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Controller Synthesis for Timeline-based Games

Renato Acampora, Luca Geatti, Nicola Gigante, Angelo Montanari, Valentino Picotti

TL;DR

This paper provides an effective and computationally optimal approach to controller synthesis for timeline-based games by providing an effective and computationally optimal approach to controller synthesis for timeline-based games.

Abstract

In the timeline-based approach to planning, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling temporal uncertainty. In order to handle general nondeterminism as well, the concept of timeline-based games has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is 2EXPTIME-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, by providing an effective and computationally optimal approach to controller synthesis for timeline-based games.

Controller Synthesis for Timeline-based Games

TL;DR

This paper provides an effective and computationally optimal approach to controller synthesis for timeline-based games by providing an effective and computationally optimal approach to controller synthesis for timeline-based games.

Abstract

In the timeline-based approach to planning, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling temporal uncertainty. In order to handle general nondeterminism as well, the concept of timeline-based games has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is 2EXPTIME-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, by providing an effective and computationally optimal approach to controller synthesis for timeline-based games.
Paper Structure (16 sections, 11 theorems, 13 equations, 4 figures)

This paper contains 16 sections, 11 theorems, 13 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related work
  3. Preliminaries
  4. Timeline-based planning
  5. Timeline-based games.
  6. Synthesis
  7. Difference Bound Matrices
  8. A deterministic automaton for timeline-based planning
  9. Plans as words
  10. Matching structures
  11. Building the automaton
  12. Soundness and Completeness
  13. Controller synthesis
  14. From the automaton to the arena
  15. Computing the Winning Strategy and Building the Controller
  16. ...and 1 more sections

Key Result

Theorem 4.6

Let $P=(\mathsf{SV}\xspace, S)$ be a timeline-based planning problem and let $\mathsf{A}\xspace_P$ be the associated automaton. Then, the size of $A_P$ is at most doubly-exponential in the size of $P$.

Figures (4)

  • Figure 1: The constraint system of \ref{['eq:example-3var-synch']}.
  • Figure 2: DBM of \ref{['eq:example-3var-synch']}. Missing entries are intended to be $+\infty$.
  • Figure 3: Example of timelines for variables $x_0, \, x_1, \, x_2, \, x_3$.
  • Figure 4: On the left, the removal of transitions ${\mu}\xspace=(A,\delta)$ with $\delta>1$ and ending actions of controllable tokens in $A$. On the right, the transformation of a transition of $A_G$ into a sequence of transitions in $A^a_G$, with $x\in\mathsf{SV}\xspace_C$, $y\in\mathsf{SV}\xspace_E$, and $\gamma_x(v_1)=\gamma_y(w_1)=\mathsf{u}$.

Theorems & Definitions (44)

  • Definition 3.1: State variable
  • Definition 3.2
  • Definition 3.3: Event sequence GiganteMOCR20
  • Definition 3.4: Atom
  • Definition 3.5: Synchronization rule
  • Definition 3.6: Matching functions Gigante19
  • Definition 3.7: Semantics of synchronization rules
  • Definition 3.8: Timeline-based planning problem
  • Definition 3.9: Timeline-based game
  • Definition 3.10: Partition of player actions
  • ...and 34 more