15 Foundation of Programming Languages and Software Engineering: The Word Problem The Word Problem Summer Term 2010 Robert Elsässer Robert Elsässer
Central Problems of Equational Reasoning 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 2
The Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 3
Solving the Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 4
An Undecidable Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 5
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
Example 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 7
Composing Relations 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 8
Notations for Reduction Relations 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 9
Terminology for Reduction Relations (1) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 10
Terminology for Reduction Relations (2) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 11
Deciding the Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 12
Church-Rosser and Confluence are Equivalent 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 13
Church-Rosser and Confluence are Equivalent 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 14
Proof (cont.) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 15
Existence and Uniqueness of Normal Forms 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 16
Another Lemma 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 17
Relating ↔ ɛ and ≈ ɛ : Auxiliary Lemma 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 18
Proof of (3) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 19
Relating ↔ ɛ and ≈ ɛ 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 20
Proof (cont.) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 21
Deciding the Word Problem 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 22
Computing Normal Forms (1) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 23
Computing Normal Forms (2) 22.06.2010 Theory 1 - Foundation of Programming Languages and Software Engineering: The word problem 24
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