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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 related but different uniform word problem for a class of recursively presented groups is the algorithmic problem of deciding, given as input a presentation for a group in the class and two words in the generators of , whether the words represent the same element of .
Word problem (mathematics education), a type of textbook exercise or exam question to have students apply abstract mathematical concepts to real-world situations; Word problem (mathematics), a decision problem for algebraic identities in mathematics and computer science; Word problem for groups, the problem of recognizing the identity element ...
In C and C++, volatile is a type qualifier, like const, and is a part of a type (e.g. the type of a variable or field). The behavior of the volatile keyword in C and C++ is sometimes given in terms of suppressing optimizations of an optimizing compiler: 1- don't remove existing volatile reads and writes, 2- don't add new volatile reads and writes, and 3- don't reorder volatile reads and writes.
For example, the word "encyclopedia" is a sequence of symbols in the English alphabet, a finite set of twenty-six letters. Since a word can be described as a sequence, other basic mathematical descriptions can be applied. The alphabet is a set, so as one would expect, the empty set is a subset. In other words, there exists a unique word of ...
The basic variadic facility in C++ is largely identical to that in C. The only difference is in the syntax, where the comma before the ellipsis can be omitted. C++ allows variadic functions without named parameters but provides no way to access those arguments since va_start requires the name of the last fixed argument of the function.
For proving bounds on this problem, it may be assumed without loss of generality that the inputs are strings over a two-letter alphabet. For, if two strings over a larger alphabet differ then there exists a string homomorphism that maps them to binary strings of the same length that also differ. Any automaton that distinguishes the binary ...
Marsaglia's add-with-carry and subtract-with-borrow PRNGs with a word size of b=2 w and lags r and s (r > s) are equivalent to LCGs with a modulus of b r ± b s ± 1. [ 37 ] [ 38 ] Multiply-with-carry PRNGs with a multiplier of a are equivalent to LCGs with a large prime modulus of ab r −1 and a power-of-2 multiplier b .