Specification and Abstraction

Specification and Abstraction A problem is specified by given input data, desired output data and a relation between the input and the output data. An algorithm starts execution with the input data, executes the statements, and finishes execution with the output data. When it finishes execution, the specified relation between the input data and the output data should be satisfied. Only then has the algorithm solved the given problem. G Polya was a Hungarian mathematician. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education, identifying systematic methods of problem solving to further discovery and invention in mathematics for students and teachers. In "How to Solve It", he suggests the following steps when solving a mathematical problem: . Understand the problem. . Devise a plan. . Carry out the plan. . Review your work. An algorithm is a step by step sequence of statements intended to solve a problem. When executed with input data, it generates a computational process, and ends with output data, satisfying the specified relation between the input data and the output data.