Assignment#1; Due January 19 at start of class Review of Formal Languages Consider some language L. For each of the following cases, write in one of (i) through (vi), to indicate what you can say conclusively about L's complexity, where (i) (ii) (iii) (iv
Sample Ques+on#1
1. Prove that the following are equivalent
a) S is an innite recursive (decidable) set.
b) S is the range of a monotonically increasing
total recursive func:on.
Note: f is monotonically increasing m
Computability &
Complexity Theory
Charles E. Hughes
COT 6410 Spring 2014
Notes
Who, What, Where and When
Instructor: Charles Hughes;
Harris Engineering 247C; 823-2762
(phone is not a good way to get me);
[email protected]
(e-mail is a good
Generally useful information.
The notation z = <x,y> denotes the pairing function with inverses x = <z>1 and y = <z>2.
The minimization notation y [P(,y)] means the least y (starting at 0) such that P(,y) is
true. The bounded minimization (acceptable in p
COT 6410
Spring 2014
Midterm#1
Name:
KEY
12 1. Choosing from among (REC) recursive, (RE) re non-recursive, (coRE) co-re non-recursive,
(NRNC) non-re/non-co-re, categorize each of the sets in a) through d). Justify your answer by
showing some minimal quant
Assignment #5 Key; Due February 20 at start of class
1. Consider the set of indices NonConstant = NC = cfw_ f | |range( f)| > 1 . Use Rices
Theorem to show that NC is not recursive (not decidable). Note that members of NC do
not need to converge for all i
Assignment #3 Key; Due February 6 at start of class
Show that prfs are closed under mutual induction. Mutual induction means that
each induction step after calculating the base is computed using the previous value
of the other function. The formal hypothe
Assignment#2 Key; Due January 28 at start of class
Let set A be non-empty recursive, B be re non-recursive and C be non-re. Using the terminology
(REC) recursive, (RE) non-recursive recursively enumerable, (NR) non-re, categorize each
set below, saying wh
Assignment #4 Key; Due February 13 at start of class
Choosing from among (REC) recursive, (RE) re non-recursive, (coRE) co-re nonrecursive, (NRNC) non-re/non-co-re, categorize each of the sets in a) through d).
Justify your answer by showing some minimal
COT 6410
Spring2014
Final Exam Sample E1 Key
1. Let set A be recursive, B be re non-recursive and C be non-re. Choosing from among (REC)
recursive, (RE) re non-recursive, (NR) non-re, categorize the set D in each of a) through d) by
listing all possible c
Generally useful information.
The notation z = <x,y> denotes the pairing function with inverses x = <z>1 and y = <z>2.
The minimization notation y [P(,y)] means the least y (starting at 0) such that P(,y) is true.
The bounded minimization (acceptable in p
COT 6410
Spring 2014
Midterm#1
Name:
KEY
12 1. Choosing from among (REC) recursive, (RE) re non-recursive, (coRE) co-re non-recursive,
(NRNC) non-re/non-co-re, categorize each of the sets in a) through d). Justify your answer by
showing some minimal quant
COT 6410
Spring2014
Final Exam Sample E1 Key
1. Let set A be recursive, B be re non-recursive and C be non-re. Choosing from among (REC)
recursive, (RE) re non-recursive, (NR) non-re, categorize the set D in each of a) through d) by
listing all possible c
COT 6410
Spring2014
Final Exam Sample E2 Key
1. We described the proof that 3SAT is polynomial reducible to Subset-Sum.
a.) Describe Subset-Sum
Let n1, n2, , nk, G be a set of k positive whole numbers and G be a goal number. The decision
problem is to det
Generally useful information.
The notation z = <x,y> denotes the pairing function with inverses x = <z>1 and y = <z>2.
The minimization notation y [P(,y)] means the least y (starting at 0) such that P(,y) is
true. The bounded minimization (acceptable in p
Assignment#1 Key; Due January 19 at start of class
Review of Formal Languages
Consider some language L. For each of the following cases, write in one of (i) through (vi), to
indicate what you can say conclusively about Ls complexity, where
(i)
(ii)
(iii)
Assignment#1; Due January 19 at start of class Review of Formal Languages Consider some language L. For each of the following cases, write in one of (i) through (vi), to indicate what you can say conclusively about L's complexity, where (i) (ii) (iii) (iv
Assignment#2; Due January 31 at start of class Let set A be non-empty recursive, B be re non-recursive and C be non-re. Using the terminology (REC) recursive, (RE) non-recursive recursively enumerable, (NR) non-re, categorize each set below, saying whethe
Assignment #3; Due February 14 at start of class a. Show that prfs are closed under mutual induction. Mutual induction means that each induction step after calculating the base is computed using the previous value of the other function. The formal hypothe
Assignment #4 Key 1. Prove that Semi-Thue systems over single letter alphabets (say, cfw_a) have decidable word problems. I did this in class. I showed two solutions. The first used a PDA; the second a Petri Net. In the first, we showed we could construct
COT 6410
Fall 2010
Exam#1
Name:
KEY
12 1. Choosing from among (REC) recursive, (RE) re non-recursive, (coRE) co-re non-recursive, (NRNC) non-re/non-co-re, categorize each of the sets in a) through d). Justify your answer by showing some minimal quantifica
COT6410 Topics for Final Exam Computability Theory Sets Use of quantified decidable predicates to categorize complexity Reduction (many-one); degrees of unsolvability (many-one) Rice's Theorem (including its proof) Applications of Rice's Theorem Relations
COT 6410
Spring2012
Final Exam Sample Questions
1. Let set A be recursive, B be re non-recursive and C be non-re. Choosing from among (REC) recursive, (RE) re non-recursive, (NR) non-re, categorize the set D in each of a) through d) by listing all possibl
COT 6410
Spring 2012
Midterm#1
Name:
KEY
12 1. Choosing from among (REC) recursive, (RE) re non-recursive, (coRE) co-re non-recursive, (NRNC) non-re/non-co-re, categorize each of the sets in a) through d). Justify your answer by showing some minimal quant
COT 6410
Spring 2012
Sample Midterm#1
Name:
1. Choosing from among (REC) recursive, (RE) re non-recursive, (coRE) co-re non-recursive, (NR) non-re/non-co-re, categorize each of the sets in a) through d). Justify your answer by showing some minimal quantif
Generally useful information. The notation z = <x,y> denotes the pairing function with inverses x = <z>1 and y = <z>2. The minimization notation y [P(.,y)] means the least y (starting at 0) such that P(.,y) is true. The bounded minimization (acceptable in
Generally useful information. The notation z = <x,y> denotes the pairing function with inverses x = <z>1 and y = <z>2. The minimization notation y [P(.,y)] means the least y (starting at 0) such that P(.,y) is true. The bounded minimization (acceptable in
Generally useful information. The notation z = <x,y> denotes the pairing function with inverses x = <z>1 and y = <z>2. The minimization notation y [P(.,y)] means the least y (starting at 0) such that P(.,y) is true. The bounded minimization (acceptable in
Generally useful information. The notation z = <x,y> denotes the pairing function with inverses x = <z>1 and y = <z>2. The minimization notation y [P(.,y)] means the least y (starting at 0) such that P(.,y) is true. The bounded minimization (acceptable in
COT 6410
Spring2014
Final Exam Sample E2 Key
1. We described the proof that 3SAT is polynomial reducible to Subset-Sum.
a.) Describe Subset-Sum
Let n1, n2, , nk, G be a set of k positive whole numbers and G be a goal number. The decision
problem is to det