Werner Kuich

Bio: Werner Kuich is an academic researcher from Vienna University of Technology. The author has contributed to research in topics: Formal power series & Semiring. The author has an hindex of 17, co-authored 102 publications receiving 2561 citations. Previous affiliations of Werner Kuich include University of Vienna & IBM.

Handbook of Weighted Automata

Abstract: Weighted finite automata are classical nondeterministic finite automata in which the transitions carry weights These weights may model, for example, the cost involved when executing a transition, the resources or time needed for this, or the probability or reliability of its successful execution Weights can also be added to classical automata with infinite state sets like pushdown automata, and this extension constitutes the general concept of weighted automata Since their introduction in the 1960s they have stimulated research in related areas of theoretical computer science, including formal language theory, algebra, logic, and discrete structures Moreover, weighted automata and weighted context-free grammars have found application in natural-language processing, speech recognition, and digital image compression This book covers all the main aspects of weighted automata and formal power series methods, ranging from theory to applications The contributors are the leading experts in their respective areas, and each chapter presents a detailed survey of the state of the art and pointers to future research The chapters in Part I cover the foundations of the theory of weighted automata, specifically addressing semirings, power series, and fixed point theory Part II investigates different concepts of weighted recognizability Part III examines alternative types of weighted automata and various discrete structures other than words Finally, Part IV deals with applications of weighted automata, including digital image compression, fuzzy languages, model checking, and natural-language processing Computer scientists and mathematicians will find this book an excellent survey and reference volume, and it will also be a valuable resource for students exploring this exciting research area

Semirings, Automata, Languages

Abstract: I. Linear Algebra.- 1. Semirings and Power Series.- 2. Convergence, Equations and Identities.- 3. Strong Convergence and Cycle-Free Power Series.- 4. Matrices, Linear Systems and Identities.- 5. Semirings with Particular Properties.- 6. Morphisms and Representations.- II. Automata.- 7. Automata in Terms of Matrices.- 8. Rational Power Series and Decidability.- 9. Rational Transductions.- 10. Pushdown Automata.- 11. Abstract Families of Power Series.- 12. Substitutions.- 13. Reset Pushdown Automata and Counter Automata.- III. Algebraic Systems.- 14. Algebraic Series and Context-Free Languages.- 15. The Super Normal Form.- 16. Commuting Variables: Decidability and Parikh's Theorem.- Historical and Bibliographical Remarks.- References.- Symbol Index.

On the entropy of context-free languages

Abstract: The information theoretical concept of the entropy (channel capacity) of context-free languages and its relation to the structure generating function is investigated in the first part of this paper. The achieved results are applied to the family of pseudolinear grammars. In the second part, relations between context-free grammars, infinite labelled digraphs and infinite nonnegative matrices are exhibited. Theorems on the convergence parameter of infinite matrices are proved and applied to the evaluation of the entropy of certain context-free languages. Finally, a stochastic process is associated with any context-free language generated by a deterministic labelled digraph, such that the stochastic process is equivalent to the language in the sense that both have the same entropy.

Semirings and Formal Power Series

Abstract: This chapter presents basic foundations for the theory of weighted automata: semirings and formal power series. A fundamental question is how to extend the star operation (Kleene iteration) from languages to series. For this, we investigate ordered, complete and continuous semirings and the related concepts of star semirings and Conway semirings. We derive natural properties for the Kleene star of cycle-free series and also of matrices often used to analyze the behavior of weighted automata. Finally, we investigate cycle-free linear equations which provide a useful tool for proving identities for formal power series.

Handbook of Formal Languages

Abstract: The theory of formal languages is the oldest and most fundamental area of theoretical computer science. It has served as a basis of formal modeling from the early stages of programming languages to the recent beginnings of DNA computing. This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field. Best specialists of various subareas, altogether 50 in number, are among the authors. The maturity of the field makes it possible to include a historical perspective in many presentations. The individual chapters can be studied independently, both as a text and as a source of reference. The Handbook is an invaluable aid for advanced students and specialists in theoretical computer science and related areas in mathematics, linguistics, and biology.

Dynamic Logic

Abstract: From the Publisher: Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications. This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter.

Tree Automata Techniques and Applications

Abstract: CONTENTS 7 Acknowledgments Many people gave substantial suggestions to improve the contents of this book. These are, in alphabetic order, Introduction During the past few years, several of us have been asked many times about references on finite tree automata. On one hand, this is the witness of the liveness of this field. On the other hand, it was difficult to answer. Besides several excellent survey chapters on more specific topics, there is only one monograph devoted to tree automata by Gécseg and Steinby. Unfortunately, it is now impossible to find a copy of it and a lot of work has been done on tree automata since the publication of this book. Actually using tree automata has proved to be a powerful approach to simplify and extend previously known results, and also to find new results. For instance recent works use tree automata for application in abstract interpretation using set constraints, rewriting, automated theorem proving and program verification, databases and XML schema languages. Tree automata have been designed a long time ago in the context of circuit verification. Many famous researchers contributed to this school which was headed by A. Church in the late 50's and the early 60's: B. Trakhtenbrot, Many new ideas came out of this program. For instance the connections between automata and logic. Tree automata also appeared first in this framework, following the work of Doner, Thatcher and Wright. In the 70's many new results were established concerning tree automata, which lose a bit their connections with the applications and were studied for their own. In particular, a problem was the very high complexity of decision procedures for the monadic second order logic. Applications of tree automata to program verification revived in the 80's, after the relative failure of automated deduction in this field. It is possible to verify temporal logic formulas (which are particular Monadic Second Order Formulas) on simpler (small) programs. Automata, and in particular tree automata, also appeared as an approximation of programs on which fully automated tools can be used. New results were obtained connecting properties of programs or type systems or rewrite systems with automata. Our goal is to fill in the existing gap and to provide a textbook which presents the basics of tree automata and several variants of tree automata which have been devised for applications in the aforementioned domains. We shall discuss only finite tree automata, and the …

Graph Kernels

Abstract: We present a unified framework to study graph kernels, special cases of which include the random walk (Gartner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahet al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n6) to O(n3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixed-point methods that take O(dn3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for d-dimensional edge kernels, and O(n4) in the infinite-dimensional case; on sparse graphs these algorithms only take O(n2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of kernel of Frohlich et al. (2006) yet provably positive semi-definite.