Alternating automata, the weak monadic theory of the tree, and its complexity
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Alternating automata on infinite trees
Theoretical Computer Science
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Reasoning about infinite computations
Information and Computation
Checking that finite state concurrent programs satisfy their linear specification
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
Model Checking of Safety Properties
Formal Methods in System Design
Nontraditional Applications of Automata Theory
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
CONCUR '00 Proceedings of the 11th International Conference on Concurrency Theory
Optimal Bounds for Transformations of omega-Automata
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
State Space Reductions for Alternating Büchi Automata
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Improved Automata Generation for Linear Temporal Logic
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
Efficient Büchi Automata from LTL Formulae
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Fast LTL to Büchi Automata Translation
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Fair Simulation Relations, Parity Games, and State Space Reduction for Büchi Automata
SIAM Journal on Computing
A Practical Introduction to PSL (Series on Integrated Circuits and Systems)
A Practical Introduction to PSL (Series on Integrated Circuits and Systems)
An Antichain Algorithm for LTL Realizability
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
From LTL to symbolically represented deterministic automata
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Lower bounds for complementation of ω-automata via the full automata technique
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Complementation constructions for nondeterministic automata on infinite words
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
The quest for a tight translation of büchi to co-büchi automata
Fields of logic and computation
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
The blow-up in translating LTL to deterministic automata
MoChArt'10 Proceedings of the 6th international conference on Model checking and artificial intelligence
Translating to Co-Büchi Made Tight, Unified, and Useful
ACM Transactions on Computational Logic (TOCL)
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Alternating automata play a key role in the automata-theoretic approach to specification, verification, and synthesis of reactive systems. Many algorithms on alternating automata, and in particular, their nonemptiness test, involve removal of alternation: a translation of the alternating automaton to an equivalent nondeterministic one. For alternating Büchi automata, the best known translation uses the "breakpoint construction" and involves an O(3n) state blowup. The translation was described by Miyano and Hayashi in 1984, and is widely used since, in both theory and practice. Yet, the best known lower bound is only 2n. In this paper we develop and present a complete picture of the problem of alternation removal in alternating Büchi automata. In the lower bound front, we show that the breakpoint construction captures the accurate essence of alternation removal, and provide a matching Ω(3n) lower bound. Our lower bound holds already for universal (rather than alternating) automata with an alphabet of a constant size. In the upper-bound front, we point to a class of alternating Büchi automata for which the breakpoint construction can be replaced by a simpler n2n construction. Our class, of ordered alternating Büchi automata, strictly contains the class of very-weak alternating automata, for which an n2n construction is known.