer Science & IT, FUUAST Theory of Computation

  28. Context-Free Languages Language Of a Grammar Dept. of Computer Science & IT, FUUAST Theory of Computation

  29. Context-Free Languages Dept. of Computer Science & IT, FUUAST Theory of Computation

  30. Context-Free Languages Dept. of Computer Science & IT, FUUAST Theory of Computation

  31. Context-Free Languages Parse Trees Dept. of Computer Science & IT, FUUAST Theory of Computation

  32. Context-Free Languages Ambiguous Grammars Dept. of Computer Science & IT, FUUAST Theory of Computation

  33. Context-Free Languages Ambiguous Grammars Dept. of Computer Science & IT, FUUAST Theory of Computation

  34. Context-Free Languages Dept. of Computer Science & IT, FUUAST Theory of Computation

  35. Context-Free Languages Useless Productions G = (V,T,S,P) is Context-free Grammar with P, S → aSb | λ | A A → aA A is useful if there is at least one w ϵ L(G) such that S xAy w • Empty Productions • A → λ, A λ b) Unit Productions A → B, A B c) Left Recursion A → Ax Dept. of Computer Science & IT, FUUAST Theory of Computation

  36. Context-Free Languages Dept. of Computer Science & IT, FUUAST Theory of Computation

  37. Context-Free Languages Dept. of Computer Science & IT, FUUAST Theory of Computation

  38. Context-Free Languages Normal Forms 1) Chomsky Normal Forms 2) Greibach Normal Forms Chomsky Normal Forms (CNF) Any context-free language without any λ- production and unit production is generated by a grammar in which productions are of the form Dept. of Computer Science & IT, FUUAST Theory of Computation

  39. Context-Free Languages 2) 3) Dept. of Computer Science & IT, FUUAST Theory of Computation

  40. END Dept. of Computer Science & IT, FUUAST Theory of Computation

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