In transition from global to modular temporal reasoning about programs
Logics and models of concurrent systems
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On the power of bounded concurrency I: finite automata
Journal of the ACM (JACM)
Abstract interpretation of reactive systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
Complexity of equivalence problems for concurrent systems of finite agents
Information and Computation
Model checking
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
Model checking of hierarchical state machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
On the complexity of verifying concurrent transition systems
Information and Computation
Modal Transition Systems: A Foundation for Three-Valued Program Analysis
ESOP '01 Proceedings of the 10th European Symposium on Programming Languages and Systems
Communicating Hierarchical State Machines
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Analysis of Recursive State Machines
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Automatic Abstraction Using Generalized Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Analysis of recursive state machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Verification of scope-dependent hierarchical state machines
Information and Computation
Taming Concurrency: A Program Verification Perspective
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Program Complexity in Hierarchical Module Checking
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Fixpoint logics on hierarchical structures
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
On-the-Fly reachability and cycle detection for recursive state machines
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Synthesis of hierarchical systems
Science of Computer Programming
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We present a unified game-based approach for branching-time model checking of hierarchical systems. Such systems are exponentially more succinct than standard state-transition graphs, as repeated sub-systems are described only once. Early work on model checking of hierarchical systems shows that one can do better than a naive algorithm that “flattens” the system and removes the hierarchy. Given a hierarchical system $\mathcal S$ and a branching-time specification ψ for it, we reduce the model-checking problem (does $\mathcal S$ satisfy ψ?) to the problem of solving a hierarchical game obtained by taking the product of $\mathcal S$ with an alternating tree automaton ${\mathcal A}_\psi$ for ψ. Our approach leads to clean, uniform, and improved model-checking algorithms for a variety of branching-time temporal logics. In particular, by improving the algorithm for solving hierarchical parity games, we are able to solve the model-checking problem for the μ-calculus in Pspace and time complexity that is only polynomial in the depth of the hierarchy. Our approach also leads to an abstraction-refinement paradigm for hierarchical systems. The abstraction maintains the hierarchy, and is obtained by merging both states and sub-systems into abstract states.