Abstract
A homomorphism ƒ from the set of words over a finite alphabet Σ 1 to the set of words over another finite alphabet Σ 2 is said to preserve star height if for all regular events R ⊆ Σ 1 * , the star height of R is equal to that of ƒ ( R ). An algorithm is presented for deciding whether an arbitrary homomorphism preserves star height or not: in our result, the injectivity of homomorphisms plays an important role, and it is shown that all homomorphisms which preserve star height are injective.
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