Turing

1912-2012 : “100 years of Genius”

Salient Points of the Presentation
 A Brief History of Turing’s Life
 Turing’s Contributions to Computer Science
 Turing Machine
 Turing Test
 Turing Completeness(Programming Language)
 ACE (Automated Computing Engine)
 AI (Artificial Intelligence)
 Artificial Life
 Halting Problem

After the War he On his return He met his
During WWII, he demise on:
Alan Mathias worked at The
reformulated from the U.S,he
Turing: Born 23 Government Code Hilbert’s decision joined the 7 June
June 1912,Maida & Cipher School at problem and gave National 1954 (aged 4
Vale, London, Bletchley Park as a his own hypothesis Physical 1)
England, United Cryptanalyst. which is now know Laboratory, in Wilmslow
Kingdom. But was Where he invented as the Halting Cheshire,
Manchester,
conceived in the bombe to England,
Problem where he United
Chatrapur Odisha, crack the German
his father worked codes. He was There after,he developed the Kingdom,
for the Indian Civil placed in Hut – 8, worked under Automated
Cause of
Sevices.He the division Alonso Church at Computing death
attended responsible for Princeton and gave Engine(ACE),wh according to
Sherbone School Intercepting and the Church-Turing ich is a the reports is
in
Dorset,thereafter
breaking the hypothesis which primitive type cyanide
German gives a formal of Computer. poisoning.
enrolled in Kings codes.According to Thereafter, he
College and where some estimates his definition of This marks
“Turing Machine” became the end of an
he passed with a work reduced the
First Class honours war time in the interested in a era and the
in Mathematics Atlantic by at least subject called beginning of
“Artificial Life” a revolution.
two years.

 A wartime hero in all respects, as he was instrumental in the defeat of the Germans in the
Atlantic.
 Popularly known as Father of Computer Science, indeed true in all respects.
 His turing machine formed the basis of the Modern Computer.
 His reformulation of the Halting Problem,which was first introduced by Hilbert as the
“Entscheidungsproblem", later led to a set of problems known as NP complete.
 The Turing Test served as the benchmark for recognizing an intelligent machine, this was
published in his 1936 paper, where he rigorously debated on the topic-”Can Machines
think”.
 This paper set the ball rolling for the development of Artificial Intelligence and Machine
Learning.
 Turing Complete- A term associated with programming languages provides the measure of
computing power of any given language.
 He himself envisioned Computers one day beating Grandmasters at Chess.(which is today a
reality).
 His contributions to Speech Cryptography is lesser known albeit he developed “Delilah” at
Bell Labs.
 In his last years he was deeply interested in mathematical biology, especially finding patterns
in Chemical Morphogenesis.
 Hence to sum it all up, his contribution to the development of Computer Science was akin to
that of the fire and wheel in the progress and survival of the human race.

 The Turing Machine which I call the “simple wonder”,
consists of a tape with symbols etched on them, and a head
which is restricted to move only forward and backward,
reading the symbols and performing necessary actions
according to a table of rules.
 The most simple Turing machine can be approximated to
a DFA(Deterministic Finite Automata).The following example
will illustrate the same. 1/0
0
1

Start State Final State

 A turing machine consists of a tape which is divided into cells,each cell has
an alphabet etched on it or it might be left blank, the alphabet can belong to
any “Formal Language” or a Regular Expression.”
 A head which is capable of movement in the left and right directions and it
reads the symbols which are written on the tape.
 A State Register which stores the state of the of the machine.
 Then there is an action table, which stores the actions to be performed on
encountering a specific symbol or state.
 Thus a complete turing machine can be thought of as a tuple of the
following:

{ Q , ∑ , δ , q0 , F }
Where:
Q : Finite Set of States
∑ : Finite Set of Input Symbols
δ : Transition State a function of f(Q,sigma)
q0 : The initial state or the start state
F : Final State or the Accept State.

The Universal Turing Machine: A
turing Machine which can mimic
any other turing machine is
known as the Universal Turing
Machine. In simple words it can
solve any problem which is posed
to it.
The Turing Oracle: It is a turing
Machine, which has an infinite
amount of tape length. Its is used
to solve decision problems,
though it fails in the halting
problem.

Can Machines Think???....
 That was the same question that Turing asked in his 1950 paper titled
“Computing Machinery and Intelligence”. Rather than going into the details and
definitions of various terms in the question . He instead decided to reframe the
question as “Can machines Imitate humans”.
 This was the most pertinent question which early researchers in the field of
Artificial Intelligence have asked and in this field Turing was the torch-bearer. His
paper countered all the objections raised against a machine thinking as intelligently
as humans.
 This was when he presented the Turing Test which has now become the Litmus
test of Machine Intelligence. It was based on the ‘Imitation Game’ , infact there are
several versions of this the most important among them are ‘Imitation Game’ and
the ‘Standard Turing Test’.
 Several machines have passed the turing test till date,first among them are
Joseph Weizenbaum’s “ELIZA” and Kenneth Colby’s “PARRY”.
 Most recently there are several chatterbots existing.
 IBM’s Watson is the most powerful and intelligent machine, till date which has
Natural Language Processing capabilities.It has beaten the all-time champions of
popular show Jeopardy,and is on it’s way to commercialization.

The Imitation Game: This is also known as
the party game,where there are two people
on man and a woman and a third person
who is the interrogator. The Interrogator can
only interact with the two people through
text , that is letters. The man tries to trick
the interrogator into believing that he is a
woman and the woman tries to befool the
interrogator that she is a man. The
interrogator must recognize the truth
behind the messages. In turing’s version of
the game either the man or the woman is
replaced by a digital computer.

The Standard Turing Test: In this test
the differences between the sexes is
dissolved , there is a computer and a
person, and an interrogator. The
Computer tricks the
Interrogator into believing that it is a
human . If it passes then it is Intelligent.

 Reverse Turing Test: This is where a computer decides for itself where it interacts with a
human or not. CAPTCHA’s are examples of this.Though breaking the CAPTCHA code is quite easy
with artificial Neural Networks.
 The Loebner Prize : Its is an annual competition held at Center for Behavioral Studies in
Cambridge , Massachusetts (U.S). This is where various intelligent machines try to deceive the
judges and since its inception in the year 1991 it has received , overwhelming participation from
various corners of the world. Though there is enough scepticism regarding the rules and the
procedure of testing , most consider this prestigious award as the recognition of their machine’s
intelligence.
 Drawbacks: The most significant one raised by John Searle which states that the Turing Test
doesnot take into account the Mental State and the previous knowledge of the interrogator
,that is whether the interrogator knows he is testing a Computer or not. Then there are
quintessential human emotions like greed & avarice, rancour & jealously. Tenacity, and most
importantly Imagination the brainchild of human survival and the harbinger of innovation which
machines lack.

1. In Computability theory a system of data-manupulation rules
which can simulate any single taped turing machine is known as
Turing Complete.
2. In practice, Turing completeness means that rules followed in
sequence on arbitrary data can produce the result of any
calculation. In imperative languages, this can be satisfied by
having, at a minimum, conditional branching (e.g., an "if" and
"goto" statement) and the ability to change
arbitrary memory locations (e.g., having variables). To show that
something is Turing complete, it is enough to show that it can be
used to simulate the most primitive computer, since even the
simplest computer can be used to simulate the most complicated
one.
3. Thus , Turing Completeness is a measure of the computational
power of any given programming language.

1. The Automatic Computing Engine (ACE) was an
early electronic stored-program computer design produced
by Alan Turing at the invitation of John R. Womersley,
superintendent of the Mathematics Division of the National
Physical Laboratory (NPL). It was based on turing’s work at
Bletchley Park , where he designed the Colossus Computers for
breaking the German Codes.

2. Turing’s draft on the construction of the Engine stated that “It
should use stored program in its memory”, he had laid out the
detailed logic diagrams and the circuits for construction of the
Computer.

3. The Pilot Model of the ACE was developed and soon after John
Von Nuemann proposed his design for the EDVAC which was
based on turing work and this is the same architecture that is
used in the Modern Computers.

Navigating through the Intelligence…
I. Artificial intelligence (AI) is the intelligence of machines and the
branch of computer science that aims to create it. AI textbooks
define the field as "the study and design of intelligent
agents" where an intelligent agent is a system that perceives its
environment and takes actions that maximize its chances of
success. John McCarthy, who coined the term in 1955, defines it as
"the science and engineering of making intelligent machines.“

II. The field of AI research was founded at a conference on the
campus of Dartmouth College in the summer of 1956.The
attendees, including John McCarthy, Marvin Minsky, Allen
Newell and Herbert Simon, became the leaders of AI research for
many decades. They and their students wrote programs that were,
to most people, simply astonishing.

Continued…
 The field of AI has seen its ups and downs, it has seen the oft termed
“AI winter” in the 70’s and the early 90’s.
 But today it is soaring high and has brought almost all the
Computational fields under its ambit.
 Popular applications of AI include : “Data Mining”, “Search
Optimization”, “Social Intelligence”, “Neural Networks”, “Logic”.
 Google’s Search Engine uses AI to optimize your search queries.
 Robotics which is soon going to a significant game-changer has AI as
its cornerstone.

 Examples of AI based systems include:

 IBM’s chess playing Deep Blue, IBM’s Watson,
 DARPA Grand Challenge.
 HOAP 2

Turing’s Contribution…
Turing worked from 1952 until his death in 1954
on mathematical biology, specifically morphogenesis. He
published one paper on the subject called The Chemical Basis
of Morphogenesis in 1952, putting forth the Turing
hypothesis of pattern formation. His central interest in the
field was understanding Fibonacci phyllotaxis the existence of
Fibonacci numbers in plant structures. He used reaction–
diffusion equations which are central to the field of pattern
formation. Later papers went unpublished until 1992 when
Collected Works of A.M. Turing was published. His
contribution is considered a seminal piece of work in this
field.

The Problem Statement is : Can there ever be a program which
can predict whether another program will halt on a specific input.

DOES-HALT(program,input) // halts if the program goes into an infinte
loop else does-not halt.

SELF-HALT(program) {
if (DOES-HALT(program,program)) {
infinite loop
} else {
halt
}
}
Now we give the input to the function self-halt as follows:
SELF-HALT(SELF-HALT)
What happens….????

A A A
Given above is a buffer gate which consists of two NOT gates .
As is evident since it undergoes a double inversion we get the output same as
the input. A turing Machine can be roughly compared to a NOT gate for the
sake of simplicity and understanding and not for any real implications. In
reality the turing machine is a DFA(Deterministic Finite Automata), that is its
states are fixed and predetermined and can transition to only one state on a
single input. Here we are trying to create a parallelism between the Buffer
gate and the Halting Problem for a better and much easier understanding of
the latter. Similar to the Buffer Gate the Output of one turing machine when
fed as the Input of another equivalent turing machine should yield the original
input but in reality it doesnot.This is the paradox and using this we can prove
that such a machine cannot exist which can predict whether a program will
stop or not

Turing

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Turing