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

05/04/2015
by   Carlo Comin, et al.
0

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 combinatorial games on 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 analyze 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 ε̂ where the CSTN transits from being, to not being, dynamically-consistent. The proof technique introduced in this analysis of ε̂ is applicable more in general when dealing with linear difference constraints which include strict inequalities.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/10/2012

The Dynamic Controllability of Conditional STNs with Uncertainty

Recent attempts to automate business processes and medical-treatment pro...
research
04/07/2023

Optimal Reads-From Consistency Checking for C11-Style Memory Models

Over the years, several memory models have been proposed to capture the ...
research
03/13/2015

Hyper Temporal Networks

Simple Temporal Networks (STNs) provide a powerful and general tool for ...
research
04/18/2023

Connectivity in the presence of an opponent

The paper introduces two player connectivity games played on finite bipa...
research
07/17/2013

Model checking coalitional games in shortage resource scenarios

Verification of multi-agents systems (MAS) has been recently studied tak...
research
07/19/2019

Provenance Analysis for Logic and Games

A model checking computation checks whether a given logical sentence is ...
research
01/08/2019

Complexity Bounds for the Controllability of Temporal Networks with Conditions, Disjunctions, and Uncertainty

In temporal planning, many different temporal network formalisms are use...

Please sign up or login with your details

Forgot password? Click here to reset