Author:
Dekker Maurice,Kloibhofer Johannes,Marti Johannes,Venema Yde
Abstract
AbstractAutomata operating on infinite objects feature prominently in the theory of the modal $$\mu $$-calculus. One such application concerns the tableau games introduced by Niwiński & Walukiewicz, of which the winning condition for infinite plays can be naturally checked by a nondeterministic parity stream automaton. Inspired by work of Jungteerapanich and Stirling we show how determinization constructions of this automaton may be used to directly obtain proof systems for the $$\mu $$-calculus. More concretely, we introduce a binary tree construction for determinizing nondeterministic parity stream automata. Using this construction we define the annotated cyclic proof system $$\textsf{BT}$$, where formulas are annotated by tuples of binary strings. Soundness and Completeness of this system follow almost immediately from the correctness of the determinization method.
Publisher
Springer Nature Switzerland
Reference26 articles.
1. Afshari, B., Enqvist, S., Leigh, G.E.: Cyclic proofs for the first-order $$\mu $$-calculus. Logic J. IGPL (2022). https://doi.org/10.1093/jigpal/jzac053
2. Afshari, B., Leigh, G.E.: Cut-free completeness for modal $$\mu $$-calculus. In: Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017, Reykjavík, Iceland. IEEE Press (2017)
3. Brotherston, J.: Sequent calculus proof systems for inductive definitions. Ph.D. thesis (2006). https://era.ed.ac.uk/handle/1842/1458
4. Calude, C., Jain, S., Khoussainov, B., Li, W., Stephan, F.: Deciding parity games in quasipolynomial time. In: Hatami, H., McKenzie, P., King, V. (eds.) Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, (STOC 2017), pp. 252–263 (2017)
5. Dekker, M., Kloibhofer, J., Marti, J., Venema, Y.: Proof systems for the modal $$\mu $$-calculus obtained by determinizing automata (2023). https://doi.org/10.48550/arXiv.2307.06897
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献