• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.347-355
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• 2000

In this paper we define linearly independent, basis, free, torsion-free and torsion-free completely on an automation. We prove a theorem describing a relationship between free and torsion-free completely on automata. Also we prove some important properties of them. Furthermore, we discuss some theorems associated with free.