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Applied Computer Science II Chapter 1 : Regular Languages

Applied Computer Science II Chapter 1 : Regular Languages. Prof. Dr. Luc De Raedt Institut für Informatik Albert-Ludwigs Universität Freiburg Germany. Overview. Deterministic finite automata Regular languages Nondeterministic finite automata Closure operations Regular expressions

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Applied Computer Science II Chapter 1 : Regular Languages

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  1. Applied Computer Science IIChapter 1 : Regular Languages Prof. Dr. Luc De Raedt Institut für Informatik Albert-Ludwigs Universität Freiburg Germany

  2. Overview • Deterministic finite automata • Regular languages • Nondeterministic finite automata • Closure operations • Regular expressions • Nonregular languages • The pumping lemma

  3. Finite Automata • An intuitive example : supermarket door controller • Figures 1,2,3 • Probabilistic counterparts exist • Markov chains, bayesian nets, etc. • Not in this course

  4. Figure 1.4 Formally A finite automaton

  5. 7,8,9 Other examples

  6. Another example

  7. Formal definition of computation

  8. Designing finite automata • Design automaton for language consisting of binary strings with an odd number of 1s • Design first states • Then transitions • Accept and reject states • Fig. 12

  9. Another example • Design an automaton to recognize the language of binary strings containing the string 001 as substring • Fig 13

  10. The regular operations

  11. Regular languages are closed under … • Proof

  12. Non deterministic finite automata • Deterministic • One successor state •  transitions not allowed • Non deterministic • Several successor states possible •  transitions possible • Figure 14

  13. Deterministic versus non deterministic computation • Figure 15

  14. Example

  15. Every NFA has an equivalent DFA • Figures 17-18

  16. Another NFA

  17. Nondeterministic finite automaton

  18. Example • Example 18

  19. Formal definition of computation

  20. Equivalence NFA and DFA

  21. Proof

  22. An example

  23. Closure under the regular operations

  24. Proof idea • INSERT FIG 1.24

  25. PROOF P 60 !

  26. Proof idea

  27. Proof idea

  28. Regular expressions

  29. Applications • Design of compilers • awk, grep, vi … in unix (search for strings) • Perl programming language • Bioinformatics • So called motifs (patterns occurring in sequences, e.g. proteins)

  30. Proof through :

  31. Two steps • DFA into GNFA (generalized nondeterministic finite automaton) • GNFA into regular expression

  32. Two states q and r are connected in both directions Exception : Start state Accept state One direction only Labels are regular expressions GNFAs

  33. Formally

  34. Convert DFA into GNFA

  35. Convert GNFA into regular expression

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