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Abstract
A new type of code, called an expanded subalphabet, is introduced. It is shown that the following four conditions on a subset L of the free monoid A ∗ over a finite or infinite alphabet A are equivalent: (1) L is the submonoid generated by an expanded subalphabet; (2) L is a retract; (3) L is the fixed language of an endomorphism; (4) L is the stationary language of an endomorphism. Expanded subalphabets are used as a tool for the investigation of fixed languages (=retracts). Special results for the case of a finite alphabet are given and the relationship with the theory of L-systems is indicated.
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†This research was supported by Grant MCS-8003348 of the National Science Foundation of the United States of America.
†This research was supported by Grant MCS-8003348 of the National Science Foundation of the United States of America.
Notes
†This research was supported by Grant MCS-8003348 of the National Science Foundation of the United States of America.