MATH 516301
MATH-516301
This question paper consists of 4 printed pages, each of which is identied by the reference MATH 516301 No calculators allowed
c UNIVERSITY OF LEEDS Examination for the Module
University of Leeds
Department of Pure Mathematics
MATH 5164M
ADVANCED COMPUTABILITY AND UNSOLVABILITY
Problems 7
1) There is nothing useful one can say about incomputability discuss.
Write an essay a
University of Leeds
Department of Pure Mathematics
MATH 3163/5164M
COMPUTABILITY AND UNSOLVABILITY
Problems 6
Read CT, pages 139154, 161166, and 287296
1) Show that T is an equivalence relation.
2) Sh
University of Leeds Department of Pure Mathematics MATH 3163 COMPUTABILITY AND UNSOLVABILITY Problems 7 1) Write an essay, covering not more than three pages, describing the background to, and consequ
University of Leeds
Department of Pure Mathematics
MATH 3163/5164M
COMPUTABILITY AND UNSOLVABILITY
Problems 4
1) A function f is increasing if f (x) < f (x + 1) for all x.
Show that an innite set A is
University of Leeds
Department of Pure Mathematics
MATH 3163/5164M
COMPUTABILITY AND UNSOLVABILITY
Problems 5
Read CT, pages 101115
1) (a) Show that if A m B and B is computable, then A is computable.
University of Leeds
Department of Pure Mathematics
MATH 3163/5164M
COMPUTABILITY AND UNSOLVABILITY
Problems 3
Read CT, pages 8799 and 6668
1) Show that: A computable A c.e.
2) Show that the following
University of Leeds
Department of Pure Mathematics
MATH 3163/5164M
COMPUTABILITY AND UNSOLVABILITY
Problems 1
Read CT, pages 325
1) Show that the following functions are primitive recursive:
(i) sg(n)
University of Leeds
Department of Pure Mathematics
MATH 3163/5164M
COMPUTABILITY AND UNSOLVABILITY
Problems 2
Read CT, pages 3334, 6166 and 6981
1) Write Turing programs for the functions:
(b) g(x, y)
1. In my opinion I agree with Paul Singer that ethically animals have an equal
concern with humans. Animals are usually also affected by things humans
do. It is non-humans who bear the most direct bur