Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

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

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 …

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Tree Automata Techniques and Applications

Conditional rewriting logic as a unified model of concurrency

The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.

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Languages, automata, and logic

Using tree automata techniques, it is proven that the theory of ground rewrite systems is decidable. Novel decision procedures are presented for most classic properties of ground rewrite systems. An example is presented to illustrate how these results could be used for specification and debugging. >

The theory of ground rewrite systems is decidable

We define an extension of tree automata by adding some tests in the rules. The goal is to handle non linearity. We obtain a family which has good closure and decidability properties and we give some applications.

Equality and Disequality Constraints on Direct Subterms in Tree Automata

The aim of this paper is to propose an algorithm to decide the confluence of finite ground term rewrite systems. Actually a more general class of possibly infinite ground term rewrite systems is studied. It is well known that the confluence is not decidable for general term rewrite systems, but this paper proves it is for ground term rewrite systems following a conjecture made by Huet and Oppen in their survey. The result is also applied to the confluence of left-linear and right-ground term rewrite systems. We also sketch an algorithm for checking this property. This algorithm is based on tree automata and tree transducers. Here, we regard them as rewrite systems and specialists in automata theory would translate that easily in their language.

Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems

We present a collection of results on regular tree languages and rewrite systems. Moreover we prove the undecidability of the preservation of regularity by rewrite systems. More precisely we prove that it is undecidable whether or not for a set E of equations the set E(R) congruence closure of set R is a regular tree language whenever R is a regular tree language. It is equally undecidable whether or not for a confluent and terminating rewrite system S the set S(R) of ground S-normal forms of set R is a regular tree language whenever R is a regular tree language. Finally we study fragments of the theory of ground term algebras modulo congruence generated by a set of equations which can be compiled in a terminating, confluent rewrite system which preserves regularity.

Sophie Tison

Papers

Tree Automata Techniques and Applications

The theory of ground rewrite systems is decidable

Equality and Disequality Constraints on Direct Subterms in Tree Automata

Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems

Regular Tree Languages And Rewrite Systems