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)

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 ($NRE_s$) from the usual XPath benchmark to nested word automata ($NW$$A_s$). The determinization of these $NW$ $A_s$, however, fails to produce reasonably small automata. In the best case, huge deterministic $NW$$A_s$ are produced after few hours, even for relatively small $NRE_s$ of the benchmark. We propose a different approach to the determinization of automata for nested words. For this, we introduce stepwise hedge automata ($SHA_s$) that generalize naturally on both (stepwise) tree automata and on finite word automata. We then show how to determinize $SHA_s$, yielding reasonably small deterministic automata for the $NRE_s$ from the XPath benchmark. The size of deterministic $SHA_s$ automata can be reduced further by a novel minimization algorithm for a subclass of $SHA_s$. In order to understand why the new approach to determinization and minimization works so nicely, we investigate the relationship between $NWA_s$ and $SHA_s$ further. Clearly, deterministic $SHA_s$ can be compiled to deterministic NWAs in linear time, and conversely, $NW$$A_s$ can be compiled to nondeterministic $SHA_s$ in polynomial time. Therefore, we can use $SHA_s$ as intermediates for determinizing $NWA_s$, while avoiding the huge size increase with the usual determinization algorithm for $NWA_s$. Notably, the NWAs obtained from the $SHA_s$ perform bottom-up and left-to-right computations only, but no top-down computations. This $NWA$-behavior can be distinguished syntactically by the (weak) single-entry property, suggesting a close relationship between $SHA_s$ and single-entry $NWA_s$. In particular, it turns out that the usual determinization algorithm for $NWA_s$ behaves well for single-entry $NWA_s$, while it quickly explodes without the single-entry property. Furthermore, it is known that the class of deterministic multi-module single-entry $NWA_s$ enjoys unique minimization. The subclass of deterministic $SHA_s$ 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 $SHA_s$, 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

Stream Firewalling of XML Constraints

As XML-based messages have become common in many client-server protocols, there is a need to protect application servers from invalid or dangerous messages. This leads to the XML stream firewalling problem; that of applying integrity constraints against a large number of simultaneous streams. We conduct the first investigation of a constraint engine optimized for the generation of XML stream firewalls. We isolate a class of DTDs and XPath constraints which support the generation of low-space filters, and provide algorithms for generating firewalls with low per-input-character time and per-stream space. We give experimental results which show that we have achieved these goals in practice