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For these models, a nondeterministic algorithm is considered to perform correctly when, for each input, there exists a run that produces the desired result, even when other runs produce incorrect results. This existential power makes nondeterministic algorithms of this sort more efficient than known deterministic algorithms for many problems.
Regular languages are a category of languages (sometimes termed Chomsky Type 3) which can be matched by a state machine (more specifically, by a deterministic finite automaton or a nondeterministic finite automaton) constructed from a regular expression. In particular, a regular language can match constructs like "A follows B", "Either A or B ...
The program keeps on permuting elements while one of them is greater than its successor. This non-deterministic bubble sort is not more efficient than its deterministic version, but easier to prove: it will not stop while the elements are not sorted and that each step it sorts at least 2 elements.
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 input in its domain , and the algorithm is a process that ...
Given a system transforming a set of inputs to output values, described by a mathematical function f, optimization refers to the generation and selection of the best solution from some set of available alternatives, [1] by systematically choosing input values from within an allowed set, computing the value of the function, and recording the best value found during the process.
Another method of choice is reinforcement learning, embodied in systems such as Alisp. [2] In such systems, rather than backtracking, the system keeps track of some measure of success and learns which choices often lead to success, and in which situations (both internal program state and environmental input may affect the choice).
These are called "non-moving" and "moving" (or, alternatively, "non-compacting" and "compacting") garbage collectors, respectively. At first, a moving algorithm may seem inefficient compared to a non-moving one, since much more work would appear to be required on each cycle.
An algorithm solves if for every input such that there exists a satisfying (,), the algorithm produces one such . This is just another way of saying that f {\displaystyle f} is a function and the algorithm solves f ( x ) {\displaystyle f(x)} for all x ∈ Σ ∗ {\displaystyle x\in \Sigma ^{*}} .