Enumeration on Trees with Tractable Combined Complexity and Efficient Updates

Amarilli, Antoine; Bourhis, Pierre; Mengel, Stefan; Niewerth, Matthias

doi:10.1145/3294052.3319702

“…Hence, also in the context of MSO enumeration, it is not known whether we can achieve linear preprocessing and constant delay in data complexity while remaining tractable in the (generally non-deterministic) automaton. The result that we show in the present paper implies that we can achieve this for MSO queries on words when all free variables are first-order, with the query being represented as a generally non-deterministic sequential VA, or as a sequential regex-formula with capture variables: note that an extension to trees is investigated in our follow-up work [5].…”

Section: Introductionmentioning

confidence: 62%

“…Connection to circuits. We remark that our mapping DAG can be seen as a kind of Boolean circuit, and our enumeration algorithm on mapping DAGs can be connected to earlier work by some of the present authors on enumeration for Boolean circuits [2,5]. Specifically, a mapping DAG can be understood as describing a kind of binary decision diagram (BDD): these are special kind of Boolean circuits where each conjunction always involves a literal.…”

mentioning

confidence: 88%

Constant-Delay Enumeration for Nondeterministic Document Spanners

Amarilli¹,

Bourhis²,

Mengel³

et al. 2020

Preprint

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We consider the information extraction framework known as document spanners, and study the problem of efficiently computing the results of the extraction from an input document, where the extraction task is described as a sequential variable-set automaton (VA). We pose this problem in the setting of enumeration algorithms, where we can first run a preprocessing phase and must then produce the results with a small delay between any two consecutive results. Our goal is to have an algorithm which is tractable in combined complexity, i.e., in the sizes of the input document and the VA; while ensuring the best possible data complexity bounds in the input document size, i.e., constant delay in the document size. Several recent works at PODS'18 proposed such algorithms but with linear delay in the document size or with an exponential dependency in size of the (generally nondeterministic) input VA. In particular, Florenzano et al. suggest that our desired runtime guarantees cannot be met for general sequential VAs. We refute this and show that, given a nondeterministic sequential VA and an input document, we can enumerate the mappings of the VA on the document with the following bounds: the preprocessing is linear in the document size and polynomial in the size of the VA, and the delay is independent of the document and polynomial in the size of the VA. The resulting algorithm thus achieves tractability in combined complexity and the best possible data complexity bounds. Moreover, it is rather easy to describe, in particular for the restricted case of so-called extended VAs. Finally, we evaluate our algorithm empirically using a prototype implementation.

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“…A second question is to generalize our result from words to trees, but this is challenging: the run of a tree automaton is no longer linear in just one direction, so it is not easy to skip parts of the input similarly to the jump function of Section 5, or to combine computation that occurs in different branches. We believe that these difficulties can be solved and that a similar result can be shown for trees, but that the resulting algorithm is far more complex: this point, and the question of updates, are explored in our follow-up work [4].…”

Section: Discussionmentioning

confidence: 89%

Constant-Delay Enumeration for Nondeterministic Document Spanners

Amarilli,

Bourhis,

Mengel

et al. 2018

Preprint

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0

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We consider the information extraction framework known as document spanners, and study the problem of efficiently computing the results of the extraction from an input document, where the extraction task is described as a sequential variable-set automaton (VA). We pose this problem in the setting of enumeration algorithms, where we can first run a preprocessing phase and must then produce the results with a small delay between any two consecutive results. Our goal is to have an algorithm which is tractable in combined complexity, i.e., in the sizes of the input document and the VA; while ensuring the best possible data complexity bounds in the input document size, i.e., constant delay in the document size. Several recent works at PODS'18 proposed such algorithms but with linear delay in the document size or with an exponential dependency in size of the (generally nondeterministic) input VA. In particular, Florenzano et al. suggest that our desired runtime guarantees cannot be met for general sequential VAs. We refute this and show that, given a nondeterministic sequential VA and an input document, we can enumerate the mappings of the VA on the document with the following bounds: the preprocessing is linear in the document size and polynomial in the size of the VA, and the delay is independent of the document and polynomial in the size of the VA. The resulting algorithm thus achieves tractability in combined complexity and the best possible data complexity bounds. Moreover, it is rather easy to describe, in particular for the restricted case of so-called extended VAs.

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“…Our study of enumeration for annotated grammars is also reminiscent of enumeration results for queries over trees expressed as tree automata. An algorithm for this was given by Bagan [8] with linear-time preprocessing and constant-delay in data complexity, for deterministic tree automata, and this was extended in [6] to nondeterministic automata. However, this is again more restricted: evaluating a tree automaton on a tree amounts to evaluating a visibly pushdown automaton over a string representation of the tree, which is again more restrictive than general context-free grammars.…”

Section: Introductionmentioning

confidence: 99%

Efficient Enumeration Algorithms for Annotated Grammars

Amarilli¹,

Jachiet²,

Muñoz³

et al. 2022

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We introduce annotated grammars, an extension of context-free grammars which allows annotations on terminals. Our model extends the standard notion of regular spanners, and has the same expressiveness as the extraction grammars recently introduced by Peterfreund. We study the enumeration problem for annotated grammars: fixing a grammar, and given a string as input, enumerate all annotations of the string that form a word derivable from the grammar. Our first result is an algorithm for unambiguous annotated grammars, which preprocesses the input string in cubic time and enumerates all annotations with output-linear delay. This improves over Peterfreund's result, which needs quintic time preprocessing to achieve this delay bound. We then study how we can reduce the preprocessing time while keeping the same delay bound, by making additional assumptions on the grammar. Specifically, we present a class of grammars which only have one derivation shape for all outputs, for which we can enumerate with quadratic time preprocessing. We also give classes generalizing regular spanners for which linear time preprocessing suffices.

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Enumeration on Trees with Tractable Combined Complexity and Efficient Updates

Cited by 22 publications

References 29 publications

Constant-Delay Enumeration for Nondeterministic Document Spanners

Constant-Delay Enumeration for Nondeterministic Document Spanners

Constant-Delay Enumeration for Nondeterministic Document Spanners

Efficient Enumeration Algorithms for Annotated Grammars

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