Alphabets‚ Strings and Languages Example : Consider the string 011 over the binary alphabet. All the prefixes‚ suffixes and substrings of this string are listed below. Prefixes: e‚ 0‚ 01‚ 011. Suffixes: e‚ 1‚ 11‚ 011. Substrings: e‚ 0‚ 1‚ 01‚ 11‚ 011. Note that x is a prefix (suffix or substring) to x‚ for any string x and e is a prefix (suffix or substring) to any string. A string x is a proper prefix (suffix) of string y if x is a prefix (suffix) of y and x y. In the above example‚ all
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C H A P T E R Finite-State Machines and Pushdown Automata 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 modeled by finite-state machines. The PDA is a model to which one appeals when
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Finite Automata Finite Automata • Two types – both describe what are called regular languages – Deterministic (DFA) – There is a fixed number of states and we can only be in one state at a time – Nondeterministic (NFA) –There is a fixed number of states but we can be in multiple states at one time • While NFA’s are more expressive than DFA’s‚ we will see that adding nondeterminism does not let us define any language that cannot be defined by a DFA. • One way to think of this is we might write
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Lesson 3 Finite Automata 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 as found in Machines‚ Languages‚ and Computation
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Implementations of: Finite automata Regular expression Pushdown automata Engineering applications of finite automata 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
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CS-Paper Code-B GATE 2011 www.gateforum.com Q. No. 1 – 25 Carry One Mark Each 1. The simplified SOP (Sum of Product) P + Q + R . P + Q + R . P + Q + R is form of the Boolean expression )( (A) (PQ + R ) QR ( )( ) (B) P + QR ( ) )( (C) PQ + R ( ) (D) (PQ + R ) Answer: - (B) Exp: P 0 00 01 1 11 1 10 1 f = P+R P+Q = P + QR ( ) 1 Alternate method (P + Q + R ) . (P + Q + R ) . (P + Q + R ) = (P + Q + R ) . (P + Q + R ) . (P + Q + R )
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Deque Automata for all classes of Formal languages B. Asha latha1 Department of computers SRKIT Engineering Vijayawada Andhra Pradesh (India) T.Vishnupriya2 Department of Electronics SRKIT Vijayawada‚ Andhra Pradesh (India) N.Himabindu3 Department of computers KBN College of Vijayawada‚ Andhra Pradesh (India) Abstract: The purpose of computation involves solving problems by communicating them to a computational model by means of a suitable language .A number of languages have been developed
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FINITE AUTOMATA AND REGULAR EXPRESSION GENERATOR (FARE) – A PROPOSED COMPUTER-AIDED INSTRUCTION TOOL LEO C. BERMUDEZ ASIAN COLLEGE OF TECHNOLOGY CEBU CITY‚ PHILIPPINES MARCH 2006 FINITE AUTOMATA AND REGULAR EXPRESSION GENERATOR (FARE) – A PROPOSED COMPUTER-AIDED INSTRUCTION TOOL A Thesis Presented to the Faculty and Staff of the Graduate School Asian College of Technology Cebu City‚ Philippines In Partial fulfillment Of the Requirement for the degree MASTER OF SCIENCE IN COMPUTER
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Practice Sheet 1 1. The language L = {w|w has exactly two 0’s and at least two 1’s } is the intersection of two simpler languages. Construct DFA’s for the simpler languages and then combine them using the idea of a product automaton to obtain a DFA that accepts L. Minimize this DFA‚ using the minimization algorithm‚ using the algorithm explained in the class. Soln: Similar to Problem 2. 2. The language L = {w|w has even length and an odd number of 0’s } is the intersection of two simpler languages
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INTRODUCTION TO THE THEORY OF COMPUTATION‚ SECOND EDITION MICHAEL SIPSER MassachusettsInstitute of Technology THOMSON COURSE TECHNOLOGY Australia * Canada * Mexico * Singapore * Spain * United Kingdom * United States THOIVISON COURSE TECHNOLOGY Introduction to the Theory of Computation‚ Second Edition by Michael Sipser Senior Product Manager: Alyssa Pratt Executive Editor: Mac Mendelsohn Associate Production Manager: Aimee Poirier Senior Marketing Manager: Karen Seitz COPYRIGHT
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