A Fragment of Dependence Logic Capturing Polynomial Time

TL;DR

This paper introduces a fragment of dependence logic called D-Horn* that precisely captures the class P over finite successor structures, linking logical expressiveness with polynomial time complexity.

Contribution

It defines D-Horn* and proves it characterizes polynomial time problems, extending the understanding of dependence logic's computational capabilities.

Findings

Horn-formulae in dependence logic can express NP-complete problems.

D-Horn* captures exactly the class P over finite successor structures.

Results suggest potential generalizations to open formulae and monotone properties.

Abstract

In this paper we study the expressive power of Horn-formulae in dependence logic and show that they can express NP-complete problems. Therefore we define an even smaller fragment D-Horn* and show that over finite successor structures it captures the complexity class P of all sets decidable in polynomial time. Furthermore we study the question which of our results can ge generalized to the case of open formulae of D-Horn* and so-called downwards monotone polynomial time properties of teams.