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The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
The problem of bounding the size of an automaton that distinguishes two given strings was first formulated by Goralčík & Koubek (1986), who showed that the automaton size is always sublinear. [2] Later, Robson (1989) proved the upper bound O ( n 2/5 (log n ) 3/5 ) on the automaton size that may be required. [ 3 ]
The word problem for an ARS is determining, given x and y, whether . An object x in A is called reducible if there exists some other y in A such that x → y {\displaystyle x\rightarrow y} ; otherwise it is called irreducible or a normal form .
A simple and inefficient way to see where one string occurs inside another is to check at each index, one by one. First, we see if there is a copy of the needle starting at the first character of the haystack; if not, we look to see if there's a copy of the needle starting at the second character of the haystack, and so forth.
In computer science, the Knuth–Morris–Pratt algorithm (or KMP algorithm) is a string-searching algorithm that searches for occurrences of a "word" W within a main "text string" S by employing the observation that when a mismatch occurs, the word itself embodies sufficient information to determine where the next match could begin, thus bypassing re-examination of previously matched characters.
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Find and replace may refer to: a feature of text processing as found: in text editors; in formal language theory; in particular programming languages;
Algebraic laws for regular expressions can be obtained using a method by Gischer which is best explained along an example: In order to check whether (X+Y) * and (X * Y *) * denote the same regular language, for all regular expressions X, Y, it is necessary and sufficient to check whether the particular regular expressions (a+b) * and (a * b ...