Introduction

An Introduction to the Theory of Automata: Course Held at by Fabrizio Luccio PDF

By Fabrizio Luccio

ISBN-10: 321181082X

ISBN-13: 9783211810828

ISBN-10: 3709128161

ISBN-13: 9783709128169

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Extra info for An Introduction to the Theory of Automata: Course Held at the Department for Automation and Information July 1971

Example text

In symbols, compatibility is indicated as Cfi. ~ CfJ Between states of a single automaton, compatibility is a less restrictive relation than inclusion. That is, for every pair of states such that qi. ~ qJ, it is also Cfi. ~ qi. For example, in automaton (20) both relations hold: From definition 15, it clearly follows that the properties are valid: q~;;;;; Cfi. for every state eh (reflexivity); if qi. ~ q4then qd ~ q i. ( symmetry) • However, the transitive property does not hold for compatibility.

CfJ Between states of a single automaton, compatibility is a less restrictive relation than inclusion. That is, for every pair of states such that qi. ~ qJ, it is also Cfi. ~ qi. For example, in automaton (20) both relations hold: From definition 15, it clearly follows that the properties are valid: q~;;;;; Cfi. for every state eh (reflexivity); if qi. ~ q4then qd ~ q i. ( symmetry) • However, the transitive property does not hold for compatibility. For example, in automaton (20) q2. and q 3 are not compatible.

Plete. Its formal definition is as follows: Definition 11. ,Ö) where: X is the finite set of inputs; a quintuple: 33 Incomplete automata: the reasons for incompleteness y is the finite set of autputs; Q is the finite set of states; A. :A -Q , A~ QxX . ' c) is a mapping of a subset A of Q x X onto Q ; that is: Obviously, the (complete) automatonof definition 1 is a particular case of the moFe general incomplete automaton. As it will be seen, several concepts about automata become vastly more complex if the hypothesis of completeness is removed.

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An Introduction to the Theory of Automata: Course Held at the Department for Automation and Information July 1971 by Fabrizio Luccio


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