Communicating sequential processes
Communicating sequential processes
On the development of reactive systems
Logics and models of concurrent systems
Model checking
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
Information and Computation - Special issue on FLOC '96
Reasoning about The Past with Two-Way Automata
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Specification and verification of concurrent systems in CESAR
Proceedings of the 5th Colloquium on International Symposium on Programming
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
Logic of Programs, Workshop
The Complexity of the Graded µ-Calculus
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
On the undecidability of logics with converse, nominals, recursion and counting
Artificial Intelligence
Enriched µ-calculi module checking
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
The complexity of enriched µ-calculi
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Pushdown module checking with imperfect information
Information and Computation
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The model checking problem for open systems (called module checking) has been intensively studied in the literature, both for finite-state and infinite-state systems. In this paper, we focus on pushdown module checking with respect to µ-calculus enriched with graded and nominals (hybrid graded µ-calulus). We show that this problem is decidable and solvable in double-exponential time in the size of the formula and in exponential time in the size of the system. This result is obtained by exploiting a classical automata-theoretic approach via pushdown nondeterministic parity tree automata. In particular, we reduce in exponential time our problem to the emptiness problem for these automata, which is known to be decidable in Exptime. As a key step of our algorithm, we show an exponential improvement of the construction of a nondeterministic parity tree automaton accepting all models of a formula of the considered logic. This result, not only allows our algorithm to match the known lower bound, but it is also interesting by itself, since it allows investigating decision problems related to enriched µ-calculus formulas in a greatly simplified manner. We conclude the paper with a discussion on the model checking w.r.t. µ-calculus formulas enriched with backward modalities as well.