Merge-and-Shrink: Merge Strategies And Label Reduction For Planning And Optimization.pdf

E12. Merge-and-Shrink: Merge Strategies and Label Reduction

This section delves into merge-and-shrink techniques, a powerful approach in planning and optimization for reducing complex systems into more manageable representations. The core idea involves merging similar transition systems while strategically reducing labels to simplify further computations.

Merge Strategies:

Linear vs Non-linear:
Linear: Follows a fixed ordering of variables (e.g., hHHH strategy). Simple but can lead to super-polynomial representation size growth.
Non-linear: Uses dynamic variable selection based on current context (e.g., MIASM, DFP strategies). More complex but allows for more efficient pruning.
Precomputed vs Stateless:
Precomputed: Fixes a merge order upfront, either globally or within components (SCC strategy).
Stateless: Decides merges based solely on current transition systems, allowing for dynamic adaptation (DFP strategy).
Hybrid: Combines elements of precomputed and stateless strategies for balanced performance.

Label Reduction:

Motivations:

1. Elimination of Redundant Labels: Replace pairs of labels with a single, more general label if they represent equivalent actions.
2. Simplification of Bisimulation: Reduce the distinction between similar states by merging labels that correspond to identical transitions.
3. Efficiency: Label reduction streamlines merge and shrink steps, reducing computational time and memory usage.

Key Examples:

MIASM (Maximum Intermediate Abstraction Size Minimizing Merging Strategy): Prioritizes clustering variables with strong interactions for merging while minimizing the size of resulting abstractions.
DFP (Dräger-Finkbeiner-Podelski): Focuses on merging transition systems that synchronize on labels near a goal state, enabling fine-grained abstraction in relevant regions.
SCC (Strongly Connected Component) Strategy: First merges variables within strongly connected components of the causal graph before considering broader merge orders.