Dynamic Complexity of Parity Games with Bounded Tree-Width

TL;DR

This paper investigates how the complexity of maintaining solutions to parity games on graphs with bounded tree-width can be efficiently managed under dynamic updates, showing it is feasible within DynFO with LOGSPACE precomputation.

Contribution

The authors demonstrate that the dynamic complexity of two-player parity games on bounded tree-width graphs is in DynFO, using a reduction to a Dyck-path problem on an acyclic automaton.

Findings

Parity games with bounded tree-width are in DynFO under dynamic updates.

The problem can be reduced to a Dyck-path problem on an acyclic automaton.

Dynamic updates include edge modifications and state property changes.

Abstract

Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of two-player parity games over graphs of bounded tree-width, where updates may add or delete edges, or change the owner or color of states. We show that this problem is in DynFO (with LOGSPACE precomputation); this is achieved by a reduction to a Dyck-path problem on an acyclic automaton.