In computer science, a deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they can be run on real machines efficiently.
Formally, a deterministic algorithm computes a mathematical function; a function has a unique value for any given input, and the algorithm is a process that produces this particular value as output.
Deterministic algorithms can be defined in terms of a state machine: a state describes what a machine is doing at a particular instant in time. State machines pass in a discrete manner from one state to another. Just after we enter the input, the machine is in its initial state or start state. If the machine is deterministic, this means that from this point onwards, its current state determines what its next state will be; its course through the set of states is predetermined. Note that a machine can be deterministic and still never stop or finish, and therefore fail to deliver a result.
A variety of factors can cause an algorithm to behave in a way which is not deterministic, or non-deterministic:
Although real programs are rarely purely deterministic, it is easier for humans as well as other programs to reason about programs that are. For this reason, most programming languages and especially functional programming languages make an effort to prevent the above events from happening except under controlled conditions.
The prevalence of multi-core processors has resulted in a surge of interest in determinism in parallel programming and challenges of non-determinism have been well documented. A number of tools to help deal with the challenges have been proposed to deal with deadlocks and race conditions.
Unfortunately, for some problems deterministic algorithms are also hard to find. For example, there are simple and efficient probabilistic algorithms that determine whether a given number is prime and have a very small chance of being wrong. These have been known since the 1970s (see for example Fermat primality test); the known deterministic algorithms remain considerably slower in practice.
As another example, NP-complete problems, which include many of the most important practical problems, can be solved quickly using a machine called a nondeterministic Turing machine, but efficient practical algorithms have never been found for any of them. At best, we can currently only find approximate solutions or solutions in special cases.
Another major problem with deterministic algorithms is that sometimes, we don't want the results to be predictable. For example, if you are playing an on-line game of blackjack that shuffles its deck using a pseudorandom number generator, a clever gambler might guess precisely the numbers the generator will choose and so determine the entire contents of the deck ahead of time, allowing him to cheat; for example, the Software Security Group at Reliable Software Technologies was able to do this for an implementation of Texas Hold 'em Poker that is distributed by ASF Software, Inc, allowing them to consistently predict the outcome of hands ahead of time. Similar problems arise in cryptography, where private keys are often generated using such a generator. This sort of problem is generally avoided using a cryptographically secure pseudo-random number generator.
Exception throwing is a usual mechanism to signal failure due to unexpected/undesired states.
(* Standard ML *) datatype 'a option = NONE | SOME of 'a (* OCaml *) type 'a option = None | Some of 'a
-- Haskell data Maybe a = Nothing | Just a
data Either errorType resultType = Right resultType | Left errorType
As Monads model sequential composition, the Left zero property (z * s = z) in a monad means that the right side of the sequence will not be evaluated.
-- Left zero in the Maybe monad Nothing >> k = Nothing Nothing >>= f = Nothing -- Left zero in the Either monad Left err >> k = Left err Left err >>= f = Left err
Haskell provides several mechanisms:
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