Randomness is very useful, but normal TMs don\'t have this property. So, let a R
ID: 3816430 • Letter: R
Question
Randomness is very useful, but normal TMs don't have this property. So, let a Random Turing Machine (RTM) be a machine model like a normal TM where each transition has a certain probability of being executed. For a given state, and given tape symbol, there may be several possible transitions that can be executed: but the sum of their probabilities is always 1, and only one of those transitions is executed (and the transition is picked randomly based on the probabilities of the transitions). For example, we could have two transitions from the same state on the same tape symbol read, one with probability 0.7 and the other with 0.3; the first will be executed with 70% probability, and the other with 30%. Of course, if we feed the input to the machine several times, the answer of whether it accepts or not may change each time. We say that a string is accepted by an RTM if there is at least one computation that accepts that string, and the language being the set of all strings that are accepted by the RTM. How do the languages that RTMs recognize compare to that of the standard model? It is not equivalent because the standard model does not have randomness, and we cannot be sure that the machine will accept in this scenario. It is not equivalent because there are some undecidable languages (via normal TMs) that are decidable in this model. It is equivalent because we can simulate the RTM for a long time and it is guaranteed, if the RTM ever accepts the string, that our machine (simulating the RTM) will accept that string. It is equivalent because we can create a TM for all possible choices of each transition being present or absent, and run all machines simultaneously (and we accept if and only if at least one of the machines accepts). There are some languages that are recognized by normal TMs and not by this model, and vice versa.Explanation / Answer
option C.
It is equivalent because we can stimulate the RTM for a long time is guarnteed, if the RTM ecer accepts the string, that our machine simulating the RTM will accept the string
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