Checking dynamic consistency of conditional hyper temporal networks via mean payoff games: Hardness and (pseudo) singly-exponential time algorithm

Abstract

Conditional Simple Temporal Network (CSTN ) is a constraint-based graph formalism for conditional temporal planning, which may be viewed as an extension of Simple Temporal Networks. Recently, STN s have been generalized into Hyper Temporal Networks (HyTN s), by considering weighted directed hypergraphs where each hyperarc models a disjunctive temporal constraint. We introduce the Conditional Hyper Temporal Network (CHyTN) model, a natural extension and generalization of both CSTN s and HyTN s, obtained by blending them together. We show that deciding whether a given CSTN is dynamically-consistent is coNP-hard, and that deciding whether a given CHyTN is dynamically-consistent is PSPACE-hard. Next, we offer the first deterministic (pseudo) singly-exponential time algorithm for checking DC in CHyTNs and CSTN s. To analyze the computational complexity of the proposed algorithm, we introduce a refined notion of DC, named ϵ-DC, presenting a sharp lower bounding analysis on the critical value of the reaction time where a conditional temporal network transits from being, to not being, dynamically-consistent.