The Origin and Definition of The Term "Algorithm"

No agreed-to definition of "algorithm" exists. A simple definition: A set of instructions for solving a problem. The algorithm is either implemented by a program or simulated by a program. Algorithms often have steps that iterate (repeat ) or require decisions such as logic or comparison. An very simple example of an algorithm is multiplying two numbers: on first computers with limited processors, this was accomplished by a routine that in a number of loop based on the first number adds the second number. The algorithm translates a method into computer commands.

Algorithms are essential to the way computers process information, because a computer program is essentially an algorithm that tells the computer what specific steps to perform (in what specific order) in order to carry out a specified task, such as calculating employees' paychecks or printing students' report cards. Thus, an algorithm can be considered to be any sequence of operations which can be performed by a Turing-complete system. Authors who assert this thesis include Savage (1987) and Gurevich (2000): "...Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine" ...according to Savage [1987], an algorithm is a computational process defined by a Turing machine." Typically, when an algorithm is associated with processing information, data is read from an input source or device, written to an output sink or device, and/or stored for further processing.

Stored data is regarded as part of the internal state of the entity performing the algorithm. In practice, the state is stored in a data structure. For any such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable). Because an algorithm is a precise list of precise steps, the order of computation will almost always be critical to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting 'from the top' and going 'down to the bottom', an idea that is described more formally by flow of control. So far, this discussion of the formalization of an algorithm has assumed the premises of imperative programming. This is the most common conception, and it attempts to describe a task in discrete, 'mechanical' means.

Unique to this conception of formalized algorithms is the assignment operation, setting the value of a variable. It derives from the intuition of 'memory' as a scratchpad. For some alternate conceptions of what constitutes an algorithm see functional programming and logic programming. The origin of the term comes from the ancients. The concept becomes more precise with the use of variables in mathematics. Algorithm in the sense of what is now used by computers appeared as soon as first mechanical engines were invented.