## Cem Say ; Abuzer Yakaryilmaz - Finite state verifiers with constant randomness

lmcs:724 - Logical Methods in Computer Science, August 19, 2014, Volume 10, Issue 3 - https://doi.org/10.2168/LMCS-10(3:6)2014
Finite state verifiers with constant randomness

Authors: Cem Say ; Abuzer Yakaryilmaz

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.

Volume: Volume 10, Issue 3
Published on: August 19, 2014
Accepted on: June 25, 2015
Submitted on: October 31, 2012
Keywords: Computer Science - Computational Complexity,Computer Science - Logic in Computer Science