Algorithms are essential to the way computers process data. Typically, when an algorithm is associated with processing information, data can be read from an input source, written to an output device and stored for further processing.Many computer programs contain algorithms that detail the specific instructions a computer should perform (in a specific order) to carry out a specified task, such as calculating employees' paychecks or printing students' report cards. Stored data are regarded as part of the internal state of the entity performing the algorithm.In the 15th century, under the influence of the Greek word ἀριθμός 'number' (cf.

In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension. Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ...

From such uncertainties, that characterize ongoing work, stems the unavailability of a definition of algorithm that suits both concrete (in some sense) and abstract usage of the term. according to Savage [1987], an algorithm is a computational process defined by a Turing machine".

This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name.

In late medieval Latin, algorismus, English 'algorism', the corruption of his name, simply meant the "decimal number system".

But various authors' attempts to define the notion indicate that the word implies much more than this, something on the order of (for the addition example): The concept of algorithm is also used to define the notion of decidability.