Exam Review

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Exam Review
CSCE 355 Foundations of Computation

• Topics
• Mathematical preliminaries
• Finite Automata
• Context free languages
• Pushdown Automata
• Turing Machines
• Undecidability

December 10, 2008
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1. Relations properties and examples
2. Proof Techniques Induction, mutual induction,
   contradiction.
3. From English description to DFA or NFA.
4. For DFA, NFA, e NFA give L(M)
5. e NFA ?DFA using subset construction
6. Given language L find a regular expression r such
   that L(r) L
7. Given regular expression r find L(r)
8. Regular Expressions to e NFA
9. Minimization of DFA
10. Non-regular languages Distinguished Prefixes,
    Pumping Lemma

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

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Relations properties and examples

• R1 (a,a), (a,b), (a,c), (a,d)
• Reflexive closure?
• Transitive closure?
• Reflexive-transitive closure, R1

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• x

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Proof Techniques Induction, mutual induction,
contradiction.
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From English description to DFA or NFA
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For DFA, NFA, e NFA give L(M)
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e NFA ?DFA using subset construction
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Given language L find a regular expression
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Given regular expression r find L(r)
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Regular Expressions to e NFA (Thompson)
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Minimization of DFA
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Non-regular languages

• Distinguished Prefixes
• Pumping Lemma

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Context Free Grammars
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Given language L find pushdown automata with
L(P)L, or N(P)L
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Show language is not context free, using pumping
lemma for CFLs.
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Flex/YACC/Ruby
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Design TM to recognize a language L.
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Convert a CFG to Chomsky-normal form.
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What does it mean for a language to be

• regular,
• context-free,
• context sensitive,
• recursively enumerable,
• recursive

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Give example languages Chomsky Hierarchy
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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

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Recursive vs R.E.
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Halting Problem