The study of automata has been acquiring increasing importance for engineers in many fields. For some time, the capabilities of these automata have been of the greatest interest to logicians and mathematicians. However, the expanding literature on the use of finite automata as probabilistic models demonstrates the growing interest in the application of these mechanisms to engineering phenomena. We, the authors, became interested in these probabilistic models in an effort to develop a general self-adaptive control scheme based on the prediction of the future of the process to be controlled. Conceivably, an adequate model of a particular process could be generated by simply observing the process parameters. With this goal in mind we began an investigation of several different modeling techniques. The ability to model stochastic data was our primary concern. We feel that the results of several modeling experiments presented here may be of interest to our readers, and we hope to encourage the use of these techniques, especially in control applications. We have seen an example of use of finite automata in describing the operation of a simplified version of vending machine. Many other systems operating in practice can also be modeled by finite automata such as control circuits of computers, computer network communication protocols, lexical analysers for compilers etc. Many of those systems fall into the class of systems called reactive system. In the case of vending machine or communication protocol, on the other hand, a system must respond to each stimulus, even to a fragment of input such as each coin tossed in for a can of soda or every message received.

Applications of Regular Expression
1.Regular expressions in Unix
In the UNIX operating system various commands use an extended...

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Finite-State Machines and PushdownAutomata
The ﬁnite-state machine (FSM) and the pushdown automaton (PDA) enjoy a special place in computer science. The FSM has proven to be a very useful model for many practical tasks and deserves to be among the tools of every practicing computer scientist. Many simple tasks, such as interpreting the commands typed into a keyboard or running a calculator, can be...

...FINITEAUTOMATA AND REGULAREXPRESSION GENERATOR (FARE) – A PROPOSED COMPUTER-AIDED INSTRUCTION TOOL
LEO C. BERMUDEZ
ASIAN COLLEGE OF TECHNOLOGY
CEBU CITY, PHILIPPINES
MARCH 2006
FINITEAUTOMATA AND REGULAREXPRESSION GENERATOR (FARE) – A PROPOSED COMPUTER-AIDED INSTRUCTION TOOL
A Thesis Presented to the
Faculty and Staff of the Graduate School
Asian College of...

...
Equivalence of FiniteAutomata and RegularExpressionsFiniteAutomata Recognize Regular Languages Theorem 1. L is a regular language iﬀ there is a regularexpression R such that L(R) = L iﬀ there is a DFA M such that L(M ) = L iﬀ there is a NFA N such that L(N ) = L. i.e., regularexpressions, DFAs and NFAs have the same...

...have,
=
= {e} {a, ab} {aa, aab, aba, abab} …
=
= {a, ab} {aa, aab, aba, abab} …
Note : e is in , for every language L, including .
The previously introduced definition of is an instance of Kleene star.
Automata and Grammars
Automata
An automata is an abstract computing device (or machine). There are different varities of such abstract machines (also called models of computation) which can be defined mathematically. Some...

...Contents
We have seen an example of use of finiteautomata in describing the operation of a simplified version of vending machine. Many other systems operating in practice can also be modeled by finiteautomata such as control circuits of computers, computer network communication protocols, lexical analysers for compilers etc. Many of those systems fall into the class of systems called reactive system. A reactive system is a system that...

...Lesson 3 FiniteAutomata with Output
Three types of automata are studied in Formal Language Theory. *
Acceptor
The symbols of the sequence
s(1) s(2) … s(i) … s(t)
are presented sequentially to a machine M. M responds with a binary signal to each input. If the string scanned so far is accepted, then the light goes on, else the light is off.
A language acceptor
* Lesson 3 employs the treatment of this subject...

...Languages, Grammars, and Automata Theory
Discrete Mathematics
Linda Chalk
Colorado Technical University
Professor Timothy Manzke
December 17, 2010
Languages, grammars and automata theory are all related to computer applications. Grammar is the rule for language structure regardless of the meaning. For computer programming languages context free grammar (CFG) is commonly used. Formal language as opposed to natural language must be used with computer...

...Figure 3: Figure for Solution of Problem 5 in Practice Sheet 1
6. Let L be the language {w|w contains an equal number of occurrences of the substrings
01 and 10 }. Thus 101 is in L, while 1010 is not. Show that L is regular.
Soln: The language corresponding to the regularexpression 1+ (0+ 1+ )∗ + (0+ 1+ )∗ 0+
describes all such strings. This is obtained by generalizing the structure of the strings
101 and 010 (Note that: a+ = aa∗ ).
2...

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