Introduction to algorithms
The size-change principle for program termination
POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Weak alternating automata are not that weak
ACM Transactions on Computational Logic (TOCL)
Proceedings of the 12th Colloquium on Automata, Languages and Programming
Program termination analysis in polynomial time
ACM Transactions on Programming Languages and Systems (TOPLAS)
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Complementation, Disambiguation, and Determinization of Büchi Automata Unified
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Büchi Complementation and Size-Change Termination
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
A portfolio approach to algorithm select
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Theories of automata on ω-tapes: A simplified approach
Journal of Computer and System Sciences
Automata-theoretic model checking revisited
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Proceedings of the 14th international SPIN conference on Model checking software
Antichains: a new algorithm for checking universality of finite automata
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
State of büchi complementation
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Advanced Ramsey-based Büchi automata inclusion testing
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
Size-change termination and satisfiability for linear-time temporal logics
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Simulation subsumption in ramsey-based büchi automata universality and inclusion testing
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Improved ramsey-based büchi complementation
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Ramsey-Based analysis of parity automata
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Advanced automata minimization
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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The complementation of Büchi automata, required for checking automata universality, remains one of the outstanding automata-theoretic challenges in formal verification. Early constructions using a Ramsey-based argument have been supplanted by rank-based constructions with exponentially better bounds. The best rank-based algorithm for Büchi universality, by Doyen and Raskin, employs a subsumption technique to minimize the size of the working set. Separately, in the context of program termination, Lee et al. have specialized the Ramsey-based approach to size-change termination (SCT) problems. In this context, Ramsey-based algorithms have proven to be surprisingly competitive. The strongest tool, from Ben-Amram and Lee, also uses a subsumption technique, although only for the special case of SCT problems. We extend the subsumption technique of Ben-Amram and Lee to the general case of Büchi universality problems, and experimentally demonstrate the necessity of subsumption for the scalability of the Ramsey-based approach. We then empirically compare the Ramsey-based tool to the rank-based tool of Doyen and Raskin over a terrain of random Büchi universality problems. We discover that the two algorithms exhibit distinct behavior over this problem terrain. As expected, on many of the most difficult areas the rank-based approach provides the superior tool. Surprisingly, there also exist several areas, including the area most difficult for rank-based tools, on which the Ramsey-based solver scales better than the rank-based solver. This result demonstrates the pitfalls of using worst-case complexity to evaluate algorithms. We suggest that a portfolio approach may be the best approach to checking the universality of Büchi automata.