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  2. Motion planning - Wikipedia

    en.wikipedia.org/wiki/Motion_planning

    Probabilistic completeness is the property that as more "work" is performed, the probability that the planner fails to find a path, if one exists, asymptotically approaches zero. Several sample-based methods are probabilistically complete. The performance of a probabilistically complete planner is measured by the rate of convergence.

  3. Turing completeness - Wikipedia

    en.wikipedia.org/wiki/Turing_completeness

    In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine [1] [2] (devised by English mathematician and computer scientist Alan Turing).

  4. Completeness (statistics) - Wikipedia

    en.wikipedia.org/wiki/Completeness_(statistics)

    This example will show that, in a sample X 1, X 2 of size 2 from a normal distribution with known variance, the statistic X 1 + X 2 is complete and sufficient. Suppose X 1 , X 2 are independent , identically distributed random variables, normally distributed with expectation θ and variance 1.

  5. Completeness (logic) - Wikipedia

    en.wikipedia.org/wiki/Completeness_(logic)

    Semantic completeness is the converse of soundness for formal systems. A formal system is complete with respect to tautologousness or "semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically valid formulas: formulas that are true under every interpretation of the language of the system ...

  6. Functional completeness - Wikipedia

    en.wikipedia.org/wiki/Functional_completeness

    There are no minimal functionally complete sets of more than three at most binary logical connectives. [11] In order to keep the lists above readable, operators that ignore one or more inputs have been omitted. For example, an operator that ignores the first input and outputs the negation of the second can be replaced by a unary negation.

  7. Halting problem - Wikipedia

    en.wikipedia.org/wiki/Halting_problem

    For example, "halts or fails to halt on input 0" is clearly true of all partial functions, so it is a trivial property, and can be decided by an algorithm that simply reports "true." Also, this theorem holds only for properties of the partial function implemented by the program; Rice's Theorem does not apply to properties of the program itself.

  8. NP-completeness - Wikipedia

    en.wikipedia.org/wiki/NP-completeness

    For example, the independent set and dominating set problems for planar graphs are NP-complete, but can be solved in subexponential time using the planar separator theorem. [13] "Each instance of an NP-complete problem is difficult." Often some instances, or even most instances, may be easy to solve within polynomial time.

  9. Completeness of the real numbers - Wikipedia

    en.wikipedia.org/wiki/Completeness_of_the_real...

    In the decimal number system, completeness is equivalent to the statement that any infinite string of decimal digits is actually a decimal representation for some real number. Depending on the construction of the real numbers used, completeness may take the form of an axiom (the completeness axiom), or may be a theorem proven from the construction.