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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)".
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 ...
A square-free word is a string that does not contain any square as a substring. In particular, it avoids repeating the same symbol consecutively, repeating the same pair of symbols, etc. Axel Thue showed that there exists an infinite square-free word using a three-symbol alphabet, the sequence of differences between consecutive elements of the ...
For a one-letter alphabet, Leiss [11] discovered the first language equation with a nonregular solution, using complementation and concatenation operations. Later, Jeż [12] showed that non-regular unary languages can be defined by language equations with union, intersection and concatenation, equivalent to conjunctive grammars.
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 ...
A string containing "=" is in L if and only if there is exactly one "=", and it separates two valid strings of L. A string containing "+" but not "=" is in L if and only if every "+" in the string separates two valid strings of L. No string is in L other than those implied by the previous rules.
For function that manipulate strings, modern object-oriented languages, like C# and Java have immutable strings and return a copy (in newly allocated dynamic memory), while others, like C manipulate the original string unless the programmer copies data to a new string. See for example Concatenation below. The most basic example of a string ...
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