Theory of Computation
Lecture 2
Bill Hollingsworth
[email protected]
Text: "Introduction to the theory of computation" by Michael Sipser
Functions
A function maps elements from one set to
elements of an
YunHa Jung
810-380-480
1. (15 points) Construct a push-down automaton that accepts the fol-
lowing context-free language:
The Square brackets and the parentheses must be properly nested. So the strate
Automata and formal languages
Bill Hollingsworth
November 18, 2013
Time Complexity
Computational hierarchy
Machine
Language
Memory
DFA, NFA
PDA
LBA
Regular
Context-free
Context-sensitive
Turing machin
Automata and formal languages
Bill Hollingsworth
November 18, 2013
NP
P
Denition
P is the class of languages that can be decided in polynomial
time by a single-tape deterministic Turing machine.
T IM
Automata and formal languages
Bill Hollingsworth
November 19, 2013
N P -complete
N P -complete
N P -complete is a class of languages belonging to N P having the special
property that if any language L
Automata and formal languages
Bill Hollingsworth
October 19, 2013
Converting a PDA to a CFG
Setup
The algorithm requires PDAs to be in a standard format.
1. There must be exactly one accept state.
2.
Automata and formal languages
Bill Hollingsworth
October 22, 2013
Reducibility
Functions
Denition
A function f : is called computable if there is a
Turing machine M such that, for each w , M halts on
Automata and formal languages
Bill Hollingsworth
October 19, 2013
Undecidability
HALTT M
HALTT M = cfw_< M, w > |M is a Turing machine accepting input w.
Theorem
HALTT M is undecidable.
Bill Hollingsw
Theory of Computation
Lecture 6
Bill Hollingsworth
[email protected]
billnet.org/cs/automata
Text: "Introduction to the theory of computation" by Michael Sipser
Regular languages
Theorem: The union of t
Automata and formal languages
Bill Hollingsworth
November 19, 2013
P and N P
P
Denition
P is the class of languages that can be decided in polynomial
time by a single-tape deterministic Turing machine
Automata and formal languages
Bill Hollingsworth
October 22, 2013
Decidability
ADF A
ADF A = cfw_< D, w > |D is a DFA that accepts the string w.
The language ADF A can be viewed as the acceptance prob
Theory of Computation
Lecture 4
Bill Hollingsworth
[email protected]
billnet.org/cs/automata
Text: "Introduction to the theory of computation" by Michael Sipser
Finite automata
A nite automaton is dened
Theory of Computation
Lecture 1
Bill Hollingsworth
[email protected]
Text: "Introduction to the theory of computation" by Michael Sipser
Overview
We want to understand the capabilities and
limitations o
Theory of Computation
Lecture 5
Bill Hollingsworth
[email protected]
billnet.org/cs/automata
Text: "Introduction to the theory of computation" by Michael Sipser
Regular languages
Denition: A language is
Theory of Computation
Lecture 3
Bill Hollingsworth
[email protected]
Text: "Introduction to the theory of computation" by Michael Sipser
Proofs
Let P and Q be statements (i.e., predicates). We
use the f
YunHa Jung
810380480
1). (10 points) Prove that the following function is computable by designing a detailed Turing machine.
Given an informal high-level description of your implementation.
f(x) = 5x