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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).
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 the 1980s, Stephen Wolfram engaged in a systematic study of one-dimensional cellular automata, or what he calls elementary cellular automata; his research assistant Matthew Cook showed that one of these rules is Turing-complete. The primary classifications of cellular automata, as outlined by Wolfram, are numbered one to four.
Counter machines with two counters are Turing complete: they can simulate any appropriately-encoded Turing machine, but there are some simple functions that they cannot compute. Counter machines with only a single counter can recognize a proper superset of the regular languages and a subset of the deterministic context free languages .
The great majority of naturally occurring oscillators have a period of 2, like the blinker and the toad, but oscillators of all periods are known to exist, [28] [29] [30] and oscillators of periods 4, 8, 14, 15, 30, and a few others have been seen to arise from random initial conditions. [31]
Several recalls were issued in 2024 for Ford Motor Company vehicles.. The recall report data is from Jan. 1, 2024, to Dec. 27, 2024. The U.S. Department of Transportation (DOT) compiles data from ...
Turing College is an online platform for professionals to enhance their tech skills. Offering self-paced, flexible programs, this platform allows learners to study under the direct supervision of ...
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