Abstract
The types of codes delt with in detail are prefix codes, suffix codes, and two special classes of biprefix codes called infix codes and outfix codes. Conditions are given under which polynomially bounded DOL languages form codes of each of these types.
A concept of homomorphism is defined for DOL systems. It is demonstrated that when E is a homomorphie image of a DOL system D and L(E) is infinite then: If L(E) is a code of any of the types listed above, L(D) is also a code of the same type. A concept of derivative is defined for DOL systems that is related to a special type of homomorphism based on the erasure of finite symbols. Code properties of linearly bounded DOL languages are studied in detail. The results are then extended to apply to polynomially bounded DOL languages through the use of the newly introduced derivative concept.
It is shown that for every polynomially bounded DOL language L, L\{1} is a commutative equivalent of a prefix code. Every DOL language is shown to be the union of (1) a finite set, (2) a finite number of DOL languages each of which has a singleton as alphabet, and (3) a commutative equivalent of a prefix code.
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© 1985 Springer-Verlag Berlin Heidelberg
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Head, T., Wilkinson, J. (1985). Code Properties and Derivatives of DOL Systems. In: Apostolico, A., Galil, Z. (eds) Combinatorial Algorithms on Words. NATO ASI Series, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82456-2_22
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DOI: https://doi.org/10.1007/978-3-642-82456-2_22
Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-642-82456-2
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