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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
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)".
In terminated strings, the terminating code is not an allowable character in any string. Strings with length field do not have this limitation and can also store arbitrary binary data. An example of a null-terminated string stored in a 10-byte buffer, along with its ASCII (or more modern UTF-8) representation as 8-bit hexadecimal numbers is:
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 ...
rfind(string,substring) returns integer Description Returns the position of the start of the last occurrence of substring in string. If the substring is not found most of these routines return an invalid index value – -1 where indexes are 0-based, 0 where they are 1-based – or some value to be interpreted as Boolean FALSE. Related instr
Definition: Split (i, S): split the string S into two new strings S 1 and S 2, S 1 = C 1, ..., C i and S 2 = C i + 1, ..., C m. Time complexity: () There are two cases that must be dealt with: The split point is at the end of a string (i.e. after the last character of a leaf node) The split point is in the middle of a string.
Certain operations on languages are common. This includes the standard set operations, such as union, intersection, and complement. Another class of operation is the element-wise application of string operations. Examples: suppose and are languages over some common alphabet .
String search, in O(m) complexity, where m is the length of the sub-string (but with initial O(n) time required to build the suffix tree for the string) Finding the longest repeated substring Finding the longest common substring