Ludwig Staiger | Martin Luther University Halle-Wittenberg (original) (raw)
Papers by Ludwig Staiger
Acta Cybernetica, 1994
Codes can be characterized by their way of acting on infinite words. Three kinds of characterizat... more Codes can be characterized by their way of acting on infinite words. Three kinds of characterizations are obtained. The first characterization is related to the uniqueness of the factorization of particular periodic words. The second characterization concerns the rational form of the factorizations of rational words. The third characteristic fact is the finiteness of the number of factorizations of the rational infinite words. A classification of codes based on the number of factorizations for different kinds of infinite words is set up. The obtained classes are compared with thé class of u-codes, the class of weakly prefix codes and the class of codes with finite deciphering delay. Complementary results are obtained in the rational case, for example a necessary and sufficient condition for a rational w-code to have a bounded deciphering delay is given. Risumé: La factorisation des mots infinis permet de caractériser les codes parmi les langages de mots finis. Les critères obtenus sont de trois types. Le premier critère est relatif à l'unicité de la factorisation de certains mots périodiques. Le second concerne la forme des factorisations des mots rationnels. Finalement, seuls les codes-nous assurent de la finitude du nombre de factorisations des mots rationnels. Les codes sont classifiés selon le nombre de factorisations de certains types de mots infinis. Les classes obtenues sont étudiées et comparées avec les classes déjà définies de v-codes, de codes faiblement préfixes et de codes à délai borné. Des résultats complémentaires sont obtenus dans le cas rationnel, en particulier il est donné une condition nécessaire et suffisante pour qu'un tu-code rationnel soit à délai borné.
Journal of Information Processing and Cybernetics / Elektronische Informationsverarbeitung und Kybernetik, 1974
Theoretical Computer Science, 1988
Lecture Notes in Computer Science, 2010
Infinite words are often considered as limits of finite words. As topological methods have been p... more Infinite words are often considered as limits of finite words. As topological methods have been proved to be useful in the theory of ω-languages it seems to be providing to include finite and infinite words into one (topological) space. The attempts so far (see [3, Section 2.4]) have their drawbacks. Therefore, in the present paper we investigate the possibility to
Grammars, 1999
We investigate the relationship between the classes of ω-languages accepted by Turing machines ac... more We investigate the relationship between the classes of ω-languages accepted by Turing machines according to two types of acceptance: 1) Machines of the first type are allowed to read only a finite part of the infinite input. 2) Machines of the second type have the additional possibility to reject by not reading the whole infinite input. It is shown that machines of the second kind are more powerful than those of the first kind.
Theoretical Informatics and Applications, 1994
We consider classes of sets of r-adic expansions of reals specified by means of thetheory of form... more We consider classes of sets of r-adic expansions of reals specified by means of thetheory of formal languages or automata theory. It is shown how these specificationsare used to calculate the Hausdorff dimension and Hausdorff measure of such sets.Since the appearence of Mandelbrot's11book "Fractals, Form, Chance and Dimension" Fractal Geometry as a means providing a theory describing many of the
Theoretical Informatics and Applications, 1986
Information and Computation, 1993
Lecture Notes in Computer Science, 1998
Information and Control, 1983
In this paper we demonstrate that among all subspaces of GF(q)!convolutional codes are best suite... more In this paper we demonstrate that among all subspaces of GF(q)!convolutional codes are best suited for error control purposes. Tothis end we regard several defining properties of convolutional codesand study the classes of subspaces defined by each of those propertiesalone. It turns out that these superclasses of the class of convolutionalcodes either achieve no better distance to rate ratio or are susceptibleto an unavoidable infinite error propagation.We consider convolutional...
Lecture Notes in Computer Science, 1999
We consider for a real number α the Kolmogorov complexities of its expansions with respect to dif... more We consider for a real number α the Kolmogorov complexities of its expansions with respect to different bases. In the paper it is shown that, for usual and self-delimiting Kolmogorov complexity, the complexity of the prefixes of their expansions with respect to different bases r and b are related in a way which depends only on the relative information of
Lecture Notes in Computer Science, 1997
Without Abstract
Numbers, Information and Complexity, 2000
We consider infinite games where a gambler plays a coin-tossi ng game against an adversary. The g... more We consider infinite games where a gambler plays a coin-tossi ng game against an adversary. The gambler puts stakes on heads or tails, and the adversary tosses a fair coin, but has to choose his outcome according to a previously given law known to the gambler. In other words, the adversary is not allowed to play all infinite heads-tails-sequences, b
Lecture Notes in Computer Science, 1981
Without Abstract
Lecture Notes in Computer Science, 1993
... We conclude with a remark on l~abin's [tta69] and Streett's [Sr82] acceptance condi... more ... We conclude with a remark on l~abin's [tta69] and Streett's [Sr82] acceptance conditions: A ICabin or Streett accepting condition consists of a pair (U, V) of subsets U, V _ N x Z. A sequence ~ EX ~ is l~abiu-accepted (Sireetl-accepted) if and only if ~ E Tae(Ai) gl Tio(A'i) for some i ...
Acta Cybernetica, 1994
Codes can be characterized by their way of acting on infinite words. Three kinds of characterizat... more Codes can be characterized by their way of acting on infinite words. Three kinds of characterizations are obtained. The first characterization is related to the uniqueness of the factorization of particular periodic words. The second characterization concerns the rational form of the factorizations of rational words. The third characteristic fact is the finiteness of the number of factorizations of the rational infinite words. A classification of codes based on the number of factorizations for different kinds of infinite words is set up. The obtained classes are compared with thé class of u-codes, the class of weakly prefix codes and the class of codes with finite deciphering delay. Complementary results are obtained in the rational case, for example a necessary and sufficient condition for a rational w-code to have a bounded deciphering delay is given. Risumé: La factorisation des mots infinis permet de caractériser les codes parmi les langages de mots finis. Les critères obtenus sont de trois types. Le premier critère est relatif à l'unicité de la factorisation de certains mots périodiques. Le second concerne la forme des factorisations des mots rationnels. Finalement, seuls les codes-nous assurent de la finitude du nombre de factorisations des mots rationnels. Les codes sont classifiés selon le nombre de factorisations de certains types de mots infinis. Les classes obtenues sont étudiées et comparées avec les classes déjà définies de v-codes, de codes faiblement préfixes et de codes à délai borné. Des résultats complémentaires sont obtenus dans le cas rationnel, en particulier il est donné une condition nécessaire et suffisante pour qu'un tu-code rationnel soit à délai borné.
Journal of Information Processing and Cybernetics / Elektronische Informationsverarbeitung und Kybernetik, 1974
Theoretical Computer Science, 1988
Lecture Notes in Computer Science, 2010
Infinite words are often considered as limits of finite words. As topological methods have been p... more Infinite words are often considered as limits of finite words. As topological methods have been proved to be useful in the theory of ω-languages it seems to be providing to include finite and infinite words into one (topological) space. The attempts so far (see [3, Section 2.4]) have their drawbacks. Therefore, in the present paper we investigate the possibility to
Grammars, 1999
We investigate the relationship between the classes of ω-languages accepted by Turing machines ac... more We investigate the relationship between the classes of ω-languages accepted by Turing machines according to two types of acceptance: 1) Machines of the first type are allowed to read only a finite part of the infinite input. 2) Machines of the second type have the additional possibility to reject by not reading the whole infinite input. It is shown that machines of the second kind are more powerful than those of the first kind.
Theoretical Informatics and Applications, 1994
We consider classes of sets of r-adic expansions of reals specified by means of thetheory of form... more We consider classes of sets of r-adic expansions of reals specified by means of thetheory of formal languages or automata theory. It is shown how these specificationsare used to calculate the Hausdorff dimension and Hausdorff measure of such sets.Since the appearence of Mandelbrot's11book "Fractals, Form, Chance and Dimension" Fractal Geometry as a means providing a theory describing many of the
Theoretical Informatics and Applications, 1986
Information and Computation, 1993
Lecture Notes in Computer Science, 1998
Information and Control, 1983
In this paper we demonstrate that among all subspaces of GF(q)!convolutional codes are best suite... more In this paper we demonstrate that among all subspaces of GF(q)!convolutional codes are best suited for error control purposes. Tothis end we regard several defining properties of convolutional codesand study the classes of subspaces defined by each of those propertiesalone. It turns out that these superclasses of the class of convolutionalcodes either achieve no better distance to rate ratio or are susceptibleto an unavoidable infinite error propagation.We consider convolutional...
Lecture Notes in Computer Science, 1999
We consider for a real number α the Kolmogorov complexities of its expansions with respect to dif... more We consider for a real number α the Kolmogorov complexities of its expansions with respect to different bases. In the paper it is shown that, for usual and self-delimiting Kolmogorov complexity, the complexity of the prefixes of their expansions with respect to different bases r and b are related in a way which depends only on the relative information of
Lecture Notes in Computer Science, 1997
Without Abstract
Numbers, Information and Complexity, 2000
We consider infinite games where a gambler plays a coin-tossi ng game against an adversary. The g... more We consider infinite games where a gambler plays a coin-tossi ng game against an adversary. The gambler puts stakes on heads or tails, and the adversary tosses a fair coin, but has to choose his outcome according to a previously given law known to the gambler. In other words, the adversary is not allowed to play all infinite heads-tails-sequences, b
Lecture Notes in Computer Science, 1981
Without Abstract
Lecture Notes in Computer Science, 1993
... We conclude with a remark on l~abin's [tta69] and Streett's [Sr82] acceptance condi... more ... We conclude with a remark on l~abin's [tta69] and Streett's [Sr82] acceptance conditions: A ICabin or Streett accepting condition consists of a pair (U, V) of subsets U, V _ N x Z. A sequence ~ EX ~ is l~abiu-accepted (Sireetl-accepted) if and only if ~ E Tae(Ai) gl Tio(A'i) for some i ...