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Exam Review

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Title: CSCE 212 Computer Architecture Author: Manton Matthews Last modified by: mmm Created Date: 8/11/1998 9:19:24 AM Document presentation format – PowerPoint PPT presentation

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Title: Exam Review


1
Exam Review
CSCE 355 Foundations of Computation
  • Topics
  • Mathematical preliminaries
  • Finite Automata
  • Context free languages
  • Pushdown Automata
  • Turing Machines
  • Undecidability

December 10, 2008
2
  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

3
  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

4
Relations properties and examples
  • R1 (a,a), (a,b), (a,c), (a,d)
  • Reflexive closure?
  • Transitive closure?
  • Reflexive-transitive closure, R1

5
(No Transcript)
6
  • x

7
Proof Techniques Induction, mutual induction,
contradiction.
8
From English description to DFA or NFA
9
For DFA, NFA, e NFA give L(M)
10
(No Transcript)
11
e NFA ?DFA using subset construction
12
Given language L find a regular expression
13
Given regular expression r find L(r)
14
Regular Expressions to e NFA (Thompson)
15
Minimization of DFA
16
(No Transcript)
17
Non-regular languages
  • Distinguished Prefixes
  • Pumping Lemma

18
Context Free Grammars
19
Given language L find pushdown automata with
L(P)L, or N(P)L
20
Show language is not context free, using pumping
lemma for CFLs.
21
Flex/YACC/Ruby
22
Design TM to recognize a language L.
23
Convert a CFG to Chomsky-normal form.
24
What does it mean for a language to be
  • regular,
  • context-free,
  • context sensitive,
  • recursively enumerable,
  • recursive

25
Give example languages Chomsky Hierarchy
26
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

27
(No Transcript)
28
Recursive vs R.E.
29
Halting Problem
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