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Iterated Function Systems and Control Languages
, 1998
"... Valuations  morphisms from (S ; \Delta; e) to ((0; ); \Delta; 1)  are a generalization of Bernoulli morphisms introduced in [10]. Here, we show how to generalize the notion of entropy (of a language) in order to obtain new formulae to determine the Hausdorff dimension of fractal sets (al ..."
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Cited by 5 (2 self)
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Valuations  morphisms from (S ; \Delta; e) to ((0; ); \Delta; 1)  are a generalization of Bernoulli morphisms introduced in [10]. Here, we show how to generalize the notion of entropy (of a language) in order to obtain new formulae to determine the Hausdorff dimension of fractal sets (also in Euclidean spaces) especially defined via regular (w)languages. By doing this, we can sharpen and generalize earlier results [1, 14, 15, 26, 38] in two ways: firstly, we treat the case where the underlying basic iterated function system contains noncontractive mappings, and secondly, we obtain results valid for nonregular languages as well. A preliminary version appeared in: "Mathematical Foundations of Computer Science" (L. Brim, J. Gruska and J. Zlatuska, eds.), Lecture Notes in Comput. Sci. No. 1450, SpringerVerlag, Berlin 1998, pp. 740  750. + email: fernau@informatik.unituebingen.de # email: staiger@informatik.unihalle.de 2 H. Fernau and L. Staiger Contents 1 Int...
Methods for Relativizing Properties of Codes
"... The usual setting for information transmission systems assumes that all words over the source alphabet need to be encoded. The demands on encodings of messages with respect to decodability, errordetection, etc. are thus relative to the whole set of words. In reality, depending on the information s ..."
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The usual setting for information transmission systems assumes that all words over the source alphabet need to be encoded. The demands on encodings of messages with respect to decodability, errordetection, etc. are thus relative to the whole set of words. In reality, depending on the information source, far fewer messages are transmitted, all belonging to some specific language. Hence the original demands on encodings can be weakened, if only the words in that language are to be considered. This leads one to relativize the properties of encodings or codes to the language at hand. We analyse methods of relativization in this sense. It seems there are four equally convincing notions of relativization. We compare those. Each of them has their own merits for specific code properties. We clarify the differences between the four approaches. We also consider the decidability of relativized properties. If P is a property defining a class of codes and L is a language, one asks, for a given language C, whether C satisfies P relative to L. We show that in the realm of regular languages this question is mostly decidable. 1 Codes in Information Systems In an information system, a source S generates messages1 which, after some modifications, enter a channel K. The channel may change a message because of physical errors or human interference or other reasons. For a given
Centre for Discrete Mathematics and Theoretical Computer ScienceThe Entropy of Łukasiewiczlanguages ∗
, 2002
"... The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of t ..."
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The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.
IOS Press Intercode Regular Languages ∗
"... Abstract. Intercodes are a generalization of commafree codes. Using the structural properties of finitestate automata recognizing an intercode we develop a polynomialtime algorithm for determining whether or not a given regular language L is an intercode. If the answer is yes, our algorithm yield ..."
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Abstract. Intercodes are a generalization of commafree codes. Using the structural properties of finitestate automata recognizing an intercode we develop a polynomialtime algorithm for determining whether or not a given regular language L is an intercode. If the answer is yes, our algorithm yields also the smallest index k such that L is a kintercode. Furthermore, we examine the prime intercode decomposition of intercode regular languages and design an algorithm for the intercode primality test of an intercode recognized by a finitestate automaton. We also propose an algorithm that computes the prime intercode decomposition of an intercode regular language in polynomial time. Finally, we demonstrate that the prime intercode decomposition need not be unique.