Probabilistic Turing machine: Difference between revisions

Revision as of 09:09, 2 April 2020

Revision as of 09:10, 2 April 2020

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{{turing}}

In [[theoretical computer science]], a '''probabilistic Turing machine''' is a [[non-deterministic Turing machine]] that chooses between the available transitions at each point according to some [[probability distribution]]. As a consequence, a probabilistic Turing machine can (unlikecan—unlike a deterministic Turing Machine) haveMachine—have [[stochastic]] results; that is, on a given input and instruction state machine, it may have different run times, or it may not halt at all; furthermore, it may accept an input in one execution and reject the same input in another execution.

In the case of equal probabilities for the transitions, it can be defined as a deterministic [[Turing machine]] having an additional "write" instruction where the value of the write is [[uniform distribution (discrete)|uniformly distributed]] in the Turing Machine's alphabet (generally, an equal likelihood of writing a '1' or a '0' on to the tape.) Another common reformulation is simply a [[deterministic Turing machine]] with an added tape full of random bits called the ''random tape''.