B401 - Fundamentals of computing theory
Assignment 2
Due September 27, 2016
1. (10 points) Design an automaton that accepts all strings over cfw_0, 1 that contain at least one 0.
2. (10 points) Design an automaton that accepts all strings over cfw_0, 1 th
Converting Regular Grammars to
NFAs and vice versa
Definition of a Grammar
Definition of a Grammar G = (V,T,S,P)
V : Set of variables
T : Set of terminal symbols
S : Start variable
P : Set of rewriting / production rules written as x y.
In general if
Supporting material for
Assignments 3 and 4
Relations
In Theory of Computation a relations is a subset of a
constructive universe.
Constructive universe can be built from a finite
number of initial objects using fin
Fundamentals of Computing Theory
Fall 2016
Ladislav Novak, Visiting Professor
Pat 2
Quasi-Effective vs Effective Computation
CSCI-B501
General constructible sets and
general computational problem
Given an alphabet , we denote by * the set
of all strings
Fundamentals of Computing Theory
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
B401 - Fundamentals of computing theory, Automata practice examples
1
Fall 2016
On DFA and NFA
1. For each of the following languages, prove that the language is regular. For part (a) give a
DFA; for parts (b) and (c), use part (a) and the closure propert
B401 Fundamentals of Computing Theory - Quiz 2
1. (45 points) Let A be a set and let R be a binary relation over A. For each of the following terms, give
the formal definition (NOT a descriptive or intuitive definition).
(a) domain of R
(b) range of R
(c)
B401
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 representation of the
B501
Quiz 1
September 2, 2016
Answer the questions in the spaces provided on the question sheets. If you run out of
room for an answer, continue on the back of the page.
Name:
IU email:
1. (10 points) Let A = cfw_a, b, a and B = cfw_b, a Which of the foll
B401- Fundamentals of computing theory
Assignment 1
Solutions outline
We say a function e : N A enumerates the set A if e is onto.
1. Consider the list 0,1,3,5,7, . , 2,4,6, . . Why it is not an enumeration of natural numbers.
Solution:
Let the list be an
HW1
Provide arguments why the list 1,3,5,7, ,
2,4,6, is not an enumeration of natural
numbers. (Hint: see definition on p.9 of B401
ppt 3)
Provide arguments why the following
repetitive list : 1,1,2,2,3,3,4,4, is an
enumeration of natural numbers (Hint:
B401 -Fundamentals of computing theory, Quiz 3, Solutions outline
Fall 2016
Answer the questions in the spaces provided on the question sheets. If you run out of
room for an answer, continue on the back of the page.
Name:
IU email:
1. For each of the foll
1
Enumerability
Our ultimate goal will be to present some celebrated theorems about inherent limits on
what can be computed and on what can be proved. Before such results can be established,
we need to undertake an analysis of computability and an analysi