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David L. Dill
Department of Computer Science
1
Outline
•
Proof guidelines.
•
Introduction to regular languages.
•
Deterministic finite automata (DFA)
•
Nondeterministic finite automata (NFA)
•
Proof that NFA and DFA languages are the same (subset construction).
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Proof Expectations
We don’t want to lose sight of the forest because of the trees.
Here are the “forestlevel” points with proofs.
•
What is the proof strategy?
–
Induction on strings.
What are the base and induction steps?
–
Induction on expressions.
What are the base and induction steps?
–
Diagonalization
–
Reduction from another problem.
Which direction is the reduction?
•
What are the key insights in the proof?
•
Often this is a construction (often something that can be implemented as a
computer program)
–
Translation between regular expressions, various finite automata.
–
Translation from one problem to another.
Make sure your document explain these things clearly in your proofs.
If we can see QUICKLY that you did the right kind of proof and got the major
points right, you’ll get nearly full credit.
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Proof Guidelines
1. State what is being proved precisely and clearly.
2. Start proof with an explanation of the strategy (e.g. “induction on
y
”)
3. Provide guideposts (e.g.,
Base
,
Induction
)
4. Highlight the interesting key parts of the proof (where did you have to be
clever?)
5. Make it easy for the graders to see these things.
4
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 Winter '08
 Motwani,R

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