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The strings over an alphabet, with the concatenation operation, form an associative algebraic structure with identity element the null string—a free monoid. Sets of strings with concatenation and alternation form a semiring, with concatenation (*) distributing over alternation (+); 0 is the empty set and 1 the set consisting of just the null ...
Definition: Concat(S1, S2): concatenate two ropes, S 1 and S 2, into a single rope. Time complexity: (or () time to compute the root weight) A concatenation can be performed simply by creating a new root node with left = S1 and right = S2, which is constant time.
The '+' operator is overloaded: it is used for string concatenation and arithmetic addition. This may cause problems when inadvertently mixing strings and numbers. As a unary operator, it can convert a numeric string to a number.
COBOL uses the STRING statement to concatenate string variables. MATLAB and Octave use the syntax "[x y]" to concatenate x and y. Visual Basic and Visual Basic .NET can also use the "+" sign but at the risk of ambiguity if a string representing a number and a number are together. Microsoft Excel allows both "&" and the function "=CONCATENATE(X,Y)".
String homomorphisms are monoid morphisms on the free monoid, preserving the empty string and the binary operation of string concatenation. Given a language , the set () is called the homomorphic image of . The inverse homomorphic image of a string is defined as
If is a set of strings, then is defined as the smallest superset of that contains the empty string and is closed under the string concatenation operation. If V {\\displaystyle V} is a set of symbols or characters, then V ∗ {\\displaystyle V^{*}} is the set of all strings over symbols in V {\\displaystyle V} , including the empty string ε ...
Dejean's theorem (formerly Dejean's conjecture) is a statement about repetitions in infinite strings of symbols. It belongs to the field of combinatorics on words ; it was conjectured in 1972 by Françoise Dejean and proven in 2009 by Currie and Rampersad and, independently, by Rao.
This is an accepted version of this page This is the latest accepted revision, reviewed on 9 December 2024. High-level programming language Not to be confused with Java (programming language), Javanese script, or ECMAScript. JavaScript Screenshot of JavaScript source code Paradigm Multi-paradigm: event-driven, functional, imperative, procedural, object-oriented Designed by Brendan Eich of ...