The Stochastic Arrival Problem

TL;DR

This paper introduces a stochastic variant of the Arrival problem, analyzing its computational complexity and providing algorithms for decision-making involving random and switching nodes.

Contribution

It extends the Arrival problem to include random and switching nodes, establishing complexity results and decision algorithms for these new variants.

Findings

Deciding if the value exceeds half is ext{ extsf{PP}}-hard.

A PSPACE decision algorithm is provided.

The work builds on Reachability Switching Games.

Abstract

We study a new modification of the Arrival problem, which allows for nodes that exhibit random as well as controlled behaviour, in addition to switching nodes. We study the computational complexity of these extensions, building on existing work on Reachability Switching Games. In particular, we show for versions of the arrival problem involving just switching and random nodes it is \PP{}-hard to decide if their value is greater than a half and we give a PSPACE decision algorithm.