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Questions tagged [probabilistic-turing-machines]

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Are there any probabilistic models of computation that can strongly simulate themselves?

I was reading this question over on the quantum computation stackexchange, and the top answer stated that you can't (strongly) simulate even a probabilistic turing machine, on itself. I was just ...
Loic Stoic's user avatar
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A synctactic property of the complexity class P

In these lecture notes the authors mentions that P is a syntactic complexity class, as we can find a decidable set of encodings for all polynomial time Turing machines. Of course, given a ...
StefanH's user avatar
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RP with very small error = P

I was asked to show the equality $ RP(1 − 2^{-2^{n}}) = P $, which seems wrong to me (?). The $ \supseteq $ direction is obvious, and I want to show the other direction. My first intuition was to run ...
Xiobiq's user avatar
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If $NP \subseteq BPP$ then $NP = RP$. Confusion on the probability that M gives at least one wrong answer in BPP in n invocations

I was looking at the proof of if $NP \subseteq BPP$ then $NP = RP$ here. At the end of the proof the author states: "Note that if $M$ always gives correct answers on calls to $M$, then when $\phi$...
venturr988's user avatar
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Is NP=RP(2^-n)?

I believe its true but struggle to prove. I know NP=union over positive c's of RP(2^-(n^c)) and from here to prove that RP(1/2^n) contained in NP is immediate. the other side is the problem. I've ...
Tomer Thaler's user avatar
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Relativizations/Oracles for the BPP and RP complexity classes

If we consider the complexity classes RP and BPP, then to show RPBPP = BPPRP my first thought is we need to use some kind of majority voting to amplify our success probabilities. The issue is I don't ...
dino-t's user avatar
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Probabilistic Turing machine - Probability that the head has moved k steps to the right on the work tape

I have a PTM with following transition: $\delta(Z_0, \square , 0) = \delta(Z_0, \square , L, R)$, $\delta(Z_0, \square , 1) = \delta(Z_0, \square , R, R)$ Suppose that this PTM executes n steps. ...
BlueMango's user avatar