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Cook proved that Rule 110 was universal (or Turing complete) by showing it was possible to use the rule to emulate another computational model, the cyclic tag system, which is known to be universal. He first isolated a number of spaceships , self-perpetuating localized patterns, that could be constructed on an infinitely repeating pattern in a ...
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).
A Turing degree is an equivalence class of the relation ≡ T. The notation [X] denotes the equivalence class containing a set X. The entire collection of Turing degrees is denoted . The Turing degrees have a partial order ≤ defined so that [X] ≤ [Y] if and only if X ≤ T Y. There is a unique Turing degree containing all the computable ...
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine. The problem is to determine, given a program and an input to the program, whether ...
Turing complete set, a related notion from recursion theory; Completeness (knowledge bases), found in knowledge base theory; Complete search algorithm, a search algorithm that is guaranteed to find a solution if there is one; Incomplete database, a compact representation of a set of possible worlds
Extra-sensory perception: In 1950, extra-sensory perception was an active area of research and Turing chooses to give ESP the benefit of the doubt, arguing that conditions could be created in which mind-reading would not affect the test. Turing admitted to "overwhelming statistical evidence" for telepathy, likely referring to early 1940s ...
Arithmetic-based Turing-complete machines use an arithmetic operation and a conditional jump. Like the two previous universal computers, this class is also Turing-complete. The instruction operates on integers which may also be addresses in memory. Currently there are several known OISCs of this class, based on different arithmetic operations:
The concept of NP-completeness was developed in the late 1960s and early 1970s in parallel by researchers in North America and the Soviet Union.In 1971, Stephen Cook published his paper "The complexity of theorem proving procedures" [2] in conference proceedings of the newly founded ACM Symposium on Theory of Computing.