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Preview of Symbolic Search Algorithm for Propositional Planning Tasks
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👤 Author: Malte Helmert and Gabriele Röger
⬇️ Downloads: 34

Summary

Planning and Optimization - C7. Symbolic Search: Full Algorithm

This section details the development of a symbolic search algorithm for propositional planning tasks using Bounded Decision Diagrams (BDDs) as a powerful data structure. BDDs offer efficient implementations with libraries like CUDD and libbdd.

Basic BDD Operations:

The core operations are:

- Full Set (⊤), Empty Set (⊥), Atom (v): Representing all assignments, none, and specific variable assignments respectively.
- Union (∪), Intersection (∩), Complement (¬): Performing logical connectives on BDDs.
- Includes (?=), Equals (==): Testing for membership and equality of BDDs.
- Conditioning (T/v, F/v), Forgetting (↔v): Restricting variable values or abstracting away from them.

These operations have defined time complexities based on the number of variables (`k`) and nodes in the BDD (`∥B∥`).

Formulas and Singletons:

- Conversion to BDDs: Formulas can be converted into BDD representations using `bdd-formula(φ)`. This involves applying logical connectives, with a time complexity of O(2n).
- Singleton BDDs: A single truth assignment `I` can be converted to a BDD representing the set `{I}` using `bdd-singleton(I)` in O(k) time.

Renaming:

- Operation: Renames variable `X` to `Y` in formula `φ`, written `φ[X → Y]`. Requires that `Y` is not present in `φ`.
- Complexity: Simple linear-time operation for formulas, O(∥B∥) for BDDs when renaming adjacent variables. General case is O(∥B∥²).

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Description

It covers key aspects of planning, including prelude, foundations, approaches, relaxation methods, abstraction, critical paths, and constraints.

Technical Information

  • File Format: PDF
  • File Size: 196 KB
  • Pages: 12
  • Language: EN
  • Author: Malte Helmert and Gabriele Röger
  • Total Downloads: 34
  • Last Updated: 3 hours ago

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