Business Glossary

adopted by the financial industry for protection of sensitive transaction information, including account balances, bank identification codes (called issuer keys), and consumer account access codes. The DES is a public standard, published by the National Institute of Standards and Technology, and is also known as the Data Encryption Algorithm (DEA), as accepted by the financial industry.

a subject of continuing theoretical study.

Computers can perform only tasks that can be reduced to mechanical procedures (algorithms). They are therefore inapplicable to tasks that cannot or should not be reduced to mechanical form, such as judging the greatness of a work of art or administering psychotherapy. Rather surprisingly, however, there are some tasks that are mathematically precise but that present-day computers cannot perform. These fall into two major types: (1) problems with no known algorithmic solution, and (2) problems whose best known algorithmic solutions require unreasonable amounts of time.

An example of a problem of the first type (one with no presently known algorithmic solution) is how to get a computer to recognize the structures of sentences in a human language such as English.Obviously, this is something computers will have to be able to do if we are ever to be able to communicate with them in English, and there is no reason to think it impossible. The difficulty is simply that English (and all other human languages) are so complicated that complete algorithms for processing them have not yet been discovered.

A good example of the second type of problem, one that takes an unreasonable amount of time to solve, is the so-called traveling salesman problem. The task is to find the shortest route by which a salesman can visit a particular set of cities (in any order). The only known way to solve this problem is to try all possible routes. A few shortcuts are possible-for instance, the testing of each route can be abandoned as soon as its length exceeds the shortest length already found, without pursuing it to the end-but the number of steps is never substantially fewer than N factorial, where N is the number of cities (see factorial). Suppose the fastest imaginable computer could perform one step in this algorithm by moving an electric charge a distance of 1 millimeter at the speed of light. This would mean that it could perform 3 × 10¹¹ steps per second. Then the times required to solve the traveling salesman problem (in N steps) would work out as follows:

And this is with a computer millions of times faster than any that presently exist. Obviously, it will never be feasible to solve the traveling salesman problem for more than a few cities unless a much better algorithm is found.

Another interesting class of computational problems, known as NP-complete problems, has been proved to be equivalent to the traveling salesman problem; if a better algorithm is found for any NP-complete problem, it will be applicable to all of them.

a method of solving problems that involves intelligent trial and error. By contrast, an algorithmic solution method is a clearly specified procedure that is guaranteed to give the correct answer. (See algorithm.) For example, there is no known algorithm that tells how to play a perfect game of chess, so computer chess-playing programs must use a heuristic method of solution, using methods that are likely but not certain to give good results in any particular case.