A Parameterized View on the Complexity of Dependence Logic

TL;DR

This paper analyzes the parameterized complexity of model checking in Dependence Logic, identifying tractable and intractable cases based on various parameters, and explores complexity in different variants of the problem.

Contribution

It provides a comprehensive classification of the parameterized complexity of model checking in Dependence Logic, considering multiple parameters and variants.

Findings

Identifies parameters leading to tractable and intractable cases.

Provides complexity classifications for data and expression variants.

Offers a detailed complexity landscape for Dependence Logic model checking.

Abstract

In this paper, we investigate the parameterized complexity of model checking for Dependence Logic which is a well studied logic in the area of Team Semantics. We start with a list of nine immediate parameterizations for this problem, namely: the number of disjunctions (i.e., splits)/(free) variables/universal quantifiers, formula-size, the tree-width of the Gaifman graph of the input structure, the size of the universe/team, and the arity of dependence atoms. We present a comprehensive picture of the parameterized complexity of model checking and obtain a division of the problem into tractable and various intractable degrees. Furthermore, we also consider the complexity of the most important variants (data and expression complexity) of the model checking problem by fixing parts of the input.