Unambiguity of extended regular expressions in SGML document grammars

Brüggemann-Klein, Anne

doi:10.1007/3-540-57273-2_45

Cited by 19 publications

(18 citation statements)

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“…(See, e.g., (Brüggemann-Klein, 1993b). More commonly, Follow relations are used for defining and constructing automata for expressions; see, e.g., (Brüggemann-Klein, 1993a) and (Aho, 1994, Sec.…”

Section: Numeric Regular Expressions and Determinismmentioning

confidence: 99%

Checking determinism of XML Schema content models in optimal time

Kilpeläinen

2011

Information Systems

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Section: Numeric Regular Expressions and Determinismmentioning

confidence: 99%

Checking determinism of XML Schema content models in optimal time

Kilpeläinen

2011

Information Systems

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“…The rst question has been answered for standard regular expressions BK92b, BK92a] and for model groups BK93a,BK93b]. This paper answers the second question for standard regular expressions.…”

Section: Discussionmentioning

confidence: 75%

One-Unambiguous Regular Languages

Brüggemann-KleinAnne¹,

WoodDerick²

1998

Information and Computation

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The ISO standard for the Standard Generalized Markup Language (SGML) provides a syntactic metalanguage for the de nition of textual markup systems. In the standard, the right-hand sides of productions are based on regular expressions; although only expressions that denote words unambiguously are allowed. In general, the fact that a word is denoted by an expression is witnessed by a sequence of occurrences of symbols in the expression that matches the word. In an unambiguous expression as de ned by Book, Even, Greibach, and Ott, each word has at most one witness. But the SGML standard also requires that a witness can be computed incrementally from the word with a one-symbol lookahead; we call such expressions 1-unambiguous. A regular language is 1-unambiguous if it is denoted by some 1-unambiguous expression. We give a Kleene theorem for 1-unambiguous languages and characterize them in terms of structural properties of the minimal deterministic automata that recognize them. This result enables us to decide whether a given regular expression denotes a 1-unambiguous language; if it does, then we can construct an equivalent 1-unambiguous expression in worst-case optimal time.

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“…until no further replacements can be made anymore. For instance, the sequence normal form of aa?a [2,5] a?bb?b?b [1,7] is a [3,8]b [2,10]. Obviously, the above algorithm to compute the sequence normal form of CHARE(a, a?, a#) expressions can be implemented in polynomial time.…”

Section: K};mentioning

confidence: 99%

“…A second reason is that, in contrast to conventional regular expressions, one-unambiguity is not yet fully understood for regular expressions with numerical occurrence constraints and interleaving operators. Some initial results are provided by Bruggemann-Klein [5], and Kilpeläinen and Tuhkanen [22] who give algorithms for deciding one-unambiguity of RE(&) and RE(#) expressions, respectively. However, the results of Bruggemann-Klein are on the SGML interleaving operator, which is not the same as the Relax NG interleaving operator considered here.…”

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confidence: 99%

Optimizing Schema Languages for XML: Numerical Constraints and Interleaving

Gelade¹,

Martens²,

Neven³

2009

SIAM J. Comput.

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The presence of a schema offers many advantages in processing, translating, querying, and storage of XML data. Basic decision problems like equivalence, inclusion, and non-emptiness of intersection of schemas form the basic building blocks for schema optimization and integration, and algorithms for static analysis of transformations. It is thereby paramount to establish the exact complexity of these problems. Most common schema languages for XML can be adequately modeled by some kind of grammar with regular expressions at right-hand sides. In this paper, we observe that apart from the usual regular operators of union, concatenation and Kleene-star, schema languages also allow numerical occurrence constraints and interleaving operators. Although the expressiveness of these operators remain within the regular languages, their presence or absence has significant impact on the complexity of the basic decision problems. We present a complete overview of the complexity of the basic decision problems for DTDs, XSDs and Relax NG with regular expressions incorporating numerical occurrence constraints and interleaving. We also discuss chain regular expressions and the complexity of the schema simplification problem incorporating the new operators.

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Unambiguity of extended regular expressions in SGML document grammars

Cited by 19 publications

References 3 publications

Checking determinism of XML Schema content models in optimal time

Checking determinism of XML Schema content models in optimal time

One-Unambiguous Regular Languages

Optimizing Schema Languages for XML: Numerical Constraints and Interleaving

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