Comparing State-Representations for DEL Model Checking

2025-11-27

AI Summary

This work addresses the scalability bottleneck of Kripke-model-based model checking for Dynamic Epistemic Logic (DEL). To overcome this limitation, it systematically compares two compact state representations: Binary Decision Diagrams (BDDs) and mental programs. First, it establishes that DEL model checking over BDD-encoded models is PSPACE-complete—yielding the first precise characterization of its computational complexity. Second, it develops a bidirectional formal translation between BDDs and mental programs, and proves that the conversion from mental programs to BDDs incurs an inherent exponential blow-up in representation size—thereby rigorously demonstrating an asymmetry in their expressive power. These results fill a long-standing theoretical gap between the two formalisms, clarify the fundamental trade-off between representational compactness and computational hardness, and provide both a complexity-theoretic benchmark and a principled transformation framework for designing scalable DEL verification tools.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

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

Abstract

Model checking with the standard Kripke models used in (Dynamic) Epistemic Logic leads to scalability issues. Hence alternative representations have been developed, in particular symbolic structures based on Binary Decision Diagrams (BDDs) and succinct models based on mental programs. While symbolic structures have been shown to perform well in practice, their theoretical complexity was not known so far. On the other hand, for succinct models model checking is known to be PSPACE-complete, but no implementations are available. We close this gap and directly relate the two representations. We show that model checking DEL on symbolic structures encoded with BDDs is also PSPACE-complete. In fact, already model checking Epistemic Logic without dynamics is PSPACE-complete on symbolic structures. We also provide direct translations between BDDs and mental programs. Both translations yield exponential outputs. For the translation from mental programs to BDDs we show that no small translation exists. For the other direction we conjecture the same.

Problem

• Analyzes scalability issues in DEL model checking with Kripke models.
• Compares symbolic BDD structures and succinct mental program representations.
• Investigates theoretical complexity and translations between these alternative representations.

Innovation

• Analyzes BDD-based symbolic structures for DEL model checking.
• Proves PSPACE-completeness for symbolic and succinct model checking.
• Provides exponential translations between BDDs and mental programs.