7 research outputs found
Earliest Query Answering for Deterministic Nested Word Automata
International audienceEarliest query answering (EQA) is an objective of many recent streaming algorithms for XML query answering, that aim for close to optimal memory management. In this paper, we show that EQA is infeasible even for a small fragment of Forward XPath except if P=NP. We then present an EQA algorithm for queries and schemas defined by deterministic nested word automata (dNWAs) and distinguish a large class of dNWAs for which streaming query answering is feasible in polynomial space and time
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)
Streamability of nested word transductions
We consider the problem of evaluating in streaming (i.e., in a single
left-to-right pass) a nested word transduction with a limited amount of memory.
A transduction T is said to be height bounded memory (HBM) if it can be
evaluated with a memory that depends only on the size of T and on the height of
the input word. We show that it is decidable in coNPTime for a nested word
transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In
this case, the required amount of memory may depend exponentially on the height
of the word. We exhibit a sufficient, decidable condition for a VPT to be
evaluated with a memory that depends quadratically on the height of the word.
This condition defines a class of transductions that strictly contains all
determinizable VPTs
Nested Regular Expressions can be Compiled to Small Deterministic Nested Word Automata
International audienceWe study the problem of whether regular expressions for nested words can be compiled to small deterministic nested word au-tomata (NWAs). In theory, we obtain a positive answer for small deter-ministic regular expressions for nested words. In practice of navigational path queries, nondeterministic NWAs are obtained for which NWA de-terminization explodes. We show that practical good solutions can be obtained by using stepwise hedge automata as intermediates
Certain Query Answering on Compressed String Patterns: From Streams to Hyperstreams (long version)
We 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
Determinization and Minimization of Automata for Nested Words Revisited
International audienceWe consider the problem of determinizing and minimizing automata for nested words in practice. For this we compile the nested regular expressions () from the usual XPath benchmark to nested word automata (). The determinization of these , however, fails to produce reasonably small automata. In the best case, huge deterministic are produced after few hours, even for relatively small of the benchmark. We propose a different approach to the determinization of automata for nested words. For this, we introduce stepwise hedge automata () that generalize naturally on both (stepwise) tree automata and on finite word automata. We then show how to determinize , yielding reasonably small deterministic automata for the from the XPath benchmark. The size of deterministic automata can be reduced further by a novel minimization algorithm for a subclass of . In order to understand why the new approach to determinization and minimization works so nicely, we investigate the relationship between and further. Clearly, deterministic can be compiled to deterministic NWAs in linear time, and conversely, can be compiled to nondeterministic in polynomial time. Therefore, we can use as intermediates for determinizing , while avoiding the huge size increase with the usual determinization algorithm for . Notably, the NWAs obtained from the perform bottom-up and left-to-right computations only, but no top-down computations. This -behavior can be distinguished syntactically by the (weak) single-entry property, suggesting a close relationship between and single-entry . In particular, it turns out that the usual determinization algorithm for behaves well for single-entry , while it quickly explodes without the single-entry property. Furthermore, it is known that the class of deterministic multi-module single-entry enjoys unique minimization. The subclass of deterministic to which our novel minimization algorithm applies is different though, in that we do not impose multiple modules. As further optimizations for reducing the sizes of the constructed , we propose schema-based cleaning and symbolic representations based on apply-else rules, that can be maintained by determinization. We implemented the optimizations and report the experimental results for the automata constructed for the XPathMark benchmark