2ª PARTE - Reunião que culminou com a criação da Comissão de Desenvolvimento de Políticas Tributárias para o setor de Revendedores de Veículos do Estado de Mato Grosso realizado, para o ano de 2016, na sede da secretaria da fazenda, (dia 14 de dezembro de 2015) com a presença do então Secretário de fazenda Paulo Brustolin.
2ª PARTE - Reunião que culminou com a criação da Comissão de Desenvolvimento de Políticas Tributárias para o setor de Revendedores de Veículos do Estado de Mato Grosso realizado, para o ano de 2016, na sede da secretaria da fazenda, (dia 14 de dezembro de 2015) com a presença do então Secretário de fazenda Paulo Brustolin.
Por este instrumento, de um lado, representando os empregados, o SINDICATO DOS EMPREGADOS NO COMÉRCIO DE CUIABÁ E VÁRZEA GRNADE, e do outro lado, representando os empregadores, o SINDICATO DOS CONCESSIONÁRIOS E DISTRIBUIDORES DE VEÍCULOS NACIONAIS E IMPORTADOS, TRATORES, COLHEITADEIRAS E MOTOS DO ESTADO DE MATO GROSSO – SINCODIV – T, tem justo e acertado firmar a presente Convenção Coletiva de Trabalho, regida pelas seguintes condições:CLÁUSULA PRIMEIRA - Abrangência e Base Territorial As partes ajustam que a presente Convenção se aplica a todas as empresas concessionárias e distribuidoras que realizam a comercialização de veículos automotores via terrestre, implementos e componentes novos, prestam assistência a esses produtos e exercem outras funções pertinentes à
atividade, nos termos da Lei N.º 6.729/79 (alterada pela Lei N.º 8.132/90), situadas nas localidades de Cuiabá e Várzea Grande, associadas ou não ao Sindicato patronal convenente, abrangendo todos os respectivos empregados, exceto os diferenciados.
Webcast - how can banks defend against fraud?Uniphore
The Annual Global Fraud Survey, commissioned by Kroll and carried out by the Economist Intelligence Unit, reports that businesses lose nearly 1.6% of their revenue to fraud. While global banks are utilizing IT solutions to safeguard themselves from cyber and online phishing attacks, our webcast helps you understand an innovative and cutting edge technology which can help you to:
* Stop revenue loss on fraud/identity thefts
* Prevent customers from cyber attacks
* Ensure 100% fail-proof customer authentication
* Provide confidence to customers and improve CSAT
* Protect banking information and customer data breach
Por este instrumento, de um lado, representando os empregados, o SINDICATO DOS EMPREGADOS NO COMÉRCIO DE CUIABÁ E VÁRZEA GRNADE, e do outro lado, representando os empregadores, o SINDICATO DOS CONCESSIONÁRIOS E DISTRIBUIDORES DE VEÍCULOS NACIONAIS E IMPORTADOS, TRATORES, COLHEITADEIRAS E MOTOS DO ESTADO DE MATO GROSSO – SINCODIV – T, tem justo e acertado firmar a presente Convenção Coletiva de Trabalho, regida pelas seguintes condições:CLÁUSULA PRIMEIRA - Abrangência e Base Territorial As partes ajustam que a presente Convenção se aplica a todas as empresas concessionárias e distribuidoras que realizam a comercialização de veículos automotores via terrestre, implementos e componentes novos, prestam assistência a esses produtos e exercem outras funções pertinentes à
atividade, nos termos da Lei N.º 6.729/79 (alterada pela Lei N.º 8.132/90), situadas nas localidades de Cuiabá e Várzea Grande, associadas ou não ao Sindicato patronal convenente, abrangendo todos os respectivos empregados, exceto os diferenciados.
Webcast - how can banks defend against fraud?Uniphore
The Annual Global Fraud Survey, commissioned by Kroll and carried out by the Economist Intelligence Unit, reports that businesses lose nearly 1.6% of their revenue to fraud. While global banks are utilizing IT solutions to safeguard themselves from cyber and online phishing attacks, our webcast helps you understand an innovative and cutting edge technology which can help you to:
* Stop revenue loss on fraud/identity thefts
* Prevent customers from cyber attacks
* Ensure 100% fail-proof customer authentication
* Provide confidence to customers and improve CSAT
* Protect banking information and customer data breach
5. How Euclid’s ‘Elements’ work
Definitions
Postulates
(公设)
Axioms
(公理)
Agreed Method
Each step in the proof is an
application of one of the above.
5
6. Hilbert’s question (1900)
Is there, or could there possibly be,
a definite method that could decide
whether a particular mathematical
expression is true?
What exactly do we mean by a
definite method?
Turing’s answer - mechanical –
algorithmic - the Turing machine
6
7. Theory Hall of Fame
Alan Turing
1912 – 1954
b. London, England.
PhD – Princeton (1938)
Research
Cambridge and Manchester U.
National Physical Lab, UK
Creator of the Turing Test
8
8. More about Turing
“Breaking the Code”
Movie about the personal life of Alan Turing
Death was by cyanide poisoning (some say suicide)
Turing worked as a code breaker for the Allies
during WWII.
Turing eventually tried to build his machine
and apply it to mathematics, code breaking,
and games (chess).
Was beat to the punch by vonNeumann
9
9. The Turing Machine
Some history
Created in response to Kurt Godel’s 1931
proof that formal mathematics was
incomplete
There exists logical statements that cannot
be proven by using formal deduction from a
set of rules
Good Reading: “Godel, Escher, Bach” by
Hofstadter
Turing set out to define a process by which
it can be decided whether a given
mathematical statement can be proven or not.
10
10. Theory Hall of Fame
Kurt Godel
1906 – 1978
b. Brünn, AustriaHungary
PhD – University of Vienna (1929)
Research
Princeton University
Godel’s Incompleteness Theorem
11
11. The Turing Machine
• Motivating idea
Build a theoretical “human computer”
Likened to a human with a paper and pencil that
can solve problems in an algorithmic way
The theoretical machine provides a means to
determine:
If an algorithm or procedure exists for a given
problem
What that algorithm or procedure looks like
How long would it take to run this algorithm or
procedure.
12
12. The Church-Turing Thesis
(1936)
Any algorithmic procedure that can
be carried out by a human or group
of humans can be carried out by some
Turing Machine
Equating algorithm with running on a TM
Turing Machine is still a valid
computational model for most modern
computers.
13
13. Theory Hall of Fame
Alonso Church
1903 – 1995
b. Washington D.C.
PhD – Princeton (1927)
Mathematics Prof (1927 – 1967)
Advisor to both Turing and Kleene
14
14. Turing’s Concept
A machine
With a finite set of states
Unrestricted input and output
Unlimited storage space
Simplest possible operations
01 00 1 11 1 10 0 0
Read/write head
Infinite tape
15
15. Basic operations of the
machine Read
Read the symbol on the current square
Change the inner state of the machine
Write
Change the symbol on the current square
Change the inner state of the machine
Move
Tape can move any distance left or right
01 00 1 11 1 10 0 0
Read/write head
Infinite tape
16
16. Turing Machine
A Machine consists of:
A state machine
An input tape
A movable r/w tape head
A move of a Turning Machine
Read the character on the tape at the
current position of the tape head
Change the character on the tape at the
current position of the tape head
Move the tape head
Change the state of the machine based on
current state and character read
17
17. Turing Machine
Tape that holds character
string
Movable tape head that reads
and writes character
Machine that changes state
based on what is read in
Input tape (input/memory)
State
Machine
(program)
Read head
…
18
18. Turing Machine
In the original Turing Machine
In the original Turing Machine
The read tape was infinite in both
directions
We describe a semi-infinite TM where
The tape is bounded on the left and
infinite on the right
It can be shown that the semi-infinite
TM is equivalent to the basic TM.
19
19. Turing Machine
About the input tape
Bounded to the left, infinite to the right
All cells on the tape are originally filled
with a special “blank” character □
Tape head is read/write
Tape head can not move to the left of the
start of the tape
If it tries, the machine “crashes”
20
20. Turing Machines
Let’s formalize this
A Turing Machine M is a 5-tuple:
M = (Q, Σ, Γ, δ, q0) where
Q = a finite set of states (assumed not to
contain the halting state h)
Σ = input alphabet (strings to be used as
input)
Γ = tape alphabet (chars that can be written
onto the tape. Includes symbols from Σ)
Both Σ and Γ are assumed not to contain the
“blank” symbol
δ = transition function
BUT WAIT, SHEN ME GUI?
21
21. What is language?
In mathematics, computer science, and
linguistics, a formal language is a set of
strings of symbols that may be constrained by
rules that are specific to it.
A programming language is a formal constructed
language designed to communicate instructions
to a machine, particularly a computer.
Programming languages can be used to create
programs to control the behavior of a machine
or to express algorithms.
22
22. Formal Languages
Finite Automata
Non Finite Automata
Regular Expressions
Context Free Languages
Pushdown Automata
Turing Machines
…
23
24. Turing Machines
Transition function:
δ: Q x (Γ { Δ }) (Q {h}) x (G { Δ }) x {R, L,
S}
Input:
Current state
Tape symbol read at current position of tape head
Output:
State in which to move the machine (can be the halting
state)
Tape symbol to write at the current position of the tape
head (can be the “blank” symbol)
Direction in which to move the tape head (R = right, L =
left, S= stationary)
25
25. Turing Machines
Transition Function
q0 q1
X / Y, R
Symbol at
current tape
Head position
Symbol to
write at the
current head
position
Direction in
which to move
the tape head
<q0, X> <q1, Y, R>
26
26. Let Σ = input alphabet = {0, 1}, then transition
functions can be shown as a table
Current Input Output Move Next
0 0 1 - 1
0 1 - R 0
1 1 - L 1
1 0 - R Stop
27
1 0 1 00 1 …
1 1 1 00 1 …
q1
q3
δ(q1, 0) = (q3, 1, L)
27. A more complicated transition table
Current Input Output Move Next
0 0 0 R 0
0 1 0 R 1
1 0 1 L 10
1 1 1 R 1
10 0 0 R 11
10 1 0 R 100
11 0 1 Stop 0
11 1 1 R 11
100 0 1 L 101
100 1 1 R 100
101 0 1 L 10
101 1 1 L 101
28
28. Live Demo
https://www.khanacademy.org/computer-
programming/double1s/6037171975487488
29
30. 31 Successor Program
Rules:
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
Let’s see how they are carried out on a piece of paper
that contains the reverse binary representation
of 47:
31. 32 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
1 1 1 1 0 1
32. 33 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 1 1 1 0 1
33. 34 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 1 1 0 1
34. 35 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 0 1 0 1
35. 36 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 0 0 0 1
36. 37 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 0 0 1 1
37. 38 Successor Program
So the successor’s output on 111101 was 000011
which is the reverse binary representation of 48.
Similarly, the successor of 127 should be 128:
38. 39 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
1 1 1 1 1 1 1
39. 40 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 1 1 1 1 1 1
40. 41 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 1 1 1 1 1
41. 42 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 0 1 1 1 1
42. 43 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 0 0 1 1 1
43. 44 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 0 0 0 1 1
44. 45 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 0 0 0 0 1
45. 46 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 0 0 0 0 0
46. 47 Successor Program
If read 1, write 0, go right, repeat.
If read 0, write 1, HALT!
If read □, write 1, HALT!
0 0 0 0 0 0 0 1
50. Turing Machine
Running a Turing Machine
The execution of a TM can result in 4 possible
cases:
The machine “halts” (ends up in the halting
state)
The machine has nowhere to go (at a state,
reading a symbol where no transition is defined)
The machine “crashes” (tries to move the tape
head to before the start of the tape)
The machine goes into an “infinite loop” (never
halts)
51
51. Turing Machine
Accepting a string
A string x is accepted by a TM, if
Starting in the initial configuration
With x on the input tape
The machine eventually ends up in the
halting state.
52
52. Turing Machine
Running a Turing Machine
The execution of a TM can result in 4
possible cases:
The machine “halts” (ACCEPT)
The machine has nowhere to go (REJECT)
The machine “crashes” (REJECT)
The machine goes into an “infinite loop”
(REJECT but keeps us guessing!)
53
53. Turing Machine
Language accepted by a Turing Machine
The language accepted by a TM is the set of
all input strings x on which the machine
halts.
54
54. Will a Turing Machine halt?
In computability theory, the halting problem
is the problem of determining, from a
description of an arbitrary computer program
and an input, whether the program will finish
running or continue to run forever.
55
Halting Machine (HM)
program +
inputs
yes
or
no
Exist?
80. 形成规则
(1) 项的形成规则
(i) 任一个体变元 x , 任一常项 c 都是一个项。
(ii) 若 F 是一个带 k 个变目的函词,t1,t2,…,tk
是项,则F(t1,t2,…,tk)是一个项。
(iii) 只有由定义 (i) ,(ii) 归纳定义得到的字符串
是项。
81
81. (2)公式的形成规则
I. F 是一个 k 目函词, t1,t2,…,tk,tk+1是项,则F(t1,t2,…,tk)=tk+1
是一公式。
II. P 是一个 k 目谓词, t1,t2,…,tk是项, P(t1,t2,…,tk)则是一
公式。
III. A, B 是公式,则~𝐀, 𝐀 ∧ 𝑩, 𝑨 ∨ 𝑩, 𝑨 → 𝑩, 𝑨 ↔ 𝑩是公式。
IV. A 是公式,x 是一变元,则∃𝒙𝑨, ∀𝒙𝑨是公式。
仅由 (1) - (iv) 归纳定义得到的字符串是公式。
82
82. (3)语句的定义
公式 A 是一个语句,如果 A 中不含任何变元的自由出现。
(即,A是一个命题)
(4)给定一阶语言 L , T 是一个一阶理论,如果它
包括:
① 谓词演算的所有公理。
② 一个 L 中的语句组成的集合,有穷或者无穷。它们称为
非逻辑公理。
③ 谓词演算的所有推理规则
83