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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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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Abstract 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.
AbstractList 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.
Author Rizzi, Romeo
Comin, Carlo
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  givenname: Romeo
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  email: romeo.rizzi@univr.it
  organization: Dept. of Comput. Sci., Univ. of Verona, Verona, Italy
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Snippet Conditional Simple Temporal Network (CSTN) is a constraint-based graph-formalism for conditional temporal planning. It offers a more flexible formalism than...
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StartPage 19
SubjectTerms 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
Title Dynamic Consistency of Conditional Simple Temporal Networks via Mean Payoff Games: A Singly-Exponential Time DC-checking
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