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Among the 88 possible unique elementary cellular automata, Rule 110 is the only one for which Turing completeness has been directly proven, although proofs for several similar rules follow as simple corollaries (e.g. Rule 124, which is the horizontal reflection of Rule 110). Rule 110 is arguably the simplest known Turing complete system. [2] [5]
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).
Golly is a cross-platform (Windows, Macintosh, Linux, iOS, and Android) open-source simulation system for the Game of Life and other cellular automata (including all Life-like cellular automata, the Generations family of cellular automata from Mirek's Cellebration, and John von Neumann's 29-state cellular automaton) by Andrew Trevorrow and ...
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 ...
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function. Lambda calculus may be untyped or typed. In typed lambda calculus ...
For more expressive formalisms, this problem can be harder, or even undecidable. For a Turing complete formalism, such as arbitrary formal grammars, not only this problem, but every nontrivial property regarding the set of strings they describe is undecidable, a fact known as Rice's Theorem.
Such a machine is called queue machine and is Turing-complete. Tape memory: The inputs and outputs of automata are often described as input and output tapes. Some machines have additional working tapes, including the Turing machine, linear bounded automaton, and log-space transducer. Transition function
Calculators supporting such programming were Turing-complete if they supported both conditional statements and indirect addressing of memory. Notable examples of Turing complete calculators were Casio FX-602P series, the HP-41 and the TI-59. Keystroke programming is still used in mid-range calculators like the HP 35s and HP-12C.