DeepAI AI Chat
Log In Sign Up

Inapproximability of Unique Games in Fixed-Point Logic with Counting

by   Jamie Tucker-Foltz, et al.

We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). We prove two new FPC-inexpressibility results for Unique Games: the existence of a (1/2, 1/3 + delta)-inapproximability gap, and inapproximability to within any constant factor. Previous recent work has established similar FPC-inapproximability results for a small handful of other problems. Our construction builds upon some of these ideas, but contains a novel technique. While most FPC-inexpressibility results are based on variants of the CFI-construction, ours is significantly different.


page 1

page 2

page 3

page 4


Approximating Constraint Satisfaction Problems Symmetrically

This thesis investigates the extent to which the optimal value of a cons...

Reasoning about Social Choice and Games in Monadic Fixed-Point Logic

Whether it be in normal form games, or in fair allocations, or in voter ...

Separating LREC from LFP

LREC= is an extension of first-order logic with a logarithmic recursion ...

Temporal Constraint Satisfaction Problems in Fixed-Point Logic

Finite-domain constraint satisfaction problems are either solvable by Da...

Strong Parallel Repetition for Unique Games on Small Set Expanders

Strong Parallel Repetition for Unique Games on Small Set Expanders The...

On stability of users equilibria in heterogeneous routing games

The asymptotic behaviour of deterministic logit dynamics in heterogeneou...

On Pitts' Relational Properties of Domains

Andrew Pitts' framework of relational properties of domains is a powerfu...