Conditional Simple Temporal Networks Research Articles

Faster Dynamic-Consistency Checking for Conditional Simple Temporal Networks

A Conditional Simple Temporal Network (CSTN) is a structure for representing and reasoning about time in domains where temporal constraints may be conditioned on outcomes of observations made in real time. A CSTN is dynamically consistent (DC) if there is a strategy for executing its time-points such that all relevant constraints will necessarily be satisfied no matter which outcomes happen to be observed. The literature on CSTNs contains only one sound-and-complete DC-checking algorithm that has been implemented and empirically evaluated. It is a graph-based algorithm that propagates labeled constraints/edges. A second algorithm has been proposed, but not evaluated. It aims to speed up DC checking by more efficiently dealing with so-called negative q-loops.This paper presents a new two-phase approach to DC-checking for CSTNs. The first phase focuses on identifying negative q-loops and labeling key time-points within them. The second phase focuses on computing (labeled) distances from each time-point to a single sink node. The new algorithm, which is also sound and complete for DC-checking, is then empirically evaluated against both pre-existing algorithms and shown to be much faster across not only previously published benchmark problems, but also a new set of benchmark problems. The results show that, on DC instances, the new algorithm tends to be an order of magnitude faster than both existing algorithms. On all other benchmark cases, the new algorithm performs better than or equivalently to the existing algorithms.

Instantaneous reaction-time in dynamic consistency checking of conditional simple temporal networks

Conditional Simple Temporal Networks (CSTNs) is a constraint based graph-formalism for conditional temporal planning. Three notions of consistency arise for CSTNs: 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, Comin and Rizzi [12] introduced ε-DC (a refined, more realistic, notion of DC), providing 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, it was offered a sharp lower bounding analysis on the critical value of the reaction-timeεˆ under which the two notions coincide. This delivered the first (pseudo) singly-exponential time algorithm for the DC-Checking of CSTNs. However, the ε-DC notion is interesting per se, and the ε-DC-Checking algorithm of Comin and Rizzi [12] 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 consistency of Hyper Temporal Networks. Thirdly, a simple reduction from π-DC to (classical) DC is identified. This allows us to design and to analyze the first sound-and-complete π-DC-Checking algorithm. Remarkably, the time complexity of the proposed algorithm remains (pseudo) singly-exponential in the number of propositional letters. Finally, it is observed that the technique can be leveraged to actually reduce from π-DC to 1-DC, this allows us to further improve the exponents in the time complexity.

Conditional Simple Temporal Networks with Uncertainty and Resources

Conditional simple temporal networks with uncertainty (CSTNUs) allow for the representation of temporal plans subject to both conditional constraints and uncertain durations. Dynamic controllability (DC) of CSTNUs ensures the existence of an execution strategy able to execute the network in real time (i.e., scheduling the time points under control) depending on how these two uncontrollable parts behave. However, CSTNUs do not deal with resources. In this paper, we define conditional simple temporal networks with uncertainty and resources (CSTNURs) by injecting resources and runtime resource constraints (RRCs) into the specification. Resources are mandatory for executing the time points and their availability is represented through temporal expressions, whereas RRCs restrict resource availability by further temporal constraints among resources.
 We provide a fully-automated encoding to translate any CSTNUR into an equivalent timed game automaton in polynomial time for a sound and complete DC-checking.

Conditional simple temporal networks with uncertainty and decisions

A Conditional Simple Temporal Network with Uncertainty (CSTNU) is a formalism able to model temporal plans subject to both conditional constraints and uncertain durations. The combination of these two characteristics represents the uncontrollable part of the network. That is, before the network starts executing, we do not know completely which time points and constraints will be taken into consideration nor how long the uncertain durations will last. Dynamic Controllability (DC) implies the existence of a strategy scheduling the time points of the network in real time depending on how the uncontrollable part behaves. Despite all this, CSTNUs fail to model temporal plans in which a few conditional constraints are under control and may therefore influence (or be influenced by) the uncontrollable part. To bridge this gap, this paper proposes Conditional Simple Temporal Networks with Uncertainty and Decisions (CSTNUDs) which introduce decision time points into the specification in order to operate on this conditional part under control. We model the dynamic controllability checking (DC-checking) of a CSTNUD as a two-player game in which each player makes his moves in his turn at a specific time instant. We give an encoding into timed game automata for a sound and complete DC-checking. We also synthesize memoryless execution strategies for CSTNUDs proved to be DC and carry out an experimental evaluation with ▪, a tool that we have designed for CSTNUDs to make the approach fully automated.