1. CSCE 355 Foundations of Computation
Exam Review
Topics:
Mathematical preliminaries
Finite Automata
Context free languages
Pushdown Automata
Turing Machines
Undecidability
December 10, 2008

2. Relations: properties and examples
Proof Techniques: Induction, mutual induction, contradiction.
From English description to DFA or NFA.
For DFA, NFA, ε NFA give L(M)
ε NFA DFA using subset construction
Given language L find a regular expression r such that L(r) = L
Given regular expression r find L(r)
Regular Expressions to ε NFA
Minimization of DFA
Non-regular languages: Distinguished Prefixes, Pumping Lemma

3. Context Free Grammars
Given language L find pushdown automata with L(P)=L, or N(P)=L.
Show language is not context free, using pumping lemma for CFLs.
Flex/YACC
Design TM to recognize a language L.
Convert a CFG to Chomsky-normal form.
What does it mean for a language to be: regular, context-free, context sensitive, recursively enumerable, recursive
Give example languages of each set of languages in the hierarchy that is not in the next set, except for context sensitive.
Design Turing machine to compute f(x) = 2x

4. Relations: properties and examples
R1 = {(a,a), (a,b), (a,c), (a,d)}
Reflexive closure?
Transitive closure?
Reflexive-transitive closure, R1*

6. x

7. Proof Techniques: Induction, mutual induction, contradiction.

8. From English description to DFA or NFA

9. For DFA, NFA, ε NFA give L(M)

11. ε NFA DFA using subset construction

12. Given language L find a regular expression

14. Given regular expression r find L(r)

15. Regular Expressions to ε NFA (Thompson)

16. Minimization of DFA

18. Non-regular languages:
Distinguished Prefixes
Pumping Lemma

21. Context Free Grammars

22. Given language L find pushdown automata with L(P)=L, or N(P)=L

23. Show language is not context free, using pumping lemma for CFLs.

29. Flex/YACC/Ruby

30. Design TM to recognize a language L.

31. Convert a CFG to Chomsky-normal form.

32. What does it mean for a language to be:
regular,
context-free,
context sensitive,
recursively enumerable,
recursive

33. Give example languages Chomsky Hierarchy

34. Design Turing machine to compute
Algorithm for computing function
f(x,y) = x – y (max {0, x-y})
f(x,y) = x + y
f(x) = 2x

36. Recursive vs R.E.

37. Halting Problem