A lower bound technique for the size of nondeterministic finite automata

Glaister, Ian; Shallit, Jeffrey

doi:10.1016/0020-0190(96)00095-6

Cited by 106 publications

(53 citation statements)

References 3 publications

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“…The two central questions studied in the present paper are as follows: First, how hard is it to minimize extended regular expressions (both with respect to their length, and with respect to the number of variables they contain), and second, how succinctly can extended 1 One can show this by proving that every NFA for Ln requires at least O(2 n ) states, e. g., by using the technique by Glaister and Shallit [14]. Due to the construction used in the proof of Theorem 2.3 in [17], this also gives a lower bound on the length of the regular expressions for Ln.…”

Section: Introductionmentioning

confidence: 99%

Extended Regular Expressions: Succinctness and Decidability

Freydenberger

2012

Theory Comput Syst

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Most modern implementations of regular expression engines allow the use of variables (also called back references). The resulting extended regular expressions (which, in the literature, are also called practical regular expressions, rewbr, or regex) are able to express non-regular languages.The present paper demonstrates that extended regular-expressions cannot be minimized effectively (neither with respect to length, nor number of variables), and that the tradeoff in size between extended and "classical" regular expressions is not bounded by any recursive function. In addition to this, we prove the undecidability of several decision problems (universality, equivalence, inclusion, regularity, and cofiniteness) for extended regular expressions. Furthermore, we show that all these results hold even if the extended regular expressions contain only a single variable.

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Section: Introductionmentioning

confidence: 99%

Extended Regular Expressions: Succinctness and Decidability

Freydenberger

2012

Theory Comput Syst

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“…It can be readily seen that τ is injective, and it is both prefix-free and suffix-free, since all words in τ (E) are of the same length. The set τ (E) is just the set of binary palindromes of length 4n, and, by chance, a proof of the non-crossing property of this set is given already in [9], albeit in a different context. Thus, by Theorems 1 and 5, the set τ (W 2 n ) has alphabetic width at least 2 2 Ω(n) .…”

Section: Theoremmentioning

confidence: 99%

Tight Bounds on the Descriptional Complexity of Regular Expressions

Gruber

Holzer

2009

Developments in Language Theory

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Abstract. We improve on some recent results on lower bounds for conversion problems for regular expressions. In particular we consider the conversion of planar deterministic finite automata to regular expressions, study the effect of the complementation operation on the descriptional complexity of regular expressions, and the conversion of regular expressions extended by adding intersection or interleaving to ordinary regular expressions. Almost all obtained lower bounds are optimal, and the presented examples are over a binary alphabet, which is best possible.

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“…Since there are 2 n binary words of length n, the are 2 n 2 n−1 different subsets of {0, 1} n of size 2 n−1 , and thus P n contains 2 n 2 n−1 pairs, which clearly belongs to 2 2 (n) . Next we show that P n satisfies the conditions of (1) and (2) of the aforementioned result by Glaister and Shallit [1996].…”

Section: Computational Problems For Incomplete Automatamentioning

confidence: 66%

“…Normally large size bounds are easy to obtain for deterministic automata, while NFAs could be exponentially smaller. Here we use techniques from Glaister and Shallit [1996] to show that even the smallest NFAs capturing certain paths in the answer to an RPQ could be doubly exponential, matching the upper bound of Proposition 6.4. THEOREM 6.11.…”

Section: Computational Problems For Incomplete Automatamentioning

confidence: 83%

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Querying Regular Graph Patterns

Barceló

Libkin

Reutter

2014

J. ACM

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Graph data appears in a variety of application domains, and many uses of it, such as querying, matching, and transforming data, naturally result in incompletely specified graph data, that is, graph patterns. While queries need to be posed against such data, techniques for querying patterns are generally lacking, and properties of such queries are not well understood.Our goal is to study the basics of querying graph patterns. The key features of patterns we consider here are node and label variables and edges specified by regular expressions. We provide a classification of patterns, and study standard graph queries on graph patterns. We give precise characterizations of both data and combined complexity for each class of patterns. If complexity is high, we do further analysis of features that lead to intractability, as well as lower-complexity restrictions. Since our patterns are based on regular expressions, query answering for them can be captured by a new automata model. These automata have two modes of acceptance: one captures queries returning nodes, and the other queries returning paths. We study properties of such automata, and the key computational tasks associated with them. Finally, we provide additional restrictions for tractability, and show that some intractable cases can be naturally cast as instances of constraint satisfaction problems.

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A lower bound technique for the size of nondeterministic finite automata

Cited by 106 publications

References 3 publications

Extended Regular Expressions: Succinctness and Decidability

Extended Regular Expressions: Succinctness and Decidability

Tight Bounds on the Descriptional Complexity of Regular Expressions

Querying Regular Graph Patterns

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