Abstract-Conditional Simple Temporal Network (CSTN) is a constraint-based graph-formalism for conditional temporal planning. Three notions of consistency arise for CSTNs and CSTPs: weak, strong, and dynamic. Dynamic-Consistency (DC) is the most interesting notion, but it is also the most challenging. In order to address the DC-Checking problem, in [5] we introduced ε-DC (a refined, more realistic, notion of DC), and provided an algorithmic solution to it. Next, given that DC implies ε-DC for some sufficiently small ε > 0, and that for every ε > 0 it holds that ε-DC implies DC, we offered a sharp lower bounding analysis onthe critical value of the reaction-timeε under which the two notions coincide. This delivered the first (pseudo) singlyexponential time algorithm for the DC-Checking of CSTNs. However, the ε-DC notion is interesting per se, and the ε-DCChecking algorithm in [5] rests on the assumption that the reaction-time satisfies ε > 0; leaving unsolved the question of what happens when ε = 0. In this work, we introduce and study π-DC, a sound notion of DC with an instantaneous reaction-time (i.e., one in which the planner can react to any observation at the same instant of time in which the observation is made). Firstly, we demonstrate by a counter-example that π-DC is not equivalent to 0-DC, and that 0-DC is actually inadequate for modeling DC with an instantaneous reaction-time. This shows that the main results obtained in our previous work do not apply directly, as they were formulated, to the case of ε = 0. Motivated by this observation, as a second contribution, our previous tools are extended in order to handle π-DC, and the notion of ps-tree is introduced, also pointing out a relationship between π-DC and HyTN-Consistency. Thirdly, a simple reduction from π-DC to DC is identified. This allows us to design and to analyze the first sound-and-complete π-DC-Checking procedure. Remarkably, the time complexity of the proposed algorithm remains (pseudo) singly-exponential in the number of propositional letters.
Finally, in REF , it is introduced and studied π-DC, a sound notion of dynamic consistency with an instantaneous reaction time, i.e., one in which the Planner is allowed to react to any observation at the same instant of time in which the observation is made.
Instantaneous Reaction-Time in Dynamic-Consistency Checking of Conditional Simple Temporal Networks
2016 23rd International Symposium on Temporal Representation and Reasoning (TIME)
2016 23rd International Symposium on Temporal Representation and Reasoning (TIME)
Mathematics Computer Science