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CSTNs is a constraint-based graph-formalism for conditional temporalplanning. In order to address the DC-Checking problem, in [Comin and Rizzi,TIME 2015] we introduced epsilon-DC (a refined, more realistic, notion of DC),and provided an algorithmic solution to it. The epsilon-DC notion isinteresting per se, and the epsilon-DC-Checking algorithm in [Comin and Rizzi,TIME 2015] rests on the assumption that the reaction-time satisfies epsilon >0; leaving unsolved the question of what happens when epsilon = 0. In thiswork, we introduce and study pi-DC, a sound notion of DC with an instantaneousreaction-time (i.e. one in which the planner can react to any observation atthe same instant of time in which the observation is made). Firstly, wedemonstrate by a counter-example that pi-DC is not equivalent to 0-DC, and that0-DC is actually inadequate for modeling DC with an instantaneousreaction-time. This shows that the main results obtained in our previous workdo not apply directly, as they were formulated, to the case of epsilon=0.Motivated by this observation, as a second contribution, our previous tools areextended in order to handle pi-DC, and the notion of ps-tree is introduced,also pointing out a relationship between pi-DC and HyTN-Consistency. Thirdly, asimple reduction from pi-DC-Checking to DC-Checking is identified. This allowsus to design and to analyze the first sound-and-complete pi-DC-Checkingprocedure. Remarkably, the time complexity of the proposed algorithm remains(pseudo) singly-exponential in the number of propositional letters. Finally, itis observed that the technique can be leveraged to actually reduce from pi-DCto 1-DC, this allows us to further improve the exponents in the time complexityof pi-DC-Checking.

Instantaneous Reaction-Time in Dynamic-Consistency Checking of  Conditional Simple Temporal Networks -- Extended version with an Improved  Upper Bound --