1. The document describes the process of converting a regular expression (RE) = (ab+c)* to an equivalent deterministic finite automaton (DFA).
2. It starts with the equivalent non-deterministic finite automaton with epsilon transitions (NFA-ε) for the given RE.
3. It then constructs the DFA by calculating the epsilon-closure of states and determining the transitions between states for each symbol in the alphabet.
4. The resulting DFA has 4 states - A, B, C, D and the transition table and diagram are shown.
This lecture slide contains:
1. Regular Languages
2. Regular Operations
3. Closure of regular languages
4. Regular expression
5. Precedence of regular operations
6. RE for different languages
7. RE to NFA conversion
8. DFA to GNFA to RE conversion
This Lecture Note discusses the followings:
- What is NFA
- DFA vs NFA
- How does NFA compute
- Designing different NFA machines
- Regular operations on NFAs
- Conversion from NFA to DFA
This lecture slide contains:
1. Regular Languages
2. Regular Operations
3. Closure of regular languages
4. Regular expression
5. Precedence of regular operations
6. RE for different languages
7. RE to NFA conversion
8. DFA to GNFA to RE conversion
This Lecture Note discusses the followings:
- What is NFA
- DFA vs NFA
- How does NFA compute
- Designing different NFA machines
- Regular operations on NFAs
- Conversion from NFA to DFA
This presentation contains:
1. Language, Regular Language
2. DFA vs. NFA
3. Components of DFA
4. Acceptability checking
5. Group-wise designing different types of DFA machines
Short Notes on Automata Theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science and discrete mathematics (a subject of study in both mathematics and computer science). The word automata (the plural of automaton) comes from the Greek word αὐτόματα, which means "self-making".
This presentation contains:
1. Language, Regular Language
2. DFA vs. NFA
3. Components of DFA
4. Acceptability checking
5. Group-wise designing different types of DFA machines
Short Notes on Automata Theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science and discrete mathematics (a subject of study in both mathematics and computer science). The word automata (the plural of automaton) comes from the Greek word αὐτόματα, which means "self-making".
Free Monads are a powerful technique that can separate the representation of programs from the messy details of how they get run.
I'll go into the details of how they work, how to use them for fun and profit in your own code, and demonstrate a live Free Monad-driven tank game.
Supporting code at https://github.com/kenbot/free
Mid-Term Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Fill in the blank with one of the words or phrases listed below.
distributive real reciprocals absolute value opposite associative
inequality commutative whole algebraic expression exponent variable
1) The of a number is the distance between the number and 0 on the number line.
A) opposite B) whole
C) absolute value D) exponent
1)
Find an equation of the line. Write the equation using function notation.
2) Through (1, -3); perpendicular to f(x) = -4x - 3
A) f(x) =
1
4
x -
13
4
B) f(x) = -
1
4
x -
13
4
C) f(x) = -4x -
13
4
D) f(x) = 4x -
13
4
2)
Multiply or divide as indicated.
3)
60
-5
A) -22 B) 12 C) - 1
12
D) -12
3)
Write the sentence using mathematical symbols.
4) Two subtracted from x is 55.
A) 2 + x = 55 B) 2 - x = 55 C) x - 2 = 55 D) 55 - 2 = x
4)
Name the property illustrated by the statement.
5) (-10) + 10 = 0
A) associative property of addition B) additive identity property
C) commutative property of addition D) additive inverse property
5)
Tell whether the statement is true or false.
6) Every rational number is an integer.
A) True B) False
6)
Add or subtract as indicated.
7) -5 - 12
A) 7 B) -17 C) 17 D) -7
7)
1
Name the property illustrated by the statement.
8) (1 + 8) + 6 = 1 + (8 + 6)
A) distributive property
B) associative property of addition
C) commutative property of multiplication
D) associative property of multiplication
8)
Simplify the expression.
9) -(10v - 6) + 10(2v + 10)
A) 30v + 16 B) -10v + 94 C) 10v + 106 D) 30v + 4
9)
Solve the equation.
10) 5(x + 3) = 3[14 - 2(3 - x) + 10]
A) -39 B) 3 C) -13 D) 39
10)
List the elements of the set.
11) If A = {x|x is an odd integer} and B = {35, 37, 38, 40}, list the elements of A ∩ B.
A) {35, 37}
B) {x|x is an odd integer}
C) {x|x is an odd integer or x = 38 or x = 40}
D) { }
11)
Solve the inequality. Graph the solution set.
12) |x| ≥ 4
A) (-∞, -4] ∪ [4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
B) [-4, 4]
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
C) [4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
D) (-∞, -4) ∪ (4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
12)
Solve.
13) The sum of three consecutive even integers is 336. Find the integers.
A) 108, 110, 112 B) 110, 112, 114 C) 112, 114, 116 D) 111, 112, 113
13)
2
Solve the inequality. Write your solution in interval notation.
14) x ≥ 4 or x ≥ -2
A) (-∞, ∞) B) [4, ∞)
C) [-2, ∞) D) (-∞, -2] ∪ [4, ∞)
14)
Use the formula A = P 1 + r
n
nt
to find the amount requested.
15) A principal of $12,000 is invested in an account paying an annual interest rate of 4%. Find the
amount in the account after 3 years if the account is compounded quarterly.
A) $1521.9 B) $13,388.02 C) $13,498.37 D) $13,521.90
15)
Graph the solution set ...
Automata theory - describes to derives string from Context free grammar - derivation and parse tree
normal forms - Chomsky normal form and Griebah normal form
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
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Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...
Automata theory - RE to DFA Conversion
1. Convert RE to DFA
1
a
2 b
4
5 6
c
7
𝜀
𝜀
𝜀
8
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
Dstates
𝜀
Transition table of DFA
Given RE = (ab+c)*
Equivalent NFA-ε is:
2. Convert RE to DFA
𝜀
NFA States
DFA
State
Next State
a b c
Dstates
Transition table of DFA
Initial state of NFA is {9}
Ε-closure(9)={9,7,1,5,10} ------
Where A is the initial state of DFA
A
3. Mark state A
1
a
2 b
4
5 6
c
7
𝜀
𝜀
𝜀
8
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A
Dstates
𝜀
Next need to find transition of (A,a) (A,b) (A,c)
4. Compute 𝜀-closure(move(A, a))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A
Dstates
𝜀
δ( A,a) = δ( (9,7,1,5,10),a) = {2}
=Ε-closure(2) = {2} ------ B
5. Compute 𝜀-closure(move(A, a))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B
{2} B
Dstates
𝜀
δ( A,a) = δ( (9,7,1,5,10),a) = {2}
Ε-closure(2) = {2} ------ B
6. Compute 𝜀-closure(move(A, b))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B -
{2} B
Dstates
𝜀
7. Compute 𝜀-closure(move(A, c))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B -
{2} B
Dstates
𝜀
δ( A,c) = δ( (9,7,1,5,10),c) = {6}
Ε-closure(6) = {6,8,10,7,1,5} ------ C
8. Mark move(A, c)) C
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B
{6,8,10,7,1,5} C
Dstates
𝜀
9. Compute 𝜀-closure(move(B, a))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B -
{6,8,10,7,1,5} C
Dstates
𝜀
10. Compute 𝜀-closure(move(B, b))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B -
{6,8,10,7,1,5} C
Dstates
𝜀
δ( B,b) = δ( (2,b) = {4}
Ε-closure(4) = {4,8,10,7,1,5} ------ D
11. Mark (move(B, b))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D
{6,8,10,7,1,5} C
{4,8,7,1,5,10} D
Dstates
𝜀
12. Mark - (move(B, c))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C
{4,8,7,1,5,10} D
Dstates
𝜀
13. Compute 𝜀-closure(move(C, a))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C B
{4,8,7,1,5,10} D
Dstates
𝜀
B
δ( C,a) = δ( (6,8,10,7,1,5)),a) = {2}
Ε-closure(2) = {2} ------
14. Mark (move(C, b))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C B -
{4,8,7,1,5,10} D
Dstates
𝜀
15. Compute 𝜀-closure(move(C, c))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C B -
{4,8,7,1,5,10} D
Dstates
𝜀
δ( C,c) = δ( (6,8,10,7,1,5)),a) = {6}
Ε-closure(6) = {6,8,10,7,1,5} ------ C
16. Mark (move(C, c))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C B - C
{4,8,7,1,5,10} D
Dstates
𝜀
17. Compute 𝜀-closure(move(D, a))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C B - C
{4,8,7,1,5,10} D
Dstates
𝜀
δ( D,a) = δ( (6,8,10,7,1,5)),a) = {2}
Ε-closure(2) = {2} ------ B
18. Mark (move(D, a))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C B - C
{4,8,7,1,5,10} D B
Dstates
𝜀
19. Mark (move(D, b))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C B - C
{4,8,7,1,5,10} D B -
Dstates
𝜀
20. Compute 𝜀-closure(move(D, c))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C B - C
{4,8,7,1,5,10} D B
Dstates
𝜀
C
( D,c) = δ( (4,8,7,1,5,10)),c) = {6}
Ε-closure(6) = {6,8,10,7,1,5} ------
21. Mark (move(D, c))
1
a
2 b
4
5 6
c
7
𝜀
𝜀
8
𝜀
𝜀
9 𝜀 𝜀
𝜀
10
NFA States
DFA
State
Next State
a b c
{9,7,1,5,10} A B - C
{2} B - D -
{6,8,10,7,1,5} C B - C
{4,8,7,1,5,10} D B - C
Dstates
𝜀
