Deterministic Algorithm - Problems With Deterministic Algorithms

Problems With Deterministic Algorithms

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.