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Probabilistic and Frequency Finite-State Transducers

This paper investigates Las Vegas transducers, which guarantee correct outputs with a non-zero probability of false answers, proving that if any Las Vegas transducer can compute a relation with a success probability over ½, a deterministic transducer can also compute it. We further analyze deterministic transducers augmented with help symbols and contrast them with Las Vegas transducers, demonstrating their comparative capabilities. Lastly, we define frequency transducers and discuss how they compute relations across multiple input and output tapes.

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Probabilistic and Frequency Finite-State Transducers

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  1. Probabilistic and Frequency Finite-StateTransducers Kaspars Balodis Anda Berina Gleb Borovitsky Rusins Freivalds Ginta Garkaje Vladimirs Kacs Janis Kalejs Ilja Kucevalovs Janis Rocans Madars Virza

  2. Probabilistic transducers • We explore so-called Las Vegas transducers, which give a false answer with probability 0, • and prove theorems, such as if any Las Vegas transducer can compute a relation with probability greater than ½, then this relation can be computed with a deterministic transducer.

  3. Deterministic transducers with help symbols • We observe deterministic transducers where one or more added help symbols are viewable at any time during the computation of a relation, • and compare these with Las Vegas transducers, proving that, for example, if you need n help symbols to compute a relation, a Las Vegas transducer can compute this relation with probability 1/n,

  4. Frequency transducers • A frequency transducer is a transducer, which has n input tapes with unique inputs and n output tapes, that (m,n)-calculates a relation on all the tapes in a way, that at least m out of the n output tapes produce a correct result.

  5. Thank you for your attention

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