Intermediate Results on the Complexity of STRIPS$_{1}^{1}$

2026-02-09

AI Summary

This study investigates whether propositional STRIPS planning with exactly one precondition and one effect per action (denoted STRIPS$_1^1$) is NP-complete. To address this question, the authors introduce a novel modeling approach that integrates literal graphs with Petri nets to formally represent STRIPS$_1^1$ instances. Leveraging this framework, they conduct empirical analyses on small-scale problems using SAT solvers. Their findings provide both theoretical insights and experimental evidence supporting the “small solution hypothesis” for STRIPS$_1^1$, suggesting that solutions—if they exist—can be represented compactly. Crucially, this work offers compelling evidence toward establishing the NP-completeness of STRIPS$_1^1$, thereby advancing the understanding of the computational complexity inherent in this restricted yet fundamental class of planning problems.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

This paper is based on Bylander's results on the computational complexity of propositional STRIPS planning. He showed that when only ground literals are permitted, determining plan existence is PSPACE-complete even if operators are limited to two preconditions and two postconditions. While NP-hardness is settled, it is unknown whether propositional STRIPS with operators that only have one precondition and one effect is NP-complete. We shed light on the question whether this small solution hypothesis for STRIPS$^1_1$ is true, calling a SAT solver for small instances, introducing the literal graph, and mapping it to Petri nets.

Problem

• STRIPS
• computational complexity
• NP-completeness
• planning
• propositional logic

Innovation

• STRIPS planning
• computational complexity
• literal graph
• Petri nets
• SAT solver