Dynamic Consistency of Conditional Simple Temporal Networks via Mean Payoff Games: A Singly-Exponential Time DC-checking

Conditional Simple Temporal Network (CSTN) is a constraint-based graph-formalism for conditional temporal planning. It offers a more flexible formalism than the equivalent CSTP model of Tsamardinos, Vidal and Pollack, from which it was derived mainly as a sound formalization. Three notions of consis...

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Bibliographic Details
Published in:Proceedings - International Workshop on Temporal Representation and Reasoning pp. 19 - 28
Main Authors: Comin, Carlo, Rizzi, Romeo
Format: Conference Proceeding
Language:English
Published: IEEE 04.01.2016
Subjects:
Algorithm design and analysis
Computational modeling
Conditional Simple Temporal Networks
Dynamic Consistency
Games
Heuristic algorithms
Hyper Temporal Networks
Mean Payoff Games
Planning
Reaction Time Analysis
Singly-Exponential Time
Terminology
Timing
ISSN:1530-1311
Online Access:Get full text
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Summary:Conditional Simple Temporal Network (CSTN) is a constraint-based graph-formalism for conditional temporal planning. It offers a more flexible formalism than the equivalent CSTP model of Tsamardinos, Vidal and Pollack, from which it was derived mainly as a sound formalization. Three notions of consistency arise for CSTNs and CSTPs: weak, strong, and dynamic. Dynamic consistency is the most interesting notion, but it is also the most challenging and it was conjectured to be hard to assess. Tsamardinos, Vidal and Pollack gave a doubly-exponential time algorithm for deciding whether a CSTN is dynamically-consistent and to produce, in the positive case, a dynamic execution strategy of exponential size. In the present work we offer a proof that deciding whether a CSTN is dynamically-consistent is coNP-hard and provide the first singly-exponential time algorithm for this problem, also producing a dynamic execution strategy whenever the input CSTN is dynamically-consistent. The algorithm is based on a novel connection with Mean Payoff Games, a family of two-player infinite games played on finite graphs, well known for having applications in model-checking and formal verification. The presentation of such connection is mediated by the Hyper Temporal Network model, a tractable generalization of Simple Temporal Networks whose consistency checking is equivalent to determining Mean Payoff Games. In order to analyse the algorithm we introduce a refined notion of dynamic-consistency, named ε-dynamic-consistency, and present a sharp lower bounding analysis on the critical value of the reaction time where the CSTN transits from being, to not being, dynamically-consistent. The proof technique introduced in this analysis of the reaction time is applicable more generally when dealing with linear difference constraints which include strict inequalities.
ISSN:1530-1311
DOI:10.1109/TIME.2015.18