密集时间域上基于时间线的规划的复杂性:探索中间地带

CoRR Pub Date : 2018-09-07 DOI:10.4204/EPTCS.277.14
L. Bozzelli, A. Molinari, A. Montanari, A. Peron
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引用次数: 5

摘要

在本文中,我们解决了密集时间域上基于时间线的规划的复杂性问题。规划问题通过一组独立但相互作用的组件来建模,每个组件由许多状态变量表示,这些状态变量随时间(时间线)的行为由一组时间约束(同步规则)控制。虽然时域通常被认为是离散的,但这里我们考虑密集的情况。密集的基于时间线的规划最近被证明在一般情况下是不可确定的;可判定性(np完备性)可以通过限制为纯存在同步规则(无触发规则)来恢复。在本文中,我们研究了这两个极端之间的中间案例的未开发区域。我们首先证明了可判定性和非原语递归硬度可以通过承认具有触发器的同步规则来证明,但强制它们仅在将来对触发器(未来简单规则)进行适当的检查约束。通过在将来的简单规则中额外约束区间的形式,可以获得更“易于处理”的结果:EXPSPACE-completeness通过避免奇异区间来保证,PSPACE-completeness通过只允许形式为[0,a]和[b, $\infty$]的区间来保证。
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Complexity of Timeline-Based Planning over Dense Temporal Domains: Exploring the Middle Ground
In this paper, we address complexity issues for timeline-based planning over dense temporal domains. The planning problem is modeled by means of a set of independent, but interacting, components, each one represented by a number of state variables, whose behavior over time (timelines) is governed by a set of temporal constraints (synchronization rules). While the temporal domain is usually assumed to be discrete, here we consider the dense case. Dense timeline-based planning has been recently shown to be undecidable in the general case; decidability (NP-completeness) can be recovered by restricting to purely existential synchronization rules (trigger-less rules). In this paper, we investigate the unexplored area of intermediate cases in between these two extremes. We first show that decidability and non-primitive recursive-hardness can be proved by admitting synchronization rules with a trigger, but forcing them to suitably check constraints only in the future with respect to the trigger (future simple rules). More "tractable" results can be obtained by additionally constraining the form of intervals in future simple rules: EXPSPACE-completeness is guaranteed by avoiding singular intervals, PSPACE-completeness by admitting only intervals of the forms [0,a] and [b,$\infty$[.
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