The instructions in the algorithm describe a calculation. When it is running, it can start from an initial state and an initial input (which may be empty), go through a series of limited and clearly defined states, and finally produce an output and stop at a final state. The transition from one state to another is not necessarily certain. Some algorithms, including randomization algorithms, contain some random inputs.
The concept of formal algorithm stems in part from trying to solve the decision-making problem put forward by Hilbert, and then trying to define effective computability or effective method. These attempts include recursive functions proposed by Kurt G?del, Jacques Herbrand and Stephen Cole Kleene at 1930, 1934 and 1935 respectively, λ calculus proposed by Allonzot Church at 1936, and formulas proposed by Emil Leon Post at 1936. Even at present, it is usually difficult to define intuitive ideas as formal algorithms.