The final exam is open in that you are allowed to bring notes as follows:
• 1 sheet of 8.5" by 11.0" piece of paper with notes written on it
• Pencil or pen
• eraser

What's covered by the exam.

• Anything in Chapter 11-14 of the text book.
• Anything in the published notes, through last Thursday, June 2, 2011.
• Anything covered by any of the Homeworks (including proofs by induction, and proofs by contradiction).
• Anything we talked about in class

Topics you should know

• Definitions of formalisms
1. Regular Language
2. Regular Expression
3. DFA
4. NFA
5. NFAe
6. GenNFA
7. Regular Grammar
8. Context Free Langauge
9. Context Free Grammars
• Normal forms
• Chommsky Normal Form
• Greibach Normal Form
10. Context Free Expressions
11. Push Down Automata (deterministic and non-deterministic)
12. Turing machines
13. Other Turing-Complete formalisms (Simple Language, Markov, Post, Lambda Calculus)
14. The Halting Problem
15. Complexity Classes: P, NP, PSpace
• Skills
1. Translating word descriptions of a language into any of the formalisms
2. Using properties of Regular Expressions (Table 11.1, page 700)
3. Executing DFA's by hand over a string
4. Executing PDAs
5. Executing Turing Machines
6. Vreating Turing machines from written descriptions.
7. Executing simple Programming language programs
8. Executing Partial Recursive Functions
9. Executing Markov algorithmsPost Algorithms
10. Carrying out reduction in the Lambda Calculus
11. Reduceability, Reducing one kind of Turing-Complete problem into another.
• Algorithms
1. RegExp to Finite automaton
• Top Down (via GenNFA, 11.4, page 711)
• Bottom up (11.7, page 729)
2. Finite automaton to RegExp (via GenNFA, 11.5, page 713) state ripping.
3. Computing Lambda-closures (page 732)
4. NFA to DFA (subset construction, 11.8, page 733-734)
5. Minimum State DFAs (11.10, page 740)
6. NFA to RegGrammar (11.11 page 748, also see the Notes on Regular Grammars).
7. RegGrammar to NFA (11.2 page 750)
8. Combining Context Free Grammars (12.3, page 761)
9. Context Free Gramma to PDA (12.5, page 770)
10. PDA to Context Free Grammar (12.6, apge 772)
• Other topics
1. Closure properties of Regular languages
2. Applying the pumping-lemma to prove a language is not regular.
3. Applying the CF pumping lemma to prove a language is not context free.
4. Church Turing Thesis
5. The Halting Problem
6. Diagonalization to show the functions from Nat to Nat are not countable.
7. Intractable problems, Travelling Salesman, Boolean Satisifiability, Pressburger Arithmetic