Computability, Complexity, and
Algorithms
Charles Brubaker and Lance Fortnow
Fast Fourier Transform - (Udacity)
Introduction - (Udacity, Youtube)
In this lesson, we will examine the Fast Fourier Transform and apply it in order to obtain an
ecient algorith

Theory of Computation
Fall 2016
Ladislav Novak, Visiting Professor
Part 1
Introduction
CSCI-B501
Basic sets and operations
empty set ,
singleton cfw_
set of natural numbers N = cfw_0, 1, 2,
Boolean like operations: (, , and relative
complement); Cartesia

B501-Theory of computing
CFLs practice examples
Fall 2016
1. Give a PDA that recognizes the language M = cfw_1n 0n | n 0 over = cfw_0, 1.
Solution:
(s, w, ) (p, w, $)
(p, 1w, ) (p, w, 1)
(p, 0w, 1) (q, w, )
(q, 0w, 1) (q, w, )
(q, , $) (f, , )
A visual re

Few important statements concerning partially computable (p.c.) functions
and
Assignment 6 (on page 2)
Def: A function f: U U, is partial-computable (p.c.), if its graph(f)UU is computably
enumerable (c.e).
Theorem: The following statements are equivalent

PROBLEM 1: Prove that
B = cfw_a^2n : n 0
is not context free.
Solution: Suppose cfw_ a^2n : n 0 is context-free. It must then have some
pumping length p. Consider string w = a2p . By the pumping lemma,