TY - GEN

T1 - On pseudodeterministic approximation algorithms

AU - Dixon, Peter

AU - Pavan, A.

AU - Vinodchandran, N. V.

N1 - Publisher Copyright:
© Peter Dixon, A. Pavan, and N. V. Vinodchandran.

PY - 2018/8/1

Y1 - 2018/8/1

N2 - We investigate the notion of pseudodeterminstic approximation algorithms. A randomized approximation algorithm A for a function f is pseudodeterministic if for every input x there is a unique value v so that A(x) outputs v with high probability, and v is a good approximation of f(x). We show that designing a pseudodeterministic version of Stockmeyer’s well known approximation algorithm for the NP-membership counting problem will yield a new circuit lower bound: if such an approximation algorithm exists, then for every k, there is a language in the complexity class ZPPNP tt that does not have nk-size circuits. While we do not know how to design such an algorithm for the NP-membership counting problem, we show a general result that any randomized approximation algorithm for a counting problem can be transformed to an approximation algorithm that has a constant number of influential random bits. That is, for most settings of these influential bits, the approximation algorithm will be pseudodeterministic.

AB - We investigate the notion of pseudodeterminstic approximation algorithms. A randomized approximation algorithm A for a function f is pseudodeterministic if for every input x there is a unique value v so that A(x) outputs v with high probability, and v is a good approximation of f(x). We show that designing a pseudodeterministic version of Stockmeyer’s well known approximation algorithm for the NP-membership counting problem will yield a new circuit lower bound: if such an approximation algorithm exists, then for every k, there is a language in the complexity class ZPPNP tt that does not have nk-size circuits. While we do not know how to design such an algorithm for the NP-membership counting problem, we show a general result that any randomized approximation algorithm for a counting problem can be transformed to an approximation algorithm that has a constant number of influential random bits. That is, for most settings of these influential bits, the approximation algorithm will be pseudodeterministic.

KW - Approximation algorithms

KW - Circuit lower bounds

KW - Pseudodeterminism

UR - http://www.scopus.com/inward/record.url?scp=85053200420&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.MFCS.2018.61

DO - 10.4230/LIPIcs.MFCS.2018.61

M3 - Conference contribution

AN - SCOPUS:85053200420

SN - 9783959770866

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018

A2 - Potapov, Igor

A2 - Worrell, James

A2 - Spirakis, Paul

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018

Y2 - 27 August 2018 through 31 August 2018

ER -