Search results
Results from the WOW.Com Content Network
Small weakly universal Turing machines that simulate the Rule 110 cellular automaton have been given for the (6, 2), (3, 3), and (2, 4) state-symbol pairs. [17] The proof of universality for Wolfram's 2-state 3-symbol Turing machine further extends the notion of weak universality by allowing certain non-periodic initial configurations.
An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an entity unspecified by Turing "apart from saying that it cannot be a machine" (Turing (1939), The Undecidable, p. 166–168).
Turing completeness. 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 [citation needed] (devised by English ...
In fact, Turing's machine does this—it prints on alternate squares, leaving blanks between figures so it can print locator symbols. Turing always left alternate squares blank so his machine could place a symbol to the left of a figure (or a letter if the machine is the universal machine and the scanned square is actually in the “program”).
Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus, the topic of this article, is a universal model of computation that can be used to simulate any Turing machine (and vice ...
Theorem 2.2 There exists a Turing machine whose halting problem is recursively unsolvable. A related problem is the printing problem for a simple Turing machine Z with respect to a symbol S i ". A possible precursor to Davis's formulation is Kleene's 1952 statement, which differs only in wording: [19] [22]
A simple generalization is the extension to Turing machines with m symbols instead of just 2 (0 and 1). [10] For example a trinary Turing machine with m = 3 symbols would have the symbols 0, 1, and 2. The generalization to Turing machines with n states and m symbols defines the following generalized busy beaver functions:
Second, digital machinery is "universal". Turing's research into the foundations of computation had proved that a digital computer can, in theory, simulate the behaviour of any other digital machine, given enough memory and time. (This is the essential insight of the Church–Turing thesis and the universal Turing machine.)