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Tree automata and XPath on compressed trees
 Proceedings of the Tenth International Conference on Implementation and Application of Automata (CIAA 2005), Sophia Antipolis (France), number 3845 in Lecture Notes in Computer Science
, 2006
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Pattern Matching of Compressed Terms and Contexts and Polynomial Rewriting
, 2011
"... A generalization of the compressed string pattern match that applies to terms with variables is investigated: Given terms s and t compressed by singleton tree grammars, the task is to find an instance of s that occurs as a subterm in t. We show that this problem is in NP and that the task can be pe ..."
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A generalization of the compressed string pattern match that applies to terms with variables is investigated: Given terms s and t compressed by singleton tree grammars, the task is to find an instance of s that occurs as a subterm in t. We show that this problem is in NP and that the task can be performed in time O(n cVar(s) ), including the construction of the compressed substitution, and a representation of all occurrences. We show that the special case where s is uncompressed can be performed in polynomial time. As a nice application we show that for an equational deduction of t to t ′ by an equality axiom l = r (a rewrite) a single step can be performed in polynomial time in the size of compression of t and l, r if the number of variables is fixed in l. We also show that n rewriting steps can be performed in polynomial time, if the equational axioms are compressed and assumed to be constant for the rewriting sequence. Another potential application are querying mechanisms on compressed XMLdata bases.
FirstOrder Unification on Compressed Terms
, 2011
"... Singleton Tree Grammars (STGs) have recently drawn considerable attention. They generalize the sharing of subtrees known from DAGs to sharing of connected subgraphs. This allows to obtain smaller inmemory representations of trees than with DAGs. In the past years some important tree algorithms were ..."
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Singleton Tree Grammars (STGs) have recently drawn considerable attention. They generalize the sharing of subtrees known from DAGs to sharing of connected subgraphs. This allows to obtain smaller inmemory representations of trees than with DAGs. In the past years some important tree algorithms were proved to perform efficiently (without decompression) over STGs; e.g., type checking, equivalence checking, and unification. We present a tool that implements an extension of the unification algorithm for STGs. This algorithm makes extensive use of equivalence checking. For the latter we implemented two variants, the classical exact one and a recent randomized one. Our experiments show that the randomized algorithm performs better. The running times are also compared to those of unification over uncompressed trees.
Automata for Positive Core XPath Queries on Compressed Documents
 In Proceedings of LPAR’06
, 2006
"... Abstract. Given any dag t representing a fully or partially compressed XML document, we present a method for evaluating any positive unary query expressed in terms of Core XPath axes, on t, without unfolding t into a tree. To each Core XPath query of a certain basic type, we associate a word automa ..."
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Abstract. Given any dag t representing a fully or partially compressed XML document, we present a method for evaluating any positive unary query expressed in terms of Core XPath axes, on t, without unfolding t into a tree. To each Core XPath query of a certain basic type, we associate a word automaton; these automata run on the graph of dependency between the nonterminals of the straightline regular tree grammar associated to the given dag, or along complete sibling chains in this grammar. Any given Core XPath query can be decomposed into queries of the basic type, and the answer to the query, on the dag t, can then be expressed as a subdag of t suitably labeled under the runs of such automata.
Compression of probabilistic xml documents
, 2009
"... Abstract. Database techniques to store, query and manipulate data that contains uncertainty receives increasing research interest. Such UDBMSs can be classified according to their underlying data model: relational, XML, or RDF. We focus on uncertain XML DBMS with as representative example the Proba ..."
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Abstract. Database techniques to store, query and manipulate data that contains uncertainty receives increasing research interest. Such UDBMSs can be classified according to their underlying data model: relational, XML, or RDF. We focus on uncertain XML DBMS with as representative example the Probabilistic XML model (PXML) of [9]. The size of a PXML document is obviously a factor in performance. There are PXMLspecific techniques to reduce the size, such as a push down mechanism, that produces equivalent but more compact PXML documents. It can only be applied, however, where possibilities are dependent. For normal XML documents there also exist several techniques for compressing a document. Since Probabilistic XML is (a special form of) normal XML, it might benefit from these methods even more. In this paper, we show that existing compression mechanisms can be combined with PXMLspecific compression techniques. We also show that best compression rates are obtained with a combination of PXMLspecific technique with a rather simple generic DAGcompression technique. 1
Certification of nontermination proofs
 In Proc. ITP 2012, volume 7406 of LNCS
, 2012
"... Abstract Automatic tools for proving (non)termination of term rewrite systems, if successful, deliver proofs as justification. In this work, we focus on how to certify nontermination proofs. Besides some techniques that allow to reduce the number of rules, the main way of showing nontermination is t ..."
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Abstract Automatic tools for proving (non)termination of term rewrite systems, if successful, deliver proofs as justification. In this work, we focus on how to certify nontermination proofs. Besides some techniques that allow to reduce the number of rules, the main way of showing nontermination is to find a loop, a finite derivation of a special shape that implies nontermination. For standard termination, certifying loops is easy. However, it is not at all trivial to certify whether a given loop also implies innermost nontermination. To this end, a complex decision procedure has been developed in [1]. We formalized this decision procedure in Isabelle/HOL and were able to simplify some parts considerably. Furthermore, from our formalized proofs it is easy to obtain a low complexity bound. Along the way of presenting our formalization, we report on generally applicable ideas that allow to reduce the formalization effort and improve the efficiency of our certifier.
The complexity of tree transducer output languages
 In Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 2008 (Available at http://arbre.is.s.utokyo.ac.jp/˜kinaba/fst.pdf
"... Abstract. Two complexity results are shown for the output languages generated by compositions of macro tree transducers. They are in NSPACE(n) and hence are contextsensitive, and the class is NPcomplete. 1 ..."
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Abstract. Two complexity results are shown for the output languages generated by compositions of macro tree transducers. They are in NSPACE(n) and hence are contextsensitive, and the class is NPcomplete. 1
XML Compression via DAGs
, 2013
"... Unranked trees can be represented using their minimal dag (directed acyclic graph). For XML this achieves high compression ratios due to their repetitive mark up. Unranked trees are often represented through first child/next sibling (fcns) encoded binary trees. We study the difference in size ( = nu ..."
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Unranked trees can be represented using their minimal dag (directed acyclic graph). For XML this achieves high compression ratios due to their repetitive mark up. Unranked trees are often represented through first child/next sibling (fcns) encoded binary trees. We study the difference in size ( = number of edges) of minimal dag versus minimal dag of the fcns encoded binary tree. One main finding is that the size of the dag of the binary tree can never be smaller than the square root of the size of the minimal dag, and that there are examples that match this bound. We introduce a new combined structure, the hybrid dag, which is guaranteed to be smaller than (or equal in size to) both dags. Interestingly, we find through experiments that last child/previous sibling encodings are much better for XML compression via dags, than fcns encodings. This is because optional elements are more likely to appear towards the end of child sequences.
XML INDEX COMPRESSION BY DTD SUBTRACTION
"... Whenever XML is used as format to exchange large amounts of data or even for data streams, the verbose behaviour of XML is one of the bottlenecks. While compression of XML data seems to be a way out, it is essential for a variety of applications that the compression result can be queried efficiently ..."
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Whenever XML is used as format to exchange large amounts of data or even for data streams, the verbose behaviour of XML is one of the bottlenecks. While compression of XML data seems to be a way out, it is essential for a variety of applications that the compression result can be queried efficiently. Furthermore, for efficient path query evaluation, an index is desired, which usually generates an additional data structure. For this purpose, we have developed a compression technique that uses structure information found in the DTD to perform a structurepreserving compression of XML data and provides a compression of an index that allows for efficient search in the compressed data. Our evaluation shows that compression factors which are close to gzip are possible, whereas the structural part of XML files can be compressed even better.
Congruence Closure of Compressed Terms in Polynomial Time
, 2011
"... The wordproblem for a finite set of equational axioms between ground terms is the question whether for terms s, t the equation s = t is a consequence. We consider this problem under grammar based compression of terms, in particular compression with singleton tree grammars (STGs) and with directed ..."
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The wordproblem for a finite set of equational axioms between ground terms is the question whether for terms s, t the equation s = t is a consequence. We consider this problem under grammar based compression of terms, in particular compression with singleton tree grammars (STGs) and with directed acyclic graphs (DAGs) as a special case. We show that given a DAGcompressed ground and reduced term rewriting system T, the Tnormal form of an STGcompressed term s can be computed in polynomial time, and hence the Tword problem can be solved in polynomial time. This implies that the word problem of STGcompressed terms w.r.t. a set of DAGcompressed ground equations can be decided in polynomial time. If the ground term rewriting system (gTRS) T is STGcompressed, we show NPhardness of Tnormalform computation. For compressed, reduced gTRSs we show a PSPACE upper bound on the complexity of the normal form computation of STGcompressed terms. Also special cases are considered and a prototypical implementation is presented.