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strictly computable

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  • Recursion theory — Recursion theory, also called computability theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability… …   Wikipedia

  • Computability theory — For the concept of computability, see Computability. Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown …   Wikipedia

  • Real number — For the real numbers used in descriptive set theory, see Baire space (set theory). For the computing datatype, see Floating point number. A symbol of the set of real numbers …   Wikipedia

  • COMPUTER SCIENCE — The term Computer Science encompasses three different types of research areas: computability, efficiency, and methodology. General Introduction Computability deals with the question of what is mechanically computable. The most natural way to… …   Encyclopedia of Judaism

  • Halting problem — In computability theory, the halting problem can be stated as follows: Given a description of a computer program, decide whether the program finishes running or continues to run forever. This is equivalent to the problem of deciding, given a… …   Wikipedia

  • Machine that always halts — In computability theory, a machine that always halts also called a decider (Sipser, 1996) or a total Turing machine (Kozen, 1997) is a Turing machine that halts for every input. Because it always halts, the machine is able to decide whether a… …   Wikipedia

  • Busy beaver — In computability theory, a busy beaver (from the colloquial expression for an industrious person) is a Turing machine that attains the maximum operational busyness (such as measured by the number of steps performed, or the number of nonblank… …   Wikipedia

  • Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …   Wikipedia

  • Reverse mathematics — is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. The method can briefly be described as going backwards from the theorems to the axioms. This contrasts with the ordinary… …   Wikipedia

  • Digital physics — In physics and cosmology, digital physics is a collection of theoretical perspectives based on the premise that the universe is, at heart, describable by information, and is therefore computable. Therefore, the universe can be conceived as either …   Wikipedia

  • Algorithmically random sequence — Intuitively, an algorithmically random sequence (or random sequence) is an infinite sequence of binary digits that appears random to any algorithm. The definition applies equally well to sequences on any finite set of characters. Random sequences …   Wikipedia

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