Concepts inDeterministic regular expressions in linear time
Regular expression
In computing, a regular expression provides a concise and flexible means to "match" (specify and recognize) strings of text, such as particular characters, words, or patterns of characters. Common abbreviations for "regular expression" include regex and regexp. The concept of regular expressions was first popularized by utilities provided by Unix distributions, in particular the editor ed and the filter grep.
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Concatenation
In computer programming, string concatenation is the operation of joining two character strings end-to-end. For example, the strings "snow" and "ball" may be concatenated to give "snowball". In many programming languages, string concatenation is a binary infix operator. For example, the following expression uses the "+" symbol as the concatenation operator to join 2 strings:, and has the value "Hello, World".
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Parse tree
A concrete syntax tree or parse tree or parsing tree is an ordered, rooted tree that represents the syntactic structure of a string according to some formal grammar. Parse trees are usually constructed according to one of two competing relations, either in terms of the constituency relation of constituency grammars or in terms of the dependency relation of dependency grammars.
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Star-free language
A regular language is said to be star-free if it can be described by a regular expression constructed from the letters of the alphabet, the empty set symbol, all boolean operators – including complementation – and concatenation but no Kleene star. For instance, the language of words over the alphabet that do not have consecutive a's can be defined by, where denotes the complement of a subset of .
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Union (set theory)
In set theory, the union (denoted as ∪) of a collection of sets is the set of all distinct elements in the collection. The union of a collection of sets gives a set .
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Bracket
Brackets are tall punctuation marks used in matched pairs within text, to set apart or interject other text. Used unqualified, brackets refer to different types of brackets in different parts of the world and in different contexts.
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XML Schema (W3C)
XML Schema, published as a W3C recommendation in May 2001, is one of several XML schema languages. It was the first separate schema language for XML to achieve Recommendation status by the W3C.
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Time complexity
In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using big O notation, which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described asymptotically, i.e. , as the input size goes to infinity.
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