Gaps, Ambiguity, and Establishing Complexity-Class Containments via Iterative Constant-Setting

09/29/2021
by   Lane A. Hemaspaandra, et al.
0

Cai and Hemachandra used iterative constant-setting to prove that Few ⊆ ⊕P (and thus that FewP ⊆ ⊕P). In this paper, we note that there is a tension between the nondeterministic ambiguity of the class one is seeking to capture, and the density (or, to be more precise, the needed "nongappy"-ness) of the easy-to-find "targets" used in iterative constant-setting. In particular, we show that even less restrictive gap-size upper bounds regarding the targets allow one to capture ambiguity-limited classes. Through a flexible, metatheorem-based approach, we do so for a wide range of classes including the logarithmic-ambiguity version of Valiant's unambiguous nondeterminism class UP. Our work lowers the bar for what advances regarding the existence of infinite, P-printable sets of primes would suffice to show that restricted counting classes based on the primes have the power to accept superconstant-ambiguity analogues of UP. As an application of our work, we prove that the Lenstra-Pomerance-Wagstaff Conjecture implies that all O(loglogn)-ambiguity NP sets are in the restricted counting class RC_PRIMES.

READ FULL TEXT

page 3

page 5

page 7

page 9

page 11

page 17

page 19

page 21

research
03/05/2020

Characterizations and approximability of hard counting classes below #P

An important objective of research in counting complexity is to understa...
research
07/08/2019

Counting and Finding Homomorphisms is Universal for Parameterized Complexity Theory

Counting homomorphisms from a graph H into another graph G is a fundamen...
research
01/09/2014

A logic for reasoning about ambiguity

Standard models of multi-agent modal logic do not capture the fact that ...
research
09/07/2019

On the complexity of counting feedback arc sets

In this note we study the computational complexity of feedback arc set c...
research
09/28/2018

Learning Confidence Sets using Support Vector Machines

The goal of confidence-set learning in the binary classification setting...
research
03/07/2023

Feeling Optimistic? Ambiguity Attitudes for Online Decision Making

As autonomous agents enter complex environments, it becomes more difficu...
research
07/22/2019

Common Belief in Choquet Rationality and Ambiguity Attitudes – Extended Abstract

We consider finite games in strategic form with Choquet expected utility...

Please sign up or login with your details

Forgot password? Click here to reset