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Register a new userComplexity of Timeline-Based Planning over Dense Temporal Domains: Exploring the Middle Ground
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Publication date
2018
fields
Informatics Engineering
and research's language is
English
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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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Planning is one of the most studied problems in computer science. In this paper, we consider the timeline-based approach, where the domain is modeled by a set of independent, but interacting, components, identified by a set of state variables, whose behavior over time (timelines) is governed by a set of temporal constraints (synchronization rules). Timeline-based planning in the dense-time setting has been recently shown to be undecidable in the general case, and undecidability relies on the high expressiveness of the trigger synchronization rules. In this paper, we strengthen the previous negative result by showing that undecidability already holds under the future semantics of the trigger rules which limits the comparison to temporal contexts in the future with respect to the trigger.
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