Turing Definition and 57 Threads

Okay, so if I have a turing machine so called M, is there a configuration alpha s beta which yields a configuration with state q? If it's decidable can someone explain the algorithm to proceed?

Complement of Universal Turing Machine - Does this exist?? I am kind of confused in terms of the creation of machine which does NOT (Universal Turing Machine). I mean I construct a TM which will simulate UTM and accept strings it rejects and rejects strings it accepts. So if L(UTM) defined as...

This may be a bit vague, as I don't remember all the details. When proving Turing's halting problem, at some point you will say something along the lines of, "given a list of all Turing Machines, assume that there exists a Turing Machine M which decides whether machine A halts on input B". The...

Homework Statement A two-dimensional Turing machine has the usual finite-state control but a tape that is a two-dimensional grid of cells, infinite in all directions. The input is placed on one row of the grid, with the head at the left end of the input and the control in the start state, as...

How can one readily determine that the reality one experiences is real, not virtual - perhaps through Turing machine logic?

This was a bonus problem that I missed on the last homework. A paper tape Turing machine (PTM) is a Turing machine whose tape alphabet is partially ordered, and if a is a symbol on a square of the tape, then b can only be written on that square if b is greater than a in the partial order...

Sorry if this is a wrong place to post this. What does it mean that a turing machine M recognize language A? Does it mean that A={w|M accepts w}? Is so then how does M accept w? Does it accept w if it ends in accept state?