On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Languages, automata, and logic
Handbook of formal languages, vol. 3
Pushdown processes: games and model-checking
Information and Computation - Special issue on FLOC '96
Information and Computation - Special issue on FLOC '96
Proceedings of the 8th European software engineering conference held jointly with 9th ACM SIGSOFT international symposium on Foundations of software engineering
Alternating-time temporal logic
Journal of the ACM (JACM)
Bebop: A Symbolic Model Checker for Boolean Programs
Proceedings of the 7th International SPIN Workshop on SPIN Model Checking and Software Verification
Symbolic Strategy Synthesis for Games on Pushdown Graphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Reachability Analysis of Pushdown Automata: Application to Model-Checking
CONCUR '97 Proceedings of the 8th International Conference on Concurrency Theory
A Decidable Class of Asynchronous Distributed Controllers
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
Infinite Games and Verification (Extended Abstract of a Tutorial)
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Interface Compatibility Checking for Software Modules
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Distributed reactive systems are hard to synthesize
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Analysis of recursive state machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Recursive markov decision processes and recursive stochastic games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Repair of boolean programs with an application to c
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Secure programming via visibly pushdown safety games
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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In this paper, we focus on solving games in recursive game graphs that can model the control flow in sequential programs with recursive procedure calls. While such games can be viewed as the pushdown games studied in the literature, the natural notion of winning in our framework requires the strategies to be modular with only local memory; that is, resolution of choices within a module does not depend on the context in which the module is invoked, but only on the history within the current invocation of the module. While reachability in (global) push-down games is known to be EXPTIME-complete, we show reachability in modular games to be NP-complete. We present a fixpoint computation algorithm for solving modular games such that the worst-case number of iterations is exponential in the total number of returned values from the modules. If the strategy within a module does not depend on the global history, but can remember the history of the past invocations of this module, that is, if memory is local but persistent, we show that reachability becomes undecidable.