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15 Foundation of Programming Languages and Software Engineering: The Word Problem The Word Problem Summer Term 2010 Robert Elssser Robert Elssser Central Problems of Equational Reasoning 22.06.2010 Theory 1 - Foundation of Programming

  1. 15 Foundation of Programming Languages and Software Engineering: The Word Problem The Word Problem Summer Term 2010 Robert Elsässer Robert Elsässer

  2. Central Problems of Equational Reasoning 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 2

  3. The Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 3

  4. Solving the Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 4

  5. An Undecidable Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 5

  6. The Reduction Relation Generated by ∑ Id ∑ -Identities i i 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 6

  7. Example 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 7

  8. Composing Relations 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 8

  9. Notations for Reduction Relations 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 9

  10. Terminology for Reduction Relations (1) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 10

  11. Terminology for Reduction Relations (2) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 11

  12. Deciding the Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 12

  13. Church-Rosser and Confluence are Equivalent 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 13

  14. Church-Rosser and Confluence are Equivalent 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 14

  15. Proof (cont.) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 15

  16. Existence and Uniqueness of Normal Forms 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 16

  17. Another Lemma 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 17

  18. Relating ↔ ɛ and ≈ ɛ : Auxiliary Lemma 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 18

  19. Proof of (3) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 19

  20. Relating ↔ ɛ and ≈ ɛ 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 20

  21. Proof (cont.) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 21

  22. Deciding the Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 22

  23. Computing Normal Forms (1) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 23

  24. Computing Normal Forms (2) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 24

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