Determinacy and rewriting of functional top–down and MSO tree transformations

A query is determined by a view, if the result of the query can be reconstructed from the result of the view. We consider the problem of deciding for two given (functional) tree transformations, whether one is determined by the other. If the view transformation is induced by a tree transducer that may copy, then determinacy is undecidable. For a large class of noncopying views, namely compositions of extended linear top–down tree transducers, we show that determinacy is decidable, where queries are either deterministic top–down tree transducers (with regular look-ahead) or deterministic MSO tree transducers. We also show that if a query is determined by a view, then it can be rewritten into a query that works over the view and is in the same class of transducers as the query. The proof relies on the decidability of equivalence for the considered classes of queries, and on their composition closure

Tree Compression with Top Trees Revisited

We revisit tree compression with top trees (Bille et al, ICALP'13) and present several improvements to the compressor and its analysis. By significantly reducing the amount of information stored and guiding the compression step using a RePair-inspired heuristic, we obtain a fast compressor achieving good compression ratios, addressing an open problem posed by Bille et al. We show how, with relatively small overhead, the compressed file can be converted into an in-memory representation that supports basic navigation operations in worst-case logarithmic time without decompression. We also show a much improved worst-case bound on the size of the output of top-tree compression (answering an open question posed in a talk on this algorithm by Weimann in 2012).Comment: SEA 201

The Equivalence Problem for Deterministic MSO Tree Transducers is Decidable

It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs

Look-ahead removal for total deterministic top-down tree transducers

Algorithms and the Foundations of Software technolog

On Functionality of Visibly Pushdown Transducers

Visibly pushdown transducers form a subclass of pushdown transducers that (strictly) extends finite state transducers with a stack. Like visibly pushdown automata, the input symbols determine the stack operations. In this paper, we prove that functionality is decidable in PSpace for visibly pushdown transducers. The proof is done via a pumping argument: if a word with two outputs has a sufficiently large nesting depth, there exists a nested word with two outputs whose nesting depth is strictly smaller. The proof uses technics of word combinatorics. As a consequence of decidability of functionality, we also show that equivalence of functional visibly pushdown transducers is Exptime-Complete.Comment: 20 page

Expressiveness and complexity of xml publishing transducers

A number of languages have been developed for specifying XML publishing, i.e., transformations of relational data into XML trees. These languages generally describe the behaviors of a middleware controller that builds an output tree iteratively, issuing queries to a relational source and expanding the tree with the query results at each step. To study the complexity and expressive power of XML publishing languages, this paper proposes a notion of pub-lishing transducers. Unlike automata for querying XML data, a publishing transducer generates a new XML tree rather than per-forming a query on an existing tree. We study a variety of pub-lishing transducers based on what relational queries a transducer can issue, what temporary stores a transducer can use during tree generation, and whether or not some tree nodes are allowed to be virtual, i.e., excluded from the output tree. We first show how exist-ing XML publishing languages can be characterized by such trans-ducers. We then study the membership, emptiness and equivalence problems for various classes of transducers and existing publish-ing languages. We establish lower and upper bounds, all matching except one, ranging from PTIME to undecidable. Finally, we inves-tigate the expressive power of these transducers and existing lan-guages. We show that when treated as relational query languages, different classes of transducers capture either complexity classes (e.g., PSPACE) or fragments of datalog (e.g., linear datalog). For tree generation, we establish connections between publishing trans-ducers and logical transductions

Regular Matching and Inclusion on Compressed Tree Patterns with Context Variables

International audienceWe study the complexity of regular matching and inclusion for compressed tree patterns extended by context variables. The addition of context variables to tree patterns permits us to properly capture compressed string patterns but also compressed patterns for unranked trees with tree and hedge variables. Regular inclusion for the latter is relevant to certain query answering on Xml streams with references

Certain Query Answering on Compressed String Patterns: From Streams to Hyperstreams

International audienceWe study the problem of certain query answering (CQA) on compressed string patterns. These are incomplete singleton context-free grammars, that can model systems of multiple streams with references to others, called hyperstreams more recently. In order to capture regular path queries on strings, we consider nondeterministic finite automata (NFAs) for query definition. It turns out that CQA for Boolean NFA queries is equivalent to regular string pattern inclusion, i.e., whether all strings completing a compressed string pattern belong to a regular language. We prove that CQA on compressed string patterns is PSpace- complete for NFA queries. The PSpace-hardness even applies to Boolean queries defined by deterministic finite automata (DFAs) and without compression. We also show that CQA on compressed linear string patterns can be solved in PTime for DFA queries. The proofs of the results presented here can be found in the long version of this paper (https://hal.inria.fr/hal-01846016)