Abstract
Thomas has presented a novel proof of the closure of ω-regular languages under complementation, using weak alternating automata. This note describes a formalization of this proof in the theorem prover Isabelle/HOL. As an application we have developed a certified translation procedure for PTL formulas to weak alternating automata inside the theorem prover.
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References
J. R. Büchi. On a decision method in restricted second-order arithmetics. In International Congress on Logic, Method and Philosophy of Science, pages 1–12. Stanford University Press, 1962.
Orna Kupferman and Moshe Y. Vardi. Weak alternating automata are not so weak. In 5th Israeli Symposium on Theory of Computing and Systems, pages 147–158. IEEE Press, 1997.
D. E. Muller, A. Saoudi, and P. E. Schupp. Alternating automata, the weak monadic theory of the tree and its complexity. In 13th ICALP, volume 226 of Lecture Notes in Computer Science, pages 275–283. Springer-Verlag, 1986.
D.E. Muller, A. Saoudi, and P.E. Schupp. Weak alternating automata give a simple explanation of why most temporal and dynamic logics are decidable in exponential time. In 3rd IEEE Symposium on Logic in Computer Science, pages 422–427. IEEE Press, 1988.
Shmuel Safra. On the complexity of ω-automata. In 29th IEEE Symposium on Foundations of Computer Science, pages 319–327. IEEE Press, 1988.
Klaus Schneider and Dirk W. Hoffmann. A HOL conversion for translating linear time temporal logic to ω-automata. In Y. Bertot et al, editor, TPHOLs’99: 12th International Conference on Theorem Proving in Higher Order Logics, volume 1690 of Lecture Notes in Computer Science, pages 255–272, Nice, Prance, 1999. Springer-Verlag.
Wolfgang Thomas. Automata on infinite objects. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B: Formal Models and Semantics, pages 133–194. Elsevier, Amsterdam, 1990.
Wolfgang Thomas. Languages, automata, and logic. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Language Theory, volume III, pages 389–455. Springer-Verlag, New York, 1997.
Wolfgang Thomas. Complementation of Büchi automata revisited. In J. Kar-humäki, editor, Jewels are Forever, Contributions on Theoretical Computer Science in Honor of Arto Salomaa, pages 109–122. Springer-Verlag, 2000.
Moshe Vardi. Verification of concurrent programs: The automata-theoretic framework. In Proceedings of the Second Symposium on Logic in Computer Science, pages 167–176. IEEE, June 1987.
Moshe Y. Vardi. Computer Science Today, volume 1000 of Lecture Notes in Computer Science, chapter Alternating Automata and Program Verification, pages 471–485. Springer-Verlag, 1995.
Markus Wenzel. Isar—a generic interpretative approach to readable formal proof documents. In Y. Bertot et al, editor, TPHOLs’99: 12th International Conference on Theorem Proving in Higher Order Logics, volume 1690 of Lecture Notes in Computer Science. Springer-Verlag, 1999.
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Merz, S. (2000). Weak Alternating Automata in Isabelle/HOL. In: Aagaard, M., Harrison, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2000. Lecture Notes in Computer Science, vol 1869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44659-1_26
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DOI: https://doi.org/10.1007/3-540-44659-1_26
Publisher Name: Springer, Berlin, Heidelberg
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