Abstract
In this work, we present multiple new optimizations and heuristics for the determinization of Büchi automata that exploit a number of semantic and structural properties, most of which may be applied together with any determinization procedure. We built a prototype implementation where all the presented heuristics can be freely combined and evaluated them, comparing our implementation with the state-of-the-art tool spot on multiple data sets with different characteristics. Our results show that the proposed optimizations and heuristics can in some cases significantly decrease the size of the resulting deterministic automaton.
A. Pirogov—This work is supported by the German research council (DFG) Research Training Group 2236 UnRAVeL.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Our prototype can be obtained at https://github.com/apirogov/nbautils.
References
Althoff, C.S., Thomas, W., Wallmeier, N.: Observations on determinization of Büchi automata. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 262–272. Springer, Heidelberg (2006). https://doi.org/10.1007/11605157_22
Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)
Boigelot, B., Jodogne, S., Wolper, P.: On the use of weak automata for deciding linear arithmetic with integer and real variables. In: Goré, R., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS, vol. 2083, pp. 611–625. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45744-5_50
Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Studies in Logic and the Foundations of Mathematics, vol. 44, pp. 1–11. Elsevier (1966)
Carton, O., Maceiras, R.: Computing the Rabin index of a parity automaton. RAIRO-Theoret. Inform. Appl. 33(6), 495–505 (1999)
Colcombet, T., Zdanowski, K.: A tight lower bound for determinization of transition labeled Büchi automata. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 151–162. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02930-1_13
Duret-Lutz, A.: Manipulating LTL formulas using spot 1.0. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 442–445. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-02444-8_31
Duret-Lutz, A., Lewkowicz, A., Fauchille, A., Michaud, T., Renault, É., Xu, L.: Spot 2.0 — a framework for LTL and \(\omega \)-automata manipulation. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 122–129. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46520-3_8
Esparza, J., Křetínský, J., Raskin, J.-F., Sickert, S.: From LTL and limit-deterministic Büchi automata to deterministic parity automata. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 426–442. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54577-5_25
Etessami, K., Holzmann, G.J.: Optimizing Büchi automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–168. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44618-4_13
Etessami, K., Wilke, T., Schuller, R.A.: Fair simulation relations, parity games, and state space reduction for Büchi automata. SIAM J. Comput. 34(5), 1159–1175 (2005)
Fisman, D., Lustig, Y.: A modular approach for Büchi determinization. In: CONCUR 2015. LIPIcs (2015)
Fogarty, S., Kupferman, O., Vardi, M.Y., Wilke, T.: Profile trees for Büchi word automata, with application to determinization. Inf. Comput. 245, 136–151 (2015)
Gastin, P., Oddoux, D.: Fast LTL to Büchi automata translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 53–65. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44585-4_6
Geldenhuys, J., Hansen, H.: Larger automata and less work for LTL model checking. In: Valmari, A. (ed.) SPIN 2006. LNCS, vol. 3925, pp. 53–70. Springer, Heidelberg (2006). https://doi.org/10.1007/11691617_4
Hopcroft, J.: An n log n algorithm for minimizing states in a finite automaton. In: Theory of Machines and Computations, pp. 189–196. Elsevier (1971)
Jacobs, S., et al.: The 4th reactive synthesis competition (syntcomp 2017): benchmarks, participants & results. arXiv preprint arXiv:1711.11439 (2017)
Kähler, D., Wilke, T.: Complementation, disambiguation, and determinization of Büchi automata unified. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5125, pp. 724–735. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70575-8_59
Klein, J.: Linear time logic and deterministic omega-automata. Diploma thesis, University of Bonn (2005)
Klein, J., Baier, C.: On-the-fly stuttering in the construction of deterministic \(\omega \)-automata. In: Holub, J., Žd’árek, J. (eds.) CIAA 2007. LNCS, vol. 4783, pp. 51–61. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76336-9_7
Křetínský, J., Meggendorfer, T., Sickert, S., Ziegler, C.: Rabinizer 4: from LTL to your favourite deterministic automaton. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10981, pp. 567–577. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96145-3_30
Kupferman, O., Rosenberg, A.: The blow-up in translating LTL to deterministic automata. In: van der Meyden, R., Smaus, J.-G. (eds.) MoChArt 2010. LNCS (LNAI), vol. 6572, pp. 85–94. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20674-0_6
Kupferman, O., Vardi, M.Y.: From linear time to branching time. TOCL 6, 273–294 (2005)
Löding, C., Pirogov, A.: Determinization of Büchi automata: unifying the approaches of Safra and Muller-Schupp. ICALP 2019 https://arxiv.org/abs/1902.02139
McNaughton, R.: Testing and generating infinite sequences by a finite automaton. Inf. Control 9(5), 521–530 (1966)
Meyer, P.J., Sickert, S., Luttenberger, M.: Strix: explicit reactive synthesis strikes back!. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10981, pp. 578–586. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96145-3_31
Michel, M.: Complementation is more difficult with automata on infinite words. Manuscript, CNET, Paris (1988)
Miyano, S., Hayashi, T.: Alternating finite automata on \(\omega \)-words. Theoret. Comput. Sci. 32(3), 321–330 (1984)
Müller, D., Sickert, S.: LTL to deterministic Emerson-Lei automata. In: GandALF 2017
Muller, D.E., Schupp, P.E.: Simulating alternating tree automata by nondeterministic automata: new results and new proofs of the theorems of Rabin, McNaughton and Safra. Theoret. Comput. Sci. 141(1–2), 69–107 (1995)
Piterman, N.: From nondeterministic Büchi and Streett automata to deterministic parity automata. In: LICS 2006. IEEE (2006)
Pnueli, A.: The temporal logic of programs. In: 1977 18th Annual Symposium on Foundations of Computer Science, pp. 46–57. IEEE (1977)
Redziejowski, R.R.: An improved construction of deterministic omega-automaton using derivatives. Fundamenta Informaticae 119(3–4), 393–406 (2012)
Safra, S.: On the complexity of omega-automata. In: 1988 29th Annual Symposium on Foundations of Computer Science, pp. 319–327. IEEE (1988)
Schewe, S.: Tighter bounds for the determinisation of Büchi automata. In: de Alfaro, L. (ed.) FoSSaCS 2009. LNCS, vol. 5504, pp. 167–181. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00596-1_13
Tabakov, D., Vardi, M.Y.: Optimized temporal monitors for systemC. In: Barringer, H., et al. (eds.) RV 2010. LNCS, vol. 6418, pp. 436–451. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16612-9_33
Thomas, W.: Automata on infinite objects. In: Handbook of Theoretical Computer Science, vol. B, pp. 133–192. Elsevier Science Publishers, Amsterdam (1990)
Thomas, W.: Languages, automata, and logic. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, pp. 389–455. Springer, Heidelberg (1997). https://doi.org/10.1007/978-3-642-59126-6_7
Thomas, W.: Church’s problem and a tour through automata theory. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 635–655. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78127-1_35
Vardi, M.Y., Wilke, T.: Automata: from logics to algorithms. In: Logic and Automata - History and Perspectives, Texts in Logic and Games, vol. 2, pp. 629–724. Amsterdam University Press (2007)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Löding, C., Pirogov, A. (2019). New Optimizations and Heuristics for Determinization of Büchi Automata. In: Chen, YF., Cheng, CH., Esparza, J. (eds) Automated Technology for Verification and Analysis. ATVA 2019. Lecture Notes in Computer Science(), vol 11781. Springer, Cham. https://doi.org/10.1007/978-3-030-31784-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-030-31784-3_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-31783-6
Online ISBN: 978-3-030-31784-3
eBook Packages: Computer ScienceComputer Science (R0)