Due 5/13
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Practice problems:
- Chapter 7, #7.1, 7.2, 7.6, 7.7, 7.12
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Hand in:
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Due 4/22
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Practice problems:
- Chapter 5, #5.4, 5.5.,5.6, 5.7
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Hand in:
- Sipser, problems 5.9, 5.12, 5.21
- Show that the language consisting of all Turing machines
which accept all palindromes is undecidable. Use a reduction
argument.
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Due 4/14
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Practice problems:
- Chapter 4: #4.2, 4.3, 4.6, 4.7, 4.8
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Hand in:
- Sipser, problems 2.14, 2.19, 4.10, 4.21 (For problem
2.19, think about parse trees.)
- In class on 4/56 we definded a relation on the set of
states of a DFA. Prove this relation is an equivalence relation.
- Find a minimal DFA for the DFA given in class on 4/7.
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Due 3/24
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Practice problems:
- Chapter 3: #3.1, 3.2,3.5, 3.15
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Hand in:
- Sipser, problems 3.8a, 3.8b, 3.8c, 3.11, 3.14
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Due 3/7
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Practice problems:
- Chapter 2, 2.3, 2.6, 2.7, 2.8
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Hand in:
- Sipser, problems 2.15, 2.16, 2.17 and 2.18a
- Find a context-free grammar for the language (over {a,b}) A
={ all strings that have twice as many a's as b's}.
- Find a pushdown automaton for the language in the previous
problem.
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Due 2/28
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Practice problems:
- Section 1.3, 1.6a, 1.7a,1.15, 1.16
- Section 1.4, 1.17, 1.18
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Hand in:
- Using problem 1.10 in Sipser
show that the intersection of two regular
languages is also regular.
- Do problem 1.41 in Sipser
- Suppose x is a string in Sigma*. Show that the set of
all strings which have x as a prefix is a regular language. Then
show that if A is a regular language, the set of all strings in A which
do not have x as a prefix is
also a
regular language.
- Show that the language P = {1^n
such that n is a (non-negative, integer) power of 2} is not regular.
- Do problem 1.37 in
Sipser. Be sure to show both things, that F satisfies the
pumping lemma and that it is
not regular.
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Due 2/17
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Practice problems:
- Chapter 0, 1 - 8
- Section 1.1, 1.1-1.4
- Section 1.2, 1.4 - 1.5, 1.7a, 1.8a, 1.12
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Hand in: Chapter 1, 1.4d
1.4i. Give both a finite
state diagram and a formal
description of the DFA
Construct a DFA that accepts the
set of strings (over 0,1)
which have at leaxt three consecutive 0's in them.
1.10, 1.24, 1.29
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