## Descriptive Complexity for counting complexity classes

- Marcelo Arenas, Martin Muñoz, Cristian Riveros
- 2017 32nd Annual ACM/IEEE Symposium on Logic in…
- 2017

1 Excerpt

- Published 2006 in Computer Science Review

Given a function based on the computation of an NP machine, can one in general eliminate some solutions? That is, can one in general decrease the ambiguity? This simple question remains, even after extensive study by many researchers over many years, mostly unanswered. However, complexity-theoretic consequences and enabling conditions are known. In this tutorial-style article we look at some of those, focusing on the most natural framings: reducing the number of solutions of NP functions, refining the solutions of NP functions, and subtracting from or otherwise shrinking #P functions. We will see how small advice strings are important here, but we also will see how increasing advice size to achieve robustness is central to the proof of a key ambiguityreduction result for NP functions.

@inproceedings{Faliszewski2006TheCO,
title={The Consequences of Eliminating NP Solutions},
author={Piotr Faliszewski and Lane A. Hemaspaandra},
booktitle={Computer Science Review},
year={2006}
}