2004
DOI: 10.1007/978-3-540-28629-5_70
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Complexity of Decision Problems for Simple Regular Expressions

Abstract: Abstract. We study the complexity of the inclusion, equivalence, and intersection problem for simple regular expressions arising in practical XML schemas. These basically consist of the concatenation of factors where each factor is a disjunction of strings possibly extended with ' * ' or '?'. We obtain lower and upper bounds for various fragments of simple regular expressions. Although we show that inclusion and intersection are already intractable for very weak expressions, we also identify some tractable cas… Show more

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Cited by 43 publications
(46 citation statements)
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References 23 publications
(33 reference statements)
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“…This proves that testing query-based restriction for non-recursive DTDs is in EXPTIME. PSPACE-hardness is proved by a simple reduction of containment of regular expressions [11]. Now, we show that if the conditions P 1 and P 2 are satisfied, then from B * we can construct a filter that proves A 1 ↕ …”
mentioning
confidence: 86%
See 1 more Smart Citation
“…This proves that testing query-based restriction for non-recursive DTDs is in EXPTIME. PSPACE-hardness is proved by a simple reduction of containment of regular expressions [11]. Now, we show that if the conditions P 1 and P 2 are satisfied, then from B * we can construct a filter that proves A 1 ↕ …”
mentioning
confidence: 86%
“…We assume the DTD to be unchanged which allows to eliminate the factor of comparing DTDs from our analysis. We recall that testing equivalence and inclusion of DTDs is known to be PSPACE-complete [11]. Also, we use again arbitrary annotations.…”
Section: Static Analysis Of Security Access Specificationsmentioning
confidence: 99%
“…(The problem of AxPRE containment is related to that of regular expression containment [14].) After finding the node, DescribeX proceeds to change α to α, which in fact modifies the description of the node and thus the neighbourhood it summarizes.…”
Section: From Xpath To Axpresmentioning
confidence: 99%
“…The automaton is an extension of the Aho-Corasick [6], the de facto standard for fast keyword scanning. Finding every instance of a regular expression pattern, including overlaps, is a "complex" problem both in space and time [5]. Matching a complete set of regular expressions adds another level of complexity: DotStar employs a novel mechanism for combining several regular expressions into a single engine while keeping the complexity of the problem under control.…”
Section: High-level Protocol Processing With Dotstarmentioning
confidence: 99%