Abstract
We establish the precise complexity of the model checking problem for the main logics of knowledge and time. While this problem was known to be non-elementary for agents with perfect recall, with a number of exponentials that increases with the alternation of knowledge operators, the precise complexity of the problem when the maximum alternation is fixed has been an open problem for twenty years. We close it by establishing improved upper bounds for CTL* with knowledge, and providing matching lower bounds that also apply for epistemic extensions of LTL and CTL.
Keywords
- Knowledge Representation and Reasoning: Reasoning about Knowlege and Belief
- Knowledge Representation and Reasoning: Computational Complexity of Reasoning
- Agent-based and Multi-agent Systems: Formal Verification, Validation and Synthesis
- Knowledge Representation and Reasoning: Non-classical Logics for Knowledge Representation
