automata_project - RESEARCH PROJECT AUTOMATA AND THEORY OF...

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RESEARCH PROJECT AUTOMATA AND THEORY OF LANGUAGES Finite Automata 108408 – Murat Aliu Dept. of Computer Science SEEU, Tetovo Email: murataliu@yahoo.com
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Table of contents: Finite Automata………………….………………. .……. 3 An Informal Picture of Finite Automata ……………. .…. ..3 The Ground Rules ……………. . …………………….4 The Protocol ………………………………………………… 4 Enabling the Automata to Ignore Actions ……………………. . 6 The Entire System as an Automaton …………………………. . 7 Using the Product Automaton to Validate the Protocol ………. 9 Deterministic Finite Automata ………………………. . 10 How a DFA Processes Strings ……………………………. .… 11 Simpler Notations for DFA's ………………………………… 12 Extending the Transition Function to Strings ………………… 13 The Language of a DFA ……………………………………… 17 Nondeterministic Finite Automata .…………………… 21 An Informal View of Nondeterministic Finite Automata ……. 22 The Extended Transition Function …………………………… 24 References ……………………………………………. . 26
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Finite Automata This project introduces the class of languages known as "regular languages." These languages are exactly the ones that can be described by finite automata. After an extended example that will provide motivation for the study to follow, we define finite automata formally. As was mentioned earlier, a finite automaton has a set of states, and its "control" moves from state to state in response to external "inputs." One of the crucial distinctions among classes of finite automata is whether that control is "deterministic," meaning that the automaton cannot be in more than one state at any one time, or "nondeterministic," meaning that it may be in several states at once. We shall discover that adding nondeterminism does not let us define any language that cannot be defined by a deterministic finite automaton, but there can be substantial efficiency in describing an application using a nondeterministic automaton. In effect, nondeterminism allows us to "program" solutions to problems using a higher-level language. The nondeterministic finite automaton is then "compiled," by an algorithm we shall learn in this chapter, into a deterministic automaton that can be "executed" on a conventional computer. We conclude the chapter with a study of an extended nondeterministic automaton that has the additional choice of making a transition from one state to another spontaneously, i.e., on the empty string as "input." 1 .1 An Informal Picture of Finite Automata In this section, we shall study an extended example of a real-world problem whose solution uses finite automata in an important role. We investigate protocols that support "electronic money" - files that a customer can use to pay for goods on the internet, and that, the seller can receive with
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automata_project - RESEARCH PROJECT AUTOMATA AND THEORY OF...

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