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Applied Computer Science II Chapter : Grammars

Applied Computer Science II Chapter : Grammars. Prof. Dr. Luc De Raedt Institut für Informatik Albert-Ludwigs Universität Freiburg Germany. Overview. Sipser : the automata/machine approach Schoening : the grammar approach State links among the two appraoches See more types of grammars :

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Applied Computer Science II Chapter : Grammars

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

  2. Overview • Sipser : the automata/machine approach • Schoening : the grammar approach • State links among the two appraoches • See more types of grammars : • Regular grammars • Context-free • Context-sensitive • Grammar • Based on : Uwe Schoening’s “Theoretische Informatik – Kurzgefasst”, Spektrum.

  3. Grammars • Most concepts carry over from CFGs, i.e. derivation, language accepted by grammar, ambiguity, leftmost derivation, …

  4. Parsing • Construct meaning (parse tree)

  5. Chomsky Hierarchy • Type 0 : every grammar; Turing recognisable language • Type 1 : context-sensitive • Type 2 : context free • Type 3 : regular • Exception for

  6. Difference Type 0 and 1 • See figure

  7. Implies figure p 20!

  8. Earlier

  9. Machines corresponding to languages • Type 3, regular languages : • Regular grammar, DFA, NFA, regular expression • Type 2, context-free languages : • Context free grammar, PDA • Type 1, context-sensitive language • Context sensitive grammar, LBA • Type 0, Turing recognizable • Grammar, Turing machine

  10. Deterministic versus non-deterministic machines • NFA and DFA are equivalent • PDA and DPA are not equivalent • DPA : deterministic subset of PDA • LBA and DLBA are not equivalent • DLBA : deterministic subset of PDA • NTM and DTM are equivalent

  11. Closure properties

  12. Decidability

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