Ludwig Staiger | Martin Luther University Halle-Wittenberg (original) (raw)

Papers by Ludwig Staiger

Research paper thumbnail of Codes and Infinite Words

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.

Research paper thumbnail of Automatentheoretische und automatenfreie Charakterisierungen topologischer Klassen regulärer Folgenmengen

Journal of Information Processing and Cybernetics / Elektronische Informationsverarbeitung und Kybernetik, 1974

Research paper thumbnail of Algebraische Codierungstheorie; Theorie der sequentiellen Codierungen

Research paper thumbnail of Erkennungs-, masz- und informationstheoretische Eigenschaften regulärer Folgenmengen

Research paper thumbnail of Ein Satz über die Entropie von Untermonoiden

Theoretical Computer Science, 1988

Research paper thumbnail of Joint Topologies for Finite and Infinite Words

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

Research paper thumbnail of On the Power of Reading the Whole Infinite Input Tape

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.

Research paper thumbnail of The Entropy of Finite-state ω-languages

Research paper thumbnail of Sequential mappings of ω-languages

Research paper thumbnail of Fractals, Dimension, and Formal Languages

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

Research paper thumbnail of Research in the Theory of ω-languages

Research paper thumbnail of On Infinitary Finite Length Codes

Theoretical Informatics and Applications, 1986

Research paper thumbnail of Kolmogorov complexity and Hausdorff dimension

Information and Computation, 1993

Research paper thumbnail of Rich ω-words and monadic second-order arithmetic

Lecture Notes in Computer Science, 1998

Research paper thumbnail of Subspaces of GF(q)^ω and convolutional codes

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...

Research paper thumbnail of The Kolmogorov complexity of real numbers

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

Research paper thumbnail of On ω-power languages

Lecture Notes in Computer Science, 1997

Without Abstract

Research paper thumbnail of How Much can You Win when Your Adversary is Handicapped?

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

Research paper thumbnail of Complexity and entropy

Lecture Notes in Computer Science, 1981

Without Abstract

Research paper thumbnail of Recursive automata on infinite words

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 ...

Research paper thumbnail of Codes and Infinite Words

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.

Research paper thumbnail of Automatentheoretische und automatenfreie Charakterisierungen topologischer Klassen regulärer Folgenmengen

Journal of Information Processing and Cybernetics / Elektronische Informationsverarbeitung und Kybernetik, 1974

Research paper thumbnail of Algebraische Codierungstheorie; Theorie der sequentiellen Codierungen

Research paper thumbnail of Erkennungs-, masz- und informationstheoretische Eigenschaften regulärer Folgenmengen

Research paper thumbnail of Ein Satz über die Entropie von Untermonoiden

Theoretical Computer Science, 1988

Research paper thumbnail of Joint Topologies for Finite and Infinite Words

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

Research paper thumbnail of On the Power of Reading the Whole Infinite Input Tape

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.

Research paper thumbnail of The Entropy of Finite-state ω-languages

Research paper thumbnail of Sequential mappings of ω-languages

Research paper thumbnail of Fractals, Dimension, and Formal Languages

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

Research paper thumbnail of Research in the Theory of ω-languages

Research paper thumbnail of On Infinitary Finite Length Codes

Theoretical Informatics and Applications, 1986

Research paper thumbnail of Kolmogorov complexity and Hausdorff dimension

Information and Computation, 1993

Research paper thumbnail of Rich ω-words and monadic second-order arithmetic

Lecture Notes in Computer Science, 1998

Research paper thumbnail of Subspaces of GF(q)^ω and convolutional codes

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...

Research paper thumbnail of The Kolmogorov complexity of real numbers

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

Research paper thumbnail of On ω-power languages

Lecture Notes in Computer Science, 1997

Without Abstract

Research paper thumbnail of How Much can You Win when Your Adversary is Handicapped?

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

Research paper thumbnail of Complexity and entropy

Lecture Notes in Computer Science, 1981

Without Abstract

Research paper thumbnail of Recursive automata on infinite words

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 ...