CS 21
Decidability and Tractability
Winter 2013
Problem Set 3
Out: January 30
Due: February 6
Reminder: you are encouraged to work in groups of two or three; however you must turn in your
own write-up and note with whom you worked. You may consult the cou
CS 21
Decidability and Tractability
Winter 2012
Problem Set 1
Out: January 11 Due: January 18
Reminder: you are encouraged to work in groups of two or three; however you must turn in your own write-up and note with whom you worked. You may consult the cou
CS 21
Decidability and Tractability
Winter 2012
Midterm Solutions
Out: February 13
1. (a) The language L1 is context free but not regular. To see it is context free, consider the
NPDA that rst pushes as onto the stack until it sees the rst b, then pops as
CS 21
Decidability and Tractability
Winter 2012
Final Exam Solutions
Posted: March 16
If you have not turned in the nal, obviously you should not consult these solutions.
1. (a) First, the problem is in PSPACE, for the usual reason for 2-player games. Giv
CS 21
Decidability and Tractability
Winter 2012
Solution Set 1
Posted: January 18
If you have not yet turned in the Problem Set, you should not consult these solutions.
1. We need to dene a language that has the same computational power as the function f
CS 21
Decidability and Tractability
Winter 2013
Final
Out: March 13
Due: March 20, noon
This is a nal exam. You may consult only the course notes and the text (Sipser). You may not
collaborate. The full honor code guidelines can be found in the course syl
CS 21
Decidability and Tractability
Winter 2013
Midterm
Out: February 6
Due: February 13
This is a midterm. You may consult only the course notes and the text (Sipser). You may not
collaborate. The full honor code guidelines can be found in the course syl
CS 21
Decidability and Tractability
Winter 2013
Solution Set 2
Posted: January 30
If you have not yet turned in the Problem Set, you should not consult these solutions.
1. We build a NPDA for L. There will be four states, labeled match, add-one, addtwo, a
CS 21
Decidability and Tractability
Winter 2012
Midterm Solutions
Out: February 8
1. (a) The language L1 is context free but not regular. To see it is context free, consider the
NPDA that rst pushes as onto the stack until it sees the rst b, then pops as
CS 21
Decidability and Tractability
Winter 2013
Final Exam Solutions
Posted: March 20
If you have not turned in the nal, obviously you should not consult these solutions.
1. (a) This problem is in PSPACE. We give a recursive algorithm. We are given a sequ
Outline
CS21
Decidability and Tractability
Lecture 14
February 6, 2015
February 6, 2015
CS21 Lecture 14
undecidable problems
1
computation histories
surprising contrasts between
decidable/undecidable
Rices Theorem
Post Correspondence problem
February 6, 2
CS21
Decidability and Tractability
Lecture 2
January 6, 2017
January 6, 2017
CS21 Lecture 2
1
Outline
Finite Automata
January 6, 2017
CS21 Lecture 2
2
Terminology
finite alphabet : a set of symbols
language L * : subset of strings over
a machine takes
CS21
Decidability and Tractability
Lecture 10
January 27, 2017
January 27, 2017
CS21 Lecture 10
1
Outline
Turing Machines and variants
multitape TMs (done last lecture)
nondeterministic TMs
Church-Turing Thesis
decidable, RE, co-RE languages
the Halting P
CS21
Decidability and Tractability
Lecture 6
January 18, 2017
January 18, 2017
CS21 Lecture 6
1
Outline
Context-Free Grammars and Languages
ambiguity
normal form
equivalence of NPDAs and CFGs
non context-free languages
January 18, 2017
CS21 Lecture 6
2
CS21
Decidability and Tractability
Lecture 18
February 17, 2017
February 17, 2017
CS21 Lecture 18
1
Outline
the complexity class NP
alternate characterization of NP
3-SAT is NP-complete
February 17, 2017
CS21 Lecture 18
2
The class NP
Definition: TIME(
CS21
Decidability and Tractability
Lecture 20
February 24, 2017
February 24, 2017
CS21 Lecture 20
1
Outline
NP complete problems
NP-complete problems: Hamilton path and
cycle,Traveling Salesperson Problem
February 24, 2017
CS21 Lecture 20
2
Hamilton Pat
CS21
Decidability and Tractability
Lecture 14
February 8, 2017
February 8, 2017
CS21 Lecture 14
1
Outline
a non-RE and non-co-RE language
the Recursion Theorem
Gdel Incompleteness Theorem
February 8, 2017
CS21 Lecture 14
2
Beyond RE and co-RE
We saw (by
CS21
Decidability and Tractability
Lecture 5
January 13, 2017
January 13, 2017
CS21 Lecture 5
1
Outline
Pushdown Automata
Context-Free Grammars and Languages
January 13, 2017
CS21 Lecture 5
2
Pushdown Automata (PDA)
We will define nondeterministic pushdo
CS21
Decidability and Tractability
Lecture 4
January 11, 2017
January 11, 2017
CS21 Lecture 4
1
Outline
Pumping Lemma
Pushdown Automata
Context-Free Grammars and Languages
January 11, 2017
CS21 Lecture 4
2
Limits on the power of FA
Is every language desc
CS21
Decidability and Tractability
Lecture 13
February 6, 2017
February 6, 2017
CS21 Lecture 13
1
Outline
undecidable problems
computation histories
surprising contrasts between
decidable/undecidable
Rices Theorem
Post Correspondence problem
a non-RE and
CS21
Decidability and Tractability
Lecture 7
January 20, 2017
January 20, 2017
CS21 Lecture 7
1
Outline
equivalence of NPDAs and CFGs
non context-free languages
deterministic PDAs
January 20, 2017
CS21 Lecture 7
2
NPDA, CFG equivalence (continued)
Theorem
CS21
Decidability and Tractability
Lecture 3
January 9, 2017
January 9, 2017
CS21 Lecture 3
1
Outline
NFA, FA equivalence
Regular Expressions
FA and Regular Expressions
January 9, 2017
CS21 Lecture 3
2
NFA, FA equivalence
Theorem: a language L is recogniz
CS 21
Decidability and Tractability
Winter 2017
Solution Set 1
Posted: January 18
If you have not yet turned in the Problem Set, you should not consult these solutions.
1. We need to define a language that has the same computational power as the function
CS 21
Decidability and Tractability
Winter 2017
Problem Set 7
Out: March 1
Due: March 8
Reminder: you are encouraged to work in groups of two or three; however you must turn in your own
write-up and note with whom you worked. You may consult the course no