arXiv subjects

Sebastian Maneth

Publications and source records attributed to Sebastian Maneth.

At least 37 records · Page 2Linked to original sources

arXiv2018

Grammar-based Compression of Unranked Trees

We introduce forest straight-line programs (FSLPs) as a compressed representation of unranked ordered node-labelled trees. FSLPs are based on the operations of forest algebra and generalize tree straight-line programs. We compare the succinctness of FSLPs with two other compression schemes for unranked trees: top dags and tree straight-line programs of first-child/next sibling encodings. Efficient translations between these formalisms are provided. Finally, we show that equality of unranked trees in the setting where certain symbols are associative or commutative can be tested in polynomial time. This generalizes previous results for testing isomorphism of compressed unordered ranked trees.

cs.DS↗

arXiv2017

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.

cs.FL↗

arXiv2017

Grammar-Based Graph Compression

We present a new graph compressor that works by recursively detecting repeated substructures and representing them through grammar rules. We show that for a large number of graphs the compressor obtains smaller representations than other approaches. Specific queries such as reachability between two nodes or regular path queries can be evaluated in linear time (or quadratic times, respectively), over the grammar, thus allowing speed-ups proportional to the compression ratio.

cs.DS↗

arXiv2017

Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable

We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total transducers with unary output alphabet (over a given top-down regular domain language), and co-randomized polynomial time for linear transducers; these results are obtained using techniques from multi-linear algebra. For our main result, we prove that equivalence can be certified by means of inductive invariants using polynomial ideals. This allows us to construct two semi-algorithms, one searching for a proof of equivalence, one for a witness of non-equivalence. Furthermore, we extend our result to deterministic top-down tree-to-string transducers which produce output not in a free monoid but in a free group.

cs.FL↗

arXiv2015

Look-Ahead Removal for Top-Down Tree Transducers

Top-down tree transducers are a convenient formalism for describing tree transformations. They can be equipped with regular look-ahead, which allows them to inspect a subtree before processing it. In certain cases, such a look-ahead can be avoided and the transformation can be realized by a transducer without look-ahead. Removing the look-ahead from a transducer, if possible, is technically highly challenging. For a restricted class of transducers with look-ahead, namely those that are total, deterministic, ultralinear, and bounded erasing, we present an algorithm that, for a given transducer from that class, (1) decides whether it is equivalent to a total deterministic transducer without look-ahead, and (2) constructs such a transducer if the answer is positive. For the whole class of total deterministic transducers with look-ahead we present a similar algorithm, which assumes that a so-called difference bound is known for the given transducer. The designer of a transducer can usually also determine a difference bound for it.

cs.FL↗

arXiv2015

Traversing Grammar-Compressed Trees with Constant Delay

A grammar-compressed ranked tree is represented with a linear space overhead so that a single traversal step, i.e., the move to the parent or the i-th child, can be carried out in constant time. Moreover, we extend our data structure such that equality of subtrees can be checked in constant time.

cs.DS↗

arXiv2015

A Survey on Methods and Systems for Graph Compression

We present an informal survey (meant to accompany another paper) on graph compression methods. We focus on lossless methods, briefly list available pproaches, and compare them where possible or give some indicators on their compression ratios. We also mention some relevant results from the field of lossy compression and algorithms specialized for the use on large graphs. --- Note: The comparison is by no means complete. This document is a first draft and will be updated and extended.

cs.DS↗

arXiv2015

Compressed Tree Canonization

Straight-line (linear) context-free tree (SLT) grammars have been used to compactly represent ordered trees. It is well known that equivalence of SLT grammars is decidable in polynomial time. Here we extend this result and show that isomorphism of unordered trees given as SLT grammars is decidable in polynomial time. The proof constructs a compressed version of the canonical form of the tree represented by the input SLT grammar. The result is generalized to unrooted trees by "re-rooting" the compressed trees in polynomial time. We further show that bisimulation equivalence of unrooted unordered trees represented by SLT grammars is decidable in polynomial time. For non-linear SLT grammars which can have double-exponential compression ratios, we prove that unordered isomorphism is PSPACE-hard and in EXPTIME. The same complexity bounds are shown for bisimulation equivalence.

cs.DS↗

arXiv2014

Equivalence Problems for Tree Transducers: A Brief Survey

The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, (2) linear size increase, i.e., MSO definable tree transducers, and (3) monadic input and output ranked alphabets. For the full class of MTTs, decidability of equivalence remains a long-standing open problem.

cs.FL↗

arXiv2013

XQuery Streaming by Forest Transducers

Streaming of XML transformations is a challenging task and only very few systems support streaming. Research approaches generally define custom fragments of XQuery and XPath that are amenable to streaming, and then design custom algorithms for each fragment. These languages have several shortcomings. Here we take a more principles approach to the problem of streaming XQuery-based transformations. We start with an elegant transducer model for which many static analysis problems are well-understood: the Macro Forest Transducer (MFT). We show that a large fragment of XQuery can be translated into MFTs --- indeed, a fragment of XQuery, that can express important features that are missing from other XQuery stream engines, such as GCX: our fragment of XQuery supports XPath predicates and let-statements. We then rely on a streaming execution engine for MFTs, one which uses a well-founded set of optimizations from functional programming, such as strictness analysis and deforestation. Our prototype achieves time and memory efficiency comparable to the fastest known engine for XQuery streaming, GCX. This is surprising because our engine relies on the OCaml built in garbage collector and does not use any specialized buffer management, while GCX's efficiency is due to clever and explicit buffer management.

cs.DB↗

arXiv2013

XPath Node Selection over Grammar-Compressed Trees

XML document markup is highly repetitive and therefore well compressible using grammar-based compression. Downward, navigational XPath can be executed over grammar-compressed trees in PTIME: the query is translated into an automaton which is executed in one pass over the grammar. This result is well-known and has been mentioned before. Here we present precise bounds on the time complexity of this problem, in terms of big-O notation. For a given grammar and XPath query, we consider three different tasks: (1) to count the number of nodes selected by the query, (2) to materialize the pre-order numbers of the selected nodes, and (3) to serialize the subtrees at the selected nodes.

cs.DB↗

arXiv2013

Proceedings Second International Workshop on Trends in Tree Automata and Tree Transducers

This volume contains the papers that were presented at the second international workshop on Trends in Tree Automata and Transducers (TTATT 2013) which took place on October 19th, 2013 in Hanoi/Vietnam. The workshop was colocated with the verification conference ATVA. The first edition of the workshop was colocated with RTA and took place in Nagoya/Japan. The interest of the workshop lies at the intersection of programming languages, verification, and database theory, which are areas to which tree automata and transducers are applied recently.

cs.FL↗

arXiv2013

XML Compression via DAGs

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. We determine the average sizes of unranked and binary dags over a given set of labels (under uniform distribution) in terms of their exact generating functions, and in terms of their asymptotical behavior.

cs.DS↗

arXiv2010

Fast and Tiny Structural Self-Indexes for XML

XML document markup is highly repetitive and therefore well compressible using dictionary-based methods such as DAGs or grammars. In the context of selectivity estimation, grammar-compressed trees were used before as synopsis for structural XPath queries. Here a fully-fledged index over such grammars is presented. The index allows to execute arbitrary tree algorithms with a slow-down that is comparable to the space improvement. More interestingly, certain algorithms execute much faster over the index (because no decompression occurs). E.g., for structural XPath count queries, evaluating over the index is faster than previous XPath implementations, often by two orders of magnitude. The index also allows to serialize XML results (including texts) faster than previous systems, by a factor of ca. 2-3. This is due to efficient copy handling of grammar repetitions, and because materialization is totally avoided. In order to compare with twig join implementations, we implemented a materializer which writes out pre-order numbers of result nodes, and show its competitiveness.

cs.DB↗

arXiv2010

Tree structure compression with RePair

In this work we introduce a new linear time compression algorithm, called "Re-pair for Trees", which compresses ranked ordered trees using linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free string grammars and allow basic tree operations, like traversal along edges, to be executed without prior decompression. Our algorithm can be considered as a generalization of the "Re-pair" algorithm developed by N. Jesper Larsson and Alistair Moffat in 2000. The latter algorithm is a dictionary-based compression algorithm for strings. We also introduce a succinct coding which is specialized in further compressing the grammars generated by our algorithm. This is accomplished without loosing the ability do directly execute queries on this compressed representation of the input tree. Finally, we compare the grammars and output files generated by a prototype of the Re-pair for Trees algorithm with those of similar compression algorithms. The obtained results show that that our algorithm outperforms its competitors in terms of compression ratio, runtime and memory usage.

cs.DS↗

arXiv2010

XPath Whole Query Optimization

Previous work reports about SXSI, a fast XPath engine which executes tree automata over compressed XML indexes. Here, reasons are investigated why SXSI is so fast. It is shown that tree automata can be used as a general framework for fine grained XML query optimization. We define the "relevant nodes" of a query as those nodes that a minimal automaton must touch in order to answer the query. This notion allows to skip many subtrees during execution, and, with the help of particular tree indexes, even allows to skip internal nodes of the tree. We efficiently approximate runs over relevant nodes by means of on-the-fly removal of alternation and non-determinism of (alternating) tree automata. We also introduce many implementation techniques which allows us to efficiently evaluate tree automata, even in the absence of special indexes. Through extensive experiments, we demonstrate the impact of the different optimization techniques.

cs.DB↗

arXiv2009

Deciding Regularity of the Set of Instances of a Set of Terms with Regular Constraints is EXPTIME-Complete

Finite-state tree automata are a well studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is restricted to instantiations of a regular set given by a tree automaton. The problem was recently proved decidable, but with an unknown complexity. Here, the exact complexity of the problem is determined by proving EXPTIME-completeness. The main contribution is a new, exponential time algorithm that performs various exponential transformations on the involved terms and tree automata, and decides regularity by analyzing formulas over inequality and height predicates.

cs.SC↗

arXiv2009

The Complexity of Translation Membership for Macro Tree Transducers

Macro tree transducers (mtts) are a useful formal model for XML query and transformation languages. In this paper one of the fundamental decision problems on translations, namely the "translation membership problem" is studied for mtts. For a fixed translation, the translation membership problem asks whether a given input/output pair is element of the translation. For call-by-name mtts this problem is shown to be NP-complete. The main result is that translation membership for call-by-value mtts is in polynomial time. For several extensions, such as addition of regular look-ahead or the generalization to multi-return mtts, it is shown that translation membership still remains in PTIME.

cs.FL↗