Finite state verifiers with constant randomness

Cem Say; Abuzer Yakaryilmaz

doi:10.2168/lmcs-10(3:6)2014

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arXiv · 1102.2719

Finite state verifiers with constant randomness

Cem Say·Abuzer Yakaryilmaz

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Abstract

We give a new characterization of $\mathsf{NL}$ as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as opposed to its conventional description in terms of deterministic logarithmic-space verifiers. It turns out that allowing two-way interaction with the prover does not change the class of verifiable languages, and that no polynomially bounded amount of randomness is useful for constant-memory computers when used as language recognizers, or public-coin verifiers. A corollary of our main result is that the class of outcome problems corresponding to O(log n)-space bounded games of incomplete information where the universal player is allowed a constant number of moves equals NL.

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BibTeX RIS

Cem Say, Abuzer Yakaryilmaz. 2011-02-14. Finite state verifiers with constant randomness. https://doi.org/10.2168/lmcs-10(3:6)2014

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