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The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
One important drawback for applications of the solution of the classical secretary problem is that the number of applicants must be known in advance, which is rarely the case. One way to overcome this problem is to suppose that the number of applicants is a random variable N {\displaystyle N} with a known distribution of P ( N = k ) k = 1 , 2 ...
Rice's theorem puts a theoretical bound on which types of static analysis can be performed automatically. One can distinguish between the syntax of a program, and its semantics . The syntax is the detail of how the program is written, or its "intention", and the semantics is how the program behaves when run, or its "extension".
There are several basic elements that can be built into every problem statement. The problem statement should focus on the end user, and the statement should not be too broad or narrow. [7] Problem statements usually follow a format. While there are several options, the following is a template often used in business analysis.
The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. The problem can be used to simulate every other problem for which we can verify quickly that a solution is correct.
A general reduction from problem to problem is a transformation that guarantees that whenever has a solution also has at least one solution and vice versa. A parsimonious reduction guarantees that for every solution of A {\displaystyle A} , there exists a unique solution of B {\displaystyle B} and vice versa.
The term "problem structuring methods" as a label for these techniques began to be used in the 1980s in the field of operations research, [8] especially after the publication of the book Rational Analysis for a Problematic World: Problem Structuring Methods for Complexity, Uncertainty and Conflict. [9]
To find all solutions, one simply makes a note and continues, rather than ending the process, when a solution is found, until all solutions have been tried. To find the best solution, one finds all solutions by the method just described and then comparatively evaluates them based upon some predefined set of criteria, the existence of which is a ...