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With regard to what actions the machine actually does, Turing (1936) [2] states the following: "This [example] table (and all succeeding tables of the same kind) is to be understood to mean that for a configuration described in the first two columns the operations in the third column are carried out successively, and the machine then goes over into the m-configuration in the final column."
As an example, an abstract base class MathSymbol may provide a pure virtual function doOperation(), and derived classes Plus and Minus implement doOperation() to provide concrete implementations. Implementing doOperation() would not make sense in the MathSymbol class, as MathSymbol is an abstract concept whose behaviour is defined solely for ...
Nested functions can be used for unstructured control flow, by using the return statement for general unstructured control flow.This can be used for finer-grained control than is possible with other built-in features of the language – for example, it can allow early termination of a for loop if break is not available, or early termination of a nested for loop if a multi-level break or ...
In calculus, an example of a higher-order function is the differential operator /, which returns the derivative of a function . Higher-order functions are closely related to first-class functions in that higher-order functions and first-class functions both allow functions as arguments and results of other functions.
A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater than 1); the ...
The terminology advanced and retarded is especially useful when the variable x corresponds to time. In such cases, the solution provided by the use of the retarded Green's function depends only on the past sources and is causal whereas the solution provided by the use of the advanced Green's function depends only on the future sources and is ...
This makes it one of the most efficient algorithms for recognizing general context-free languages in practice. Valiant (1975) gave an extension of the CYK algorithm. His algorithm computes the same parsing table as the CYK algorithm; yet he showed that algorithms for efficient multiplication of matrices with 0-1-entries can be utilized for ...
It turns out that the Weierstrass function is far from being an isolated example: although it is "pathological", it is also "typical" of continuous functions: In a topological sense: the set of nowhere-differentiable real-valued functions on [0, 1] is comeager in the vector space C ([0, 1]; R ) of all continuous real-valued functions on [0, 1 ...