Computer Algorithm

In computer systems, an algorithm is basically an instance of logic written in software by software developers to be effective for the intended "target" computer(s), in order for the software on the target machines to do something. For instance, if a person is writing software that is supposed to print out a PDF document located at the operating system folder "/My Documents" at computer drive "D:" every Friday at 10PM, they will write an algorithm that specifies the following actions: "If today's date (computer time) is 'Friday,' open the document at 'D:/My Documents' and call the 'print' function". While this simple algorithm does not look into whether the printer has enough paper or whether the document has been moved into a different location, one can make this algorithm more robust and anticipate these problems by rewriting it as a formal CASE statement or as a (carefully crafted) sequence of IF-THEN-ELSE statements^[15]. For example the CASE statement might appear as follows (there are other possibilities):

CASE 1: IF today's date is NOT Friday THEN exit this CASE instruction ELSE

CASE 2: IF today's date is Friday AND the document is located at 'D:/My Documents' AND there is paper in the printer THEN print the document (and exit this CASE instruction) ELSE

CASE 3: IF today's date is Friday AND the document is NOT located at 'D:/My Documents' THEN display 'document not found' error message (and exit this CASE instruction) ELSE

CASE 4: IF today's date is Friday AND the document is located at 'D:/My Documents' AND there is NO paper in the printer THEN (i) display 'out of paper' error message and (ii) exit.

Note that CASE 3 includes two possibilities: (i) the document is NOT located at 'D:/My Documents' AND there's paper in the printer OR (ii) the document is NOT located at 'D:/My Documents' AND there's paper in the printer.

The sequence of IF-THEN-ELSE tests might look like this:

TEST 1: IF today's date is NOT Friday THEN done ELSE TEST 2:

TEST 2: IF the document is NOT located at 'D:/My Documents' THEN display 'document not found' error message ELSE TEST 3:

TEST 3: IF there is NO paper in the printer THEN display 'out of paper' error message ELSE print the document.

These examples' logic grants precedence to the instance of "NO document at 'D:/My Documents' ". Also observe that in a well-crafted CASE statement or sequence of IF-THEN-ELSE statements the number of distinct actions -- 4 in these examples: do nothing, print the document, display 'document not found', display 'out of paper' -- equals the number of cases.

Because a computational machine equipped with unbounded memory and the ability to execute CASE statements or a sequence of IF-THEN-ELSE statements together with just a few other instructions is Turing complete, anything that is computable will be computable by this machine. Thus this form of algorithm is fundamental to computer programming in all its forms (see more at McCarthy formalism).