Example:
Consider the CFG
A BC|0
B BA| 1 |CC
C AB| 0
C
B
B
B
1
B
A
A
C
0
A
1
Derivation of the string
11100001
A
1
B
B
C
C
C
1
0
0
0
A BC BAC 1AC 1BCC 11CC 11ABC
11BCBC 111CBC 1110BC 1110CCC 11100CC
111000C 111000AB 1110000B 11100001
1
SCS 4008
Dr. T. S
Pumping Lemma for Regular Languages
By: Dr.T.Sritharan
1
SCS 4008
Dr. T. Sritharan
9/20/2016
Non Regular Languages
To show that a language L is regular we can do any one of the
following:
1.
2.
3.
4.
Construct a DFA that accepts L
Construct a NFA that acc
Computability and
Decidability
By: Dr.T.Sritharan
Text Book: Languages and Machines
By: Thomas A. Sudkamp
SCS 4008
Dr. T. Sritharan
11/15/2016
Recursive & Recursively Enumerable Languages
A Language L over the alphabet is Recursive if there exists a
Turin
Topic 5:
Chomsky Normal Form
By: Dr.T.Sritharan
UCSC
1
Dr. T. Sritharan
10/3/2016
Leftmost Derivation
Let G be a
grammar
G: S AB
A AA | a
B BB | b
Consider the following derivations of aaabb
1
S AB
AAB
aAB
aABB
aAABB
aAABb
aAaBb
aaaBb
aaabb
2
S AB
Topic 7:
Pushdown Automata
By: Dr.T.Sritharan
UCSC
1
SCS 4008
Dr. Sritharan
10/10/2016
Pushdown Automata(PDA)
Class of PDAs recognize exactly the class of Context- Free
Languages (CFLs).
Consider the language = 0 1 | 0 .
We know that L is not regular but
UNIVERSITY OF COLOMBO, SRI LANKA
UNIVERSITY OF COLOMBO SCHOOL OF COMPUTING
DEGREE OF BACHELOR OF INFORMATION TECHNOLOGY (EXTERNAL)
nd
Academic Year 2010/2011 2 Year Examination Semester 3
IT3304: Mathematics for Computing-II
PART 2 - Structured Question P
Creating Direction Fields with DERIVE 5
Last updated: January 22, 2007 Steve Billups, modified by Lance Lana This tutorial describes how to use DERIVE 5 to generate a direction field for the first order differential equation:
dy -dx = r(x,y)
Direction fie
Laplace Transform Table
(Adapted from Table 5.1 of Kohler and Johnson) Time Domain Function f (t), t 0 Laplace Transform F (s) a h(t) = tn , et sin(t) cos(t) sinh(t) cosh(t) et f (t), with |f (t)| M eat et h(t) et tn , et sin(t) et cos(t) n = 1, 2, 3. 1,
Math 3200 Mini-Projects
(modied from Bill Briggs 2004) This collection of assorted mini-projects is supported by the material that we will study this semester. You must complete two (2) mini-projects during the semester. The rst mini-project is due no lat
Form of Particular Solution
(Adapted from Table 3.1 of Kohler and Johnson) The right-hand column gives the proper form to assume for a particular solution of ay + by + cy = g (t). In the right-hand column, choose r to be the smallest nonegative integer su
MATH 3200
Review for Test 1
Bennethum
These are practice problems for test 1. For this exam, one side of an 8.5x11 sheet of paper will be allowed for notes. No technology of any kind will be allowed. The topics covered on this exam include material covere
MATH 3200
Review for Test 2
Bennethum
These are practice problems for test 2. For this exam, one side of an 8.5x11 sheet of paper will be allowed for notes. No technology of any kind will be allowed. The topics covered on this exam include material covere
MATH 3200 Bennethum Review Problems for Final Exam: Laplace Transforms
These are practice problems on the Laplace trasform for the nal exam. For this exam, two sides of an 8.5x11 sheet of paper will be allowed for notes (it can be on two separate sheets).
Review of Dierentiation and Integration for MATH 3200 UCD Department of Mathematical and Statistical Sciences
This is a packet of prerequisite material necessary for understanding material covered in ordinary dierential equations. Many students take this
BC x
Name:
TI-89 Slope Fields, Euler, etc.
(assuming basic TI-89 knowledge) Mode Graph Diff Equations Y= F1 (9) Graph Formats Set: Solution Method Euler Fields Slpfld
To graph a slope field:
Under Y= , enter the differential equation in y1' =. Example: y1
Appendix A Review of Mathematical Results
A.1 Local Minimum and Maximum for Multi-Variable Functions
Recall that for a single-variable function, f (x), local extrema (local maxima or minima) can occur only at critical points. For single-variable functions
Appendix A Review of Mathematical Results
A.1 Local Minimum and Maximum for Multi-Variable Functions
Recall that for a single-variable function, f (x), local extrema (local maxima or minima) can occur only at critical points. For single-variable functions
Chapter 2 Deformation and Strain
In this chapter we explain how deformation is described precisely. This gives us the framework to model the deformation of a metal beam for example, which is holding up a building (although we wont do this problem here).
2
Chapter 3 Balance Laws
In this chapter we explore the governing eld equations: the conservation of mass and linear momentum, the balance of angular momentum, and the conservation of energy. Although we refer to these principles as laws, they are postulate
Chapter 4 Introduction to Thermodynamics
In this chapter we introduce the topic of thermodynamics which are needed to develop governing equations (specically constitutive equations) for a continuous medium. The development of constitutive equations will b
Chapter 5 The Entropy Inequality and Constitutive Equations
In the 1950s and 1960s, thermodynamics was combined with classical continuum mechanics to form a rational method for developing constitutive equations. These methods were pioneered by A. C. Ering
Chapter 6 Miscellaneous Topics
6.1 Boundary Conditions
After determining the governing equations one must determine appropriate boundary and initial conditions which make the problem physically meaningful and mathematically possible to solve. Mathematical
Project Information
Continuum Mechanics, Spring 2008 Due 4pm, Friday May 9, 2008 The project for this course consists of two parts: the written report and the oral report. The written report (worth 80% of the project grade) may be hand written or typed an