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A Universal Turing machine is a machine that can simulate any Turing machine i.e An algorithm that can simulate any algorithm. Intuitively it may seem that this algorithm that can simulate any other algorithm must be really complex BUT it turns out that this algorithm is really the dumbest algorithm possible.
A Turing machine can be compared to a program. It takes some input and generates some output. A UTM can be compared to a computer. It can take any program and run it with some input and generates some output. The UTM is a Turing machine in itself, so the interesting idea here is that any Turing machine can be encoded as input understood by ...
4. I am trying to understand Rogozhin's (2, 18) universal turing machine by stepping through a simple 2-tag encoding that I believe should loop forever: a -> aa. For example, using an initial input of aaa: aaa. aaa. aaa. .... etc. Apologies for the extremely specific question, but it's what I've narrowed my issue down to and I've been stuck for ...
16. You're right that physical computers have finite memory and so are not Turing-complete. There are other ways in which computability theory is not a good model for computing - it doesn't take into account time and memory constraints. Complexity theory was invented (perhaps) as a more realistic depiction of computing, but IMHO suffers from ...
Oblivious Universal Turing Machine in O(T log(T)) time. Ask Question Asked 8 years, 3 months ago.
Other descriptions of universal Turing machines I've seen online use a more expansive alphabet, so that the machine can use a special character to mark where it needs to return when it is has completed doing something else. How would a Turing machine which only uses '0's and '1's for both input and output do its bookkeeping?
notice that the Turing machine basically has the same "architecture," esp the universal computer, which can run programs stored on the tape. the state table and tape head functions somewhat like the CPU (in this analogy the ALU would be a subset of all TM states that control arithmetic logic) and the tape as memory. of course many early real ...
A Turing machine is a finite state machine plus a tape memory. Each transition may be accompanied by an operation on the tape (move, read, write). I have understood from it that a turing machine uses/has a a finite state machine as part of its operating procedure, plus adding some editable memory to it.
Jun 23, 2018 at 19:39. 1. The UTM is only necessary because Turing machines have separate code and data (described in totally different ways). If you want arbitrary computations to be describable by a single input to the machine, you have to invent an encoding for programs and write a new program that interprets it.
$\begingroup$ Is that true? a general Turing machine's move function is $(q,a)\rightarrow (q',a',d)$ which can be encoded as $01^q01^a01^{q'}01^{a'}01^d0$. However, to encode an Universal Turing machine you need to specific its move function first, and then to encode its move functions to binary string. $\endgroup$ –