Journal Article•

# On The Power of Distributed Bottom-up Tree Automata

TL;DR: This paper considers bottom-up tree automata and discusses the sequential distributed version of this model, and finds that the ∗- mode does not increase the power, whereas the other modes increase thePower.

Abstract: Tree automata have been defined to accept trees. Different types of acceptance like bottom-up, top-down, tree walking have been considered in the literature. In this paper, we consider bottom-up tree automata and discuss the sequential distributed version of this model. Generally, this type of distribution is called cooperative distributed automata or the blackboard model. We define the traditional five modes of cooperation, viz. ∗-mode, t-mode, = k, ≥ k, ≤ k (k ≥ 1) modes on bottom-up tree automata. We discuss the accepting power of cooperative distributed tree automata under these modes of cooperation. We find that the ∗- mode does not increase the power, whereas the other modes increase the power. We discuss a few results comparing the acceptance power under different modes of cooperation.

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01 Jan 2020TL;DR: In the practice of computer engineering, various forms of automata are used to express the behavior of concurrent components and UML state diagrams are a good example.

Abstract: In the practice of computer engineering, various forms of automata are used to express the behavior of concurrent components. There are two reasons: graphical representation and individual modeling of separate components. UML state diagrams are a good example (UML n.d.).

1 citations

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31 Dec 2019

TL;DR: DA3 formalism is compared to other concepts of distributed automata known from the literature and it is possible to simulate a verified system on distributed components in DA3.

Abstract: Integrated Model of Distributed Systems is used for modeling and verification. In formalism, the distributed system is modeled as a collection of server states and agent messages. The evolution of the system takes the form of actions that transform the global system configuration (states and messages) into a new configuration. Formalism is used in the Dedan verification environment for finding different kinds of deadlocks: communication deadlocks in the server view and resource deadlocks in the agent view. For other purposes, a conversion has been developed to equivalent models: to Petri nets for structural analysis and do Distributed Autonomous and Asynchronous Automata (DA3) for easy graphical modeling in terms of system components. In addition, it is possible to simulate a verified system on distributed components in DA3. The automata have two forms: Server-DA3 (S-DA3) for the server view and Agent-DA3 (A-DA3) for the agent view. DA3 formalism is compared to other concepts of distributed automata known from the literature.

### Additional excerpts

...They are called distributed automata in [32]....

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##### References

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01 Jan 1979

TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.

Abstract: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.

13,779 citations

### "On The Power of Distributed Bottom-..." refers background in this paper

...The theory of tree automata arises as a straight forward extension of the theory of finite automata [6]....

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01 Jan 1997TL;DR: The goal of this book is to provide a textbook which presents the basics ofTree automata and several variants of tree automata which have been devised for applications in the aforementioned domains.

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 …

1,492 citations

### "On The Power of Distributed Bottom-..." refers background in this paper

...The proof can be generalized into a theorem, similar to pumping lemma for recognizable string languages, to recognizable tree languages [1]....

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...Non-deterministi c top-down tree automata are equivalent to non-deterministi c bottom-up tree automata [1]....

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IBM

^{1}TL;DR: The standard closure theorems are proved for the class of sets “recognizable” by finite algebras, and a generalization of Kleene's regularity theory is presented.

Abstract: Many of the important concepts and results of conventional finite automata theory are developed for a generalization in which finite algebras take the place of finite automata The standard closure theorems are proved for the class of sets “recognizable” by finite algebras, and a generalization of Kleene's regularity theory is presented The theorems of the generalized theory are then applied to obtain a positive solution to a decision problem of second-order logic

790 citations

### "On The Power of Distributed Bottom-..." refers background in this paper

...Tree automata were introduced in [4], [5] and [12] to solve certain decision problems in logic....

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TL;DR: It is shown here that the weak secondorder theory of two successors is decidable, thus settling a problem of Buchi, and this result is applied to obtain positive solutions to the decision problems for various other theories, e.g., the weaksecond-order theories of order types built up from the finite types.

Abstract: This paper concerns a generalization of finite automata, the ''tree acceptors,'' which have as their inputs finite trees of symbols rather than the usual sequences of symbols. Ordinary finite automata prove to be special cases of tree acceptors, and many of the results of finite automata theory continue to hold in their appropriately generalized forms. The tree acceptors provide new characterizations of the classes of regular sets and of context-free languages. The theory of tree acceptors is applied to a decision problem of mathematical logic. It is shown here that the weak secondorder theory of two successors is decidable, thus settling a problem of Buchi. This result is in turn applied to obtain positive solutions to the decision problems for various other theories, e.g., the weak second-order theories of order types built up from the finite types, @w, and @h (the type of the rationals) by finitely many applications of the operations of order type addition, multiplication, and converse; and the weak second-order theory of locally free algebras with only unary operations.

504 citations

### "On The Power of Distributed Bottom-..." refers background in this paper

...Tree automata were introduced in [4], [5] and [12] to solve certain decision problems in logic....

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IBM

^{1}, Pennsylvania State University^{2}, Worcester Polytechnic Institute^{3}, Sun Microsystems^{4}TL;DR: This work presents a formal framework for XML schema languages based on regular tree grammars that helps to describe, compare, and implement such schema languages in a rigorous manner.

Abstract: On the basis of regular tree grammars, we present a formal framework for XML schema languages. This framework helps to describe, compare, and implement such schema languages in a rigorous manner. Our main results are as follows: (1) a simple framework to study three classes of tree languages (local, single-type, and regular); (2) classification and comparison of schema languages (DTD, W3C XML Schema, and RELAX NG) based on these classes; (3) efficient document validation algorithms for these classes; and (4) other grammatical concepts and advanced validation algorithms relevant to an XML model (e.g., binarization, derivative-based validation).

495 citations