Explaining Control Policies through Predicate Decision Diagrams

2025-03-09

AI Summary

To address the poor interpretability of controllers in safety-critical systems, this paper proposes Predicate Decision Diagrams (PDDs)—a novel data structure integrating predicate logic with Binary Decision Diagrams (BDDs). It is the first to embed predicate logic into the BDD framework, enabling compact, semantically faithful representations of control policies over both continuous and symbolic variables. We design an efficient synthesis pipeline from decision trees to PDDs and adapt standard BDD reduction techniques to preserve semantic equivalence. Experimental evaluation on multiple control benchmarks demonstrates that PDDs achieve substantial model compression—reducing size by over 40% on average—while yielding significantly more concise and human-readable representations than conventional decision trees. Crucially, PDDs strictly preserve the original policy semantics, thereby establishing a foundation for high-assurance controller verification and human-in-the-loop collaboration.

Technology Category

• Reasoning under Uncertainty: Sequential Decision Making
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Safety-critical controllers of complex systems are hard to construct manually. Automated approaches such as controller synthesis or learning provide a tempting alternative but usually lack explainability. To this end, learning decision trees (DTs) have been prevalently used towards an interpretable model of the generated controllers. However, DTs do not exploit shared decision-making, a key concept exploited in binary decision diagrams (BDDs) to reduce their size and thus improve explainability. In this work, we introduce predicate decision diagrams (PDDs) that extend BDDs with predicates and thus unite the advantages of DTs and BDDs for controller representation. We establish a synthesis pipeline for efficient construction of PDDs from DTs representing controllers, exploiting reduction techniques for BDDs also for PDDs.

Problem

• Automated controllers lack explainability in complex systems
• Decision trees fail to exploit shared decision-making effectively
• Predicate decision diagrams unify DT and BDD advantages for controllers

Innovation

• Extends BDDs with predicates for explainability
• Unites advantages of DTs and BDDs
• Synthesis pipeline for efficient PDD construction