Regular Expression Quantifiers - m to n Occurrences

Michał Trybulec

Formalized Mathematics (2007)

  • Volume: 15, Issue: 2, page 53-58
  • ISSN: 1426-2630

Abstract

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This article includes proofs of several facts that are supplemental to the theorems proved in [10]. Next, it builds upon that theory to extend the framework for proving facts about formal languages in general and regular expression operators in particular. In this article, two quantifiers are defined and their properties are shown: m to n occurrences (or the union of a range of powers) and optional occurrence. Although optional occurrence is a special case of the previous operator (0 to 1 occurrences), it is often defined in regex applications as a separate operator - hence its explicit definition and properties in the article. Notation and terminology were taken from [13].

How to cite

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Michał Trybulec. " Regular Expression Quantifiers - m to n Occurrences ." Formalized Mathematics 15.2 (2007): 53-58. <http://eudml.org/doc/267364>.

@article{MichałTrybulec2007,
abstract = {This article includes proofs of several facts that are supplemental to the theorems proved in [10]. Next, it builds upon that theory to extend the framework for proving facts about formal languages in general and regular expression operators in particular. In this article, two quantifiers are defined and their properties are shown: m to n occurrences (or the union of a range of powers) and optional occurrence. Although optional occurrence is a special case of the previous operator (0 to 1 occurrences), it is often defined in regex applications as a separate operator - hence its explicit definition and properties in the article. Notation and terminology were taken from [13].},
author = {Michał Trybulec},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {53-58},
title = { Regular Expression Quantifiers - m to n Occurrences },
url = {http://eudml.org/doc/267364},
volume = {15},
year = {2007},
}

TY - JOUR
AU - Michał Trybulec
TI - Regular Expression Quantifiers - m to n Occurrences
JO - Formalized Mathematics
PY - 2007
VL - 15
IS - 2
SP - 53
EP - 58
AB - This article includes proofs of several facts that are supplemental to the theorems proved in [10]. Next, it builds upon that theory to extend the framework for proving facts about formal languages in general and regular expression operators in particular. In this article, two quantifiers are defined and their properties are shown: m to n occurrences (or the union of a range of powers) and optional occurrence. Although optional occurrence is a special case of the previous operator (0 to 1 occurrences), it is often defined in regex applications as a separate operator - hence its explicit definition and properties in the article. Notation and terminology were taken from [13].
LA - eng
UR - http://eudml.org/doc/267364
ER -

References

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  9. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  10. [2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  11. [3] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  12. [4] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  13. [5] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990. 
  14. [6] Karol Pαk. The Catalan numbers. Part II. Formalized Mathematics, 14(4):153-159, 2006. 

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