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Catmull–Clark surfaces are defined recursively, using the following refinement scheme. [1]Start with a mesh of an arbitrary polyhedron.All the vertices in this mesh shall be called original points.
The only known odd Catalan numbers that do not have last digit 5 are C 0 = 1, C 1 = 1, C 7 = 429, C 31, C 127 and C 255. The odd Catalan numbers, C n for n = 2 k − 1, do not have last digit 5 if n + 1 has a base 5 representation containing 0, 1 and 2 only, except in the least significant place, which could also be a 3. [3]
In computability theory, a set of natural numbers is called computable, recursive, or decidable if there is an algorithm which takes a number as input, terminates after a finite amount of time (possibly depending on the given number) and correctly decides whether the number belongs to the set or not.
Though undecidable languages are not recursive languages, they may be subsets of Turing recognizable languages: i.e., such undecidable languages may be recursively enumerable. Many, if not most, undecidable problems in mathematics can be posed as word problems : determining when two distinct strings of symbols (encoding some mathematical ...
In computer science, corecursion is a type of operation that is dual to recursion.Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case.
The main form of computability studied in the field was introduced by Turing in 1936. [9] A set of natural numbers is said to be a computable set (also called a decidable, recursive, or Turing computable set) if there is a Turing machine that, given a number n, halts with output 1 if n is in the set and halts with output 0 if n is not in
The predicates can be used to obtain Kleene's normal form theorem for computable functions (Soare 1987, p. 15; Kleene 1943, p. 52—53). This states there exists a fixed primitive recursive function such that a function : is computable if and only if there is a number such that for all , …, one has
A recursive operator is an enumeration operator that, when given the graph of a partial recursive function, always returns the graph of a partial recursive function. A fixed point of an enumeration operator Φ is a set F such that Φ(F) = F. The first enumeration theorem shows that fixed points can be effectively obtained if the enumeration ...