Generalizing prediction models to arbitrary finite alphabets

Develop suitable generalizations of the prediction models used for Boolean Max-CSPs to Max-CSPs defined over arbitrary q-ary alphabets.

Background

The paper’s prediction model is tailored to Boolean Max-CSPs: each variable receives a binary prediction in {−1,+1}, independently matching a fixed optimal assignment with probability 1/2+ε. The algorithms exploit this binary symmetric-noise structure to decode statistics of an optimal assignment through linear estimators and concentration arguments.

The authors explicitly identify as unresolved the development of analogous prediction models for Max-CSPs whose variables take values from arbitrary q-ary alphabets. Such a generalization would extend the learning-augmented streaming framework beyond Boolean domains and would require addressing how noisy multi-valued predictions should be modeled and decoded.