Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

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The knowledge complexity of interactive proof-systems

Publisher Summary This chapter focuses on finite automata on infinite sequences and infinite trees. The chapter discusses the complexity of the complementation process and the equivalence test. Deterministic Muller automata and nondeterministic Buchi automata are equivalent in recognition power. Any nonempty Rabin recognizable set contains a regular tree and shows that the emptiness problem for Rabin tree automata is decidable. The chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree. A short overview of the work that studies the fine structure of the class of Rabin recognizable sets of trees is also presented in the chapter. Depending on the formalism in which tree properties are classified, the results fall in three categories: monadic second-order logic, tree automata, and fixed-point calculi.

Automata on infinite objects

It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) "neutrosophy" - study of neutralities as an extension of dialectics; b) and its derivative "neutrosophic", such as "neutrosophic logic", "neutrosophic set", "neutrosophic probability", and "neutrosophic statistics" and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics.

/pdf/a-unifying-field-in-logics-neutrosophic-logic-neutrosophy-3lylkw0u8b.pdf

A unifying field in logics: neutrosophic logic. neutrosophy, neutrosophic set, neutrosophic probability and statistics

This is the first volume of a systematic two-volume presentation of the various areas of research on structural complexity. The theory of algorithmic complexity, a part of the mathematical theory of computation, can be approached from several points of view, one of which is the structural one. This volume is written for undergraduate students who have taken a first course in Formal Language Theory. It presents the basic concepts of structural complexity, thus providing the background necessary for the understanding of complexity theory. The second corrected edition has been extended by an appendix with recent results on nondeterministic space classes and updated with regard to the bibliographical remarks and the references.

Structural Complexity I

This is a reissue of the book Tree Automata by F G\'ecseg and M Steinby originally published in 1984 by Akad\'emiai Kiad\'o, Budapest Some mistakes have been corrected and a few obscure passages have been clarified Moreover, some more recent contributions and current lines of research are reviewed in an appendix that also contains several new references

Tree automata

Every word to utter from the writer involves the element of this life. The writer really shows how the simple words can maximize how the impression of this book is uttered directly for the readers. Even you have known about the content of sichtweisen der informatik so much, you can easily do it for your better connection. In delivering the presence of the book concept, you can find out the boo site here.

Sichtweisen der Informatik

The monadic second order theory of ?1.- Axiomatization of the monadic second order theory of ?1.

The monadic second order theory of all countable ordinals

Büchi's monadic second order successor arithmetic

1 Concepts and Notations in Discrete Mathematics.- 2 The Structure Theory of Transition Algebras.- 3 The Structure and Behavior of Finite Automata.- 4 Transition Systems and Regular Events.- 5 Regular Canonical Systems.- 6 General Algebras: How They Function as Tree Acceptors and Push-down Automata.- 7 General Alphabets: The Theory of Push-down Automata and Context-free Languages.- Conclusion.- List of Symbols.- References.

Dirk Siefkes

Papers

Sichtweisen der Informatik

The monadic second order theory of all countable ordinals

Büchi's monadic second order successor arithmetic

Finite Automata, Their Algebras and Grammars: Towards a Theory of Formal Expressions

Undecidable Extensions of Monadic Second Order Successor Arithmetic