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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).
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, [1] as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible.
A machine cannot be the subject of its own thought (or can't be self-aware). A program which can report on its internal states and processes, in the simple sense of a debugger program, can certainly be written. Turing asserts "a machine can undoubtably be its own subject matter." A machine cannot have much diversity of behaviour. He notes that ...
In computability theory, the Church–Turing thesis (also known as computability thesis, [ 1 ] the Turing–Church thesis, [ 2 ] the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a thesis about the nature of computable functions. It states that a function on the natural numbers can be calculated by an ...
An nth busy beaver, BB-n or simply "busy beaver" is a Turing machine that wins the n -state busy beaver game. [ 5 ] Depending on definition, it either attains the highest score, or runs for the longest time, among all other possible n -state competing Turing machines.
e. In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees, unlike a deterministic Turing machine.
The statement that the halting problem cannot be solved by a Turing machine [7] is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate and impossible to solve using a Turing machine. Much of computability theory builds on the halting problem result.
A Turing machine that "solves" a problem is generally meant to mean one that decides the language. Turing machines enable intuitive notions of "time" and "space". The time complexity of a TM on a particular input is the number of elementary steps that the Turing machine takes to reach either an accept or reject state.