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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 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.
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.
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"... ABSTRACT. Twocomplexityresultsareshownfortheoutputlanguagesgeneratedbycompositions of macro tree transducers. They are in NSPACE(n) and hence are contextsensitive, and the class is NPcomplete. 1 ..."
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ABSTRACT. Twocomplexityresultsareshownfortheoutputlanguagesgeneratedbycompositions of macro tree transducers. They are in NSPACE(n) and hence are contextsensitive, and the class is NPcomplete. 1
COMPLEXITY AND EXPRESSIVENESS OF MODELS OF XML TRANSLATIONS
"... XML has become widely used in computer industry, and the importance of static analysis and verification of applications manipulating XML documents is increasing. For analyzing or proving any properties on XML manipulating programs, it is essential to have some model with theoretically welldefined s ..."
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XML has become widely used in computer industry, and the importance of static analysis and verification of applications manipulating XML documents is increasing. For analyzing or proving any properties on XML manipulating programs, it is essential to have some model with theoretically welldefined semantics. After a long history of researches on models of treetotree translations, a recent trend is to regard macro tree transducers (mtts) as a standard model for XML manipulation. Mtts are known to cover tree translations expressible by other models such as attributed tree transducers, MSOdefinable tree translations, or pebble tree transducers, and the high expressiveness allows representing a vast range of practical XML translations. Yet, they ensure various good properties such as exact typechecking, streaming, decidable emptiness, and so on. Nevertheless, mtts still lack some properties desired for modeling XML translations. In particular, (1) mtts have poor closure properties on composition and (2) computational complexities for many problems on mtts are still unknown. A consequence of the first point is that, for example, an mtt composed with even a very simple pre or post tree translation cannot be represented by a single mtt. The lack of the compositionality implies difficulty of modular modeling; even if we could construct a
Autor: Betreuer:
"... Front page line art drawing by Pearson Scott Foresman. While every precaution has been taken in the preparation of this work, the author assumes no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein. ..."
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Front page line art drawing by Pearson Scott Foresman. While every precaution has been taken in the preparation of this work, the author assumes no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein.
Fast Equality Test for StraightLine Compressed Strings
, 2011
"... Abstract. The paper describes a simple and fast randomized test for equality of grammarcompressed strings. The thorough running time analysis is done by applying a logarithmic cost measure. Keywords compression ..."
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Abstract. The paper describes a simple and fast randomized test for equality of grammarcompressed strings. The thorough running time analysis is done by applying a logarithmic cost measure. Keywords compression
Functional Programs as Compressed Data Naoki Kobayashi
"... We propose an application of programming language techniques to lossless data compression, where tree data are compressed as functional programs that generate them. This “functional programs as compressed data ” approach has several advantages. First, it follows from the standard argument of Kolmogo ..."
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We propose an application of programming language techniques to lossless data compression, where tree data are compressed as functional programs that generate them. This “functional programs as compressed data ” approach has several advantages. First, it follows from the standard argument of Kolmogorov complexity that the size of compressed data can be optimal up to an additive constant. Secondly, a compression algorithm is clean: it is just a sequence of βexpansions for λterms. Thirdly, one can use program verification and transformation techniques (higherorder model checking, in particular) to apply certain operations on data without decompression. In the paper, we present algorithms for data compression and manipulation based on the approach, and prove their correctness. We also report preliminary experiments on prototype data compression/transformation systems. 1.
Congruence Closure of Compressed Terms in Polynomial Time
"... Abstract. 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 ..."
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Abstract. 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.
On the complexity of Bounded SecondOrder Unification and Stratified Context Unification
"... Bounded SecondOrder Unification is a decidable variant of undecidable SecondOrder Unification. Stratified Context Unification is a decidable restriction of Context Unification, whose decidability is a longstanding open problem. This paper is a join of two separate previous, preliminary papers on ..."
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Bounded SecondOrder Unification is a decidable variant of undecidable SecondOrder Unification. Stratified Context Unification is a decidable restriction of Context Unification, whose decidability is a longstanding open problem. This paper is a join of two separate previous, preliminary papers on NPcompleteness of Bounded SecondOrder Unification and Stratified Context Unification. It clarifies some omissions in these papers, joins the algorithmic parts that construct a minimal solution, and gives a clear account of a method of using singleton tree grammars for compression that may have potential usage for other algorithmic questions in related areas.