Abstract
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). Our motivation is to provide an efficient way to compute the quotient and inclusion of regular languages without the need to determinize the underlying automata. These operations are the building blocks of several verification algorithms that can be interpreted as language equation solving problems. We provide a construction for computing a FFA accepting the quotient and product of languages that is compositional and that does not incur an exponential blow up in size. This makes flanked automata a good candidate as a formalism for compositional design and verification of systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abdulla, P.A., Chen, Y.-F., Holík, L., Mayr, R., Vojnar, T.: When simulation meets antichains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 158–174. Springer, Heidelberg (2010)
Avellaneda, F., Dal Zilio, S., Raclet, J.: On the complexity of flanked finite state automata. CoRR abs/1509.06501 (2015)
Bauer, S.S., Fahrenberg, U., Juhl, L., Larsen, K.G., Legay, A., Thrane, C.R.: Weighted modal transition systems. Formal Methods Syst. Des. 42(2), 193–220 (2013)
Bauer, S.S., David, A., Hennicker, R., Guldstrand Larsen, K., Legay, A., Nyman, U., Wąsowski, A.: Moving from specifications to contracts in component-based design. In: Lara, J., Zisman, A. (eds.) Fundamental Approaches to Software Engineering. LNCS, vol. 7212, pp. 43–58. Springer, Heidelberg (2012)
Beneš, N., Delahaye, B., Fahrenberg, U., Křetínský, J., Legay, A.: Hennessy-Milner logic with greatest fixed points as a complete behavioural specification theory. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013 – Concurrency Theory. LNCS, vol. 8052, pp. 76–90. Springer, Heidelberg (2013)
Benveniste, A., Caillaud, B., Ferrari, A., Mangeruca, L., Passerone, R., Sofronis, C.: Multiple viewpoint contract-based specification and design. In: Boer, F.S., Bonsangue, M.M., Graf, S., Roever, W.-P. (eds.) FMCO 2007. LNCS, vol. 5382, pp. 200–225. Springer, Heidelberg (2008). Revised Lectures
Benveniste, A., Caillaud, B., Nickovic, D., Passerone, R., Raclet, J.B., Reinkemeier, P., Sangiovanni-Vincentelli, A., Damm, W., Henzinger, T., Larsen, K.G.: Contracts for system design (2012)
Colcombet, T.: Forms of determinism for automata. In: Symposium on Theoretical Aspects of Computer Science (STACS), vol. 14, pp. 1–23 (2012)
David, A., Larsen, K.G., Legay, A., Nyman, U., Wasowski, A.: Timed I/O automata: a complete specification theory for real-time systems. In: HSCC, pp. 91–100. ACM (2010)
Fahrenberg, U., Křetínský, J., Legay, A., Traonouez, L.-M.: Compositionality for quantitative specifications. In: Lanese, I., Madelaine, E. (eds.) FACS 2014. LNCS, vol. 8997, pp. 306–324. Springer, Heidelberg (2015)
Gierds, C., Mooij, A.J., Wolf, K.: Reducing adapter synthesis to controller synthesis. IEEE Trans. Serv. Comput. 5(1), 72–85 (2012)
Henzinger, T.A., Qadeer, S., Rajamani, S.K.: You assume, we guarantee: methodology and case studies. In: Hu, A.J., Vardi, M.Y. (eds.) Computer Aided Verification. LNCS, vol. 1427, pp. 440–451. Springer, Heidelberg (1998)
Heymann, M., Lin, F.: Discrete-event control of nondeterministic systems. IEEE Trans. Autom. Control 43(1), 3–17 (1998)
Isaak, D., Löding, C.: Efficient inclusion testing for simple classes of unambiguous \(\omega \)-automata. Inf. Process. Lett. 112, 14–15 (2012)
Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM J. Comput. 22(6), 1117–1141 (1993)
Kao, J.Y., Rampersad, N., Shallit, J.: On NFAs where all states are final, initial, or both. Theor. Comput. Sci. 410(4749), 5010–5021 (2009)
Kretínský, J., Sickert, S.: MoTraS: a tool for modal transition systems and their extensions. In: 11th International Symposium Automated Technology for Verification and Analysis (ATVA) (2013)
Raclet, J.B.: Residual for component specifications. ENTCS 215, 93–110 (2008). Workshop on Formal Aspects of Component Software (FACS)
Ramadge, P., Wonham, W.: The control of discrete event systems. Proc. IEEE 77(1), 81–98 (1989)
Schmidt, E.M.: Succinctness of description of context-free, regular and unambiguous languages. Ph.D. thesis, Cornell University (1978)
Stearns, R.E., Hunt III, H.B.: On the equivalence and containment problems for unambiguous regular expressions, regular grammars and finite automata. SIAM J. Comput. 14(3), 598–611 (1985)
Villa, T., Petrenko, A., Yevtushenko, N., Mishchenko, A., Brayton, R.: Component-based design by solving language equations. Proc. IEEE 99, 1–16 (2015)
Villa, T., Yevtushenko, N., Brayton, R.K., Mishchenko, A., Petrenko, A., Sangiovanni-Vincentelli, A.: The Unknown Component Problem: Theory and Applications. Springer, Heidelberg (2011)
Yellin, D., Strom, R.: Protocol specifications and component adaptors. ACM Trans. Programm. Lang. Syst. (TOPLAS) 19(2), 292–333 (1997)
Acknowledgments
We thank Denis Kuperberg, Thomas Colcombet, and Jean-Eric Pin for providing their expertise and insight and for suggesting the example that led to the proof of Theorem 6.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Avellaneda, F., Dal Zilio, S., Raclet, JB. (2016). Solving Language Equations Using Flanked Automata. In: Artho, C., Legay, A., Peled, D. (eds) Automated Technology for Verification and Analysis. ATVA 2016. Lecture Notes in Computer Science(), vol 9938. Springer, Cham. https://doi.org/10.1007/978-3-319-46520-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-46520-3_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-46519-7
Online ISBN: 978-3-319-46520-3
eBook Packages: Computer ScienceComputer Science (R0)