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Automatic Structures: Richness and Limitations
 PROCEEDINGS OF THE 19TH IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (IEEE COMPUTER SOCIETY
, 2004
"... This paper addresses the question of whether a given algebraic structure has an automatic presentation and, in the case that it has, how similar its presentations are. That is, what is the complexity of finding out whether two presentations stand for the same algebraic structure. So the first topic ..."
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Cited by 26 (9 self)
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This paper addresses the question of whether a given algebraic structure has an automatic presentation and, in the case that it has, how similar its presentations are. That is, what is the complexity of finding out whether two presentations stand for the same algebraic structure. So the first topic is that of characterising the class of automatic structures. The automatic Boolean algebras are characterised, and it is proven that the free Abelian group of infinite rank and many Frasse limits do not have automatic presentations. In particular, the countably infinite random graph and the universal partial order do not have automatic presentations. Furthermore, no infinite integral domain is automatic. The second topic of the paper is the isomorphism problem. We prove that the complexity of the isomorphism problem for the class of all automatic ... complete.
XML: model, schemas, types, logics, and queries
 IN LOGICS FOR EMERGING APPLICATIONS OF DATABASES
, 2003
"... ... In this chapter, we shall see that the suspicion is easy dispelled. We look at techniques now used in practice for dealing with XML trees, and we note how they depart from oldfashioned uses. Since trees are objects that are very complicated to manipulate directly through pointer updates, declar ..."
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Cited by 16 (0 self)
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... In this chapter, we shall see that the suspicion is easy dispelled. We look at techniques now used in practice for dealing with XML trees, and we note how they depart from oldfashioned uses. Since trees are objects that are very complicated to manipulate directly through pointer updates, declarative techniques are becoming increasingly important, especially when it comes to exploring, mining, and constructing treeshaped data. In particular, we will contrast conventional concepts of database theory such as relational calculus with that of more procedural notations for trees. We explore why the essential problem of locating data in trees is intimately linked with tree automata and decidable logics, somewhat in parallel to the link between query algebras and firstorder logic in relational database theory. So, we shall see why logic and automata create interesting new research opportunities.
Logical Definability and Query Languages over Unranked Trees
 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science (LICS
, 2003
"... Unranked trees, that is, trees with no restriction on the number of children of nodes, have recently attracted much attention, primarily as an abstraction of XML documents. In this paper, we study logical definability over unranked trees, as well as collections of unranked trees, that can be viewed ..."
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Cited by 4 (1 self)
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Unranked trees, that is, trees with no restriction on the number of children of nodes, have recently attracted much attention, primarily as an abstraction of XML documents. In this paper, we study logical definability over unranked trees, as well as collections of unranked trees, that can be viewed as databases of XML documents. The traditional approach to definability is to view each tree as a structure of a fixed vocabulary, and study the expressive power of various logics on trees. A different approach, based on model theory, considers a structure whose universe is the set of all trees, and studies definable sets and relations; this approach extends smoothly to the setting of definability over collections of trees. We study the latter, modeltheoretic approach. We find sets of operations on unranked trees that define regular tree languages, and show that some natural restrictions correspond to logics studied in the context of XML pattern languages. We then look at relational calculi over collections of unranked trees, and obtain quantifierrestriction results that give us bounds on the expressive power and complexity. As unrestricted relational calculi can express problems complete for each level of the polynomial hierarchy, we look at their restrictions, corresponding to the restricted logics over the family of all unranked trees, and find several calculi with low (NC ) data complexity, that can express important XML properties like DTD validation and XPath evaluation.
Model Theoretic Complexity of Automatic Structures
 PROC. TAMC ’08, LNCS 4978
, 2008
"... We study the complexity of automatic structures via wellestablished concepts from both logic and model theory, including ordinal heights (of wellfounded relations), Scott ranks of structures, and CantorBendixson ranks (of trees). We prove the following results: 1) The ordinal height of any autom ..."
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Cited by 4 (2 self)
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We study the complexity of automatic structures via wellestablished concepts from both logic and model theory, including ordinal heights (of wellfounded relations), Scott ranks of structures, and CantorBendixson ranks (of trees). We prove the following results: 1) The ordinal height of any automatic wellfounded partial order is bounded by ωω; 2) The ordinal heights of automatic wellfounded relations are unbounded below ωCK 1, the first noncomputable ordinal; 3) For any computable ordinal α, there is an automatic structure of Scott rank at least α. Moreover, there are automatic structures of Scott rank ωCK 1, ωCK 1 +1; 4) For any computable ordinal α, there is an automatic successor tree of CantorBendixson rank α.
Queries on Xml Streams with Bounded Delay and Concurrency
"... Streaming algorithms for Xml query answering call for efficient memory management. Tractable queries are distinguished by a bounded number of concurrently alive answer candidates at every time point, and a bounded delay for node selection, for every candidate. We show that both properties are decida ..."
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Cited by 4 (1 self)
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Streaming algorithms for Xml query answering call for efficient memory management. Tractable queries are distinguished by a bounded number of concurrently alive answer candidates at every time point, and a bounded delay for node selection, for every candidate. We show that both properties are decidable in polynomial time for queries defined by deterministic tree automata. Our results are obtained by reduction to the bounded valuedness problem for recognizable relations between unranked trees, a problem that we show to be decidable in polynomial time. Key words: streaming, tree automata, Xml, databases. 1.
Automatabased presentations of infinite structures
, 2009
"... The model theory of finite structures is intimately connected to various fields ..."
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The model theory of finite structures is intimately connected to various fields