Enumeration Complexity of Poor Man's Propositional Dependence Logic

TL;DR

This paper explores the enumeration complexity of propositional dependence logic, presenting algorithms with various delay and space properties, and establishing complexity limitations for general cases.

Contribution

It introduces the first study of enumeration complexity in dependence logics, providing algorithms with polynomial and fixed-parameter tractable delays, and analyzing space constraints.

Findings

Polynomial delay enumeration for polynomial-sized teams

FPT delay in the parametrized team size setting

Existence of polynomial space incremental polynomial delay algorithm

Abstract

Dependence logics are a modern family of logics of independence and dependence which mimic notions of database theory. In this paper, we aim to initiate the study of enumeration complexity in the field of dependence logics and thereby get a new point of view on enumerating answers of database queries. Consequently, as a first step, we investigate the problem of enumerating all satisfying teams of formulas from a given fragment of propositional dependence logic. We distinguish between restricting the team size by arbitrary functions and the parametrised version where the parameter is the team size. We show that a polynomial delay can be reached for polynomials and otherwise in the parametrised setting we reach FPT delay. However, the constructed enumeration algorithm with polynomial delay requires exponential space. We show that an incremental polynomial delay algorithm exists which uses polynomial space only. Negatively, we show that for the general problem without restricting the team size, an enumeration algorithm running in polynomial space cannot exist.