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APPLICATIONS OF AUTOMATA THEORY IN INFORMATION AGE

1. DEFINITION
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, under discrete mathematics (a section of Mathematics and also of Computer Science). Automaton comes from the Greek word αὐτόματα meaning "self-acting".
So, Automata Theory is the study of self-operating virtual machines to help in logical understanding of input and output process, without or with intermediate stage(s) of computation (or any function / process).
2. APPLICATIONS

2.1 Vending Machines

Figure 1 presents a DFA that describes the behavior of a vending machine which accepts dollars and quarters, and charges $1.25 per soda. Once the machine receives at least $1.25, corresponding to the blue-colored states in the diagram, it will allow the user to select a soda. Self-loops represent ignored input: the machine will not dispense a soda until at least $1.25 has been deposited, and it will not accept more money once it has already received greater than or equal to $1.25.

To express the DFA as a 5-tuple, the components are defined as follows:

1. Q = {$0:00; $0:25; $0:50; $0:75; $1:00; $1:25; $1:50; $1:75; $2:00} are the states
2. ∑= {$0:25; $1:00; select} is the alphabet
3. ∂, the transition function, is described by the state diagram.
4. qₒ = $0:00 is the start state
5. F = ᵠ; is the set of accept states

[pic]

2.2 Washing Machines

A basic washing machine is easily modeled as a finite automaton. Now that you understand Finite State Machines, you can get really clean clothes.

[pic]

2.3 Modeling TCP
Internet protocols also lend themselves to descriptions as DFAs. The state diagram below represents a simplified version of the Transmission Control Protocol (TCP).
The state machine in Figure 4 describes the “life stages” of a TCP connection.

[pic] [pic]

(a)TCP Client Diagram (b) TCP Server Diagram

2.4 Biology

Cellular automata are used in the field of biology, the most common example being John Conway's Game of Life."Life" is probably the most frequently written program in elementary computer science. The basic structure of Life is a two-dimensional cellular automaton that is given a start state of any number of filled cells. Each time step, or generation, switches cells on or off depending on the state of the cells that surround it. The rules are defined as follows: • All eight of the cells surrounding the current one are checked to see if they are on or not. • Any cells that are on are counted, and this count is then used to determine what will happen to the current cell: 1. Death: if the count is less than 2 or greater than 3, the current cell is switched off. 2. Survival: if (a) the count is exactly 2, or (b) the count is exactly 3 and the current cell is on, the current cell is left unchanged. 3. Birth: if the current cell is off and the count is exactly 3, the current cell is switched on.
Like any manifestation of automata theory, the Game of Life can be defined using extremely simple and concise rules, but can produce incredibly complex and intricate patterns.

2.5 Compiler Design

The first phase of compiler is lexical analysis. Lexical analysis phase takes given source program as input and gives tokens as output. The tokens are keywords, identifiers, operators, special symbols, constants and strings. An automaton has the ability of recognizing given strings based on the rule hence deterministic finite automata is used to perform lexical analysis. Lexical analyzer will be designed as per the following steps.
1. Write down the regular expression for the given language
2. Build Non deterministic finite automata
3. Convert NFA to DFA
4. Systematically minimize DFA
5. Convert DFA into code which is lexical analyzer

2.6 Intrusion Detections Systems

An intrusion is a malicious harm on information resources in which the troublemaker attempts to gain doorway into a system or disturb the normal operations. Incident response is the recognition of, classification of, response to, and revival from an incident called Intrusion Detection System (IDS). IDS are broadly classified into anomaly detection system and misuse detection model. Context free grammar is used to analyse the traffic pattern in the network which can help to decide whether traffic is normal or an attack. Automated, conservative, intrusion detection techniques, i.e. techniques which do not require human intervention and do not suffer from false positives. An important consideration for on-the-fly intrusion detection is to reduce the performance overhead caused by monitoring. Compared to the existing approaches, our in lined automaton model (IAM) presents a good tradeoff between accuracy and performance. Expressive power of regular expressions has been often exploited in network intrusion detection systems, virus scanners, and spam filtering applications. However, the flexible pattern matching functionality of regular expressions in these systems comes with significant overheads in terms of both memory and CPU cycles, since every bite of the inspected input needs to be processed and compared against a large set of regular expressions. The timed automaton is constructed by the way of manually abstracting the correct behavior of the node according to the routing protocol of dynamic source routing (DSR). The monitor nodes can verify the behavior of every node by timed automata, and validly detect real-time attacks without signatures of intrusion or trained data.

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