Abstract
In this paper, we revisit the problem of translating LTL formulas to Büchi automata. We first translate the given LTL formula into a special disjuctive-normal form (DNF). The formula will be part of the state, and its DNF normal form specifies the atomic properties that should hold immediately (labels of the transitions) and the formula that should hold afterwards (the corresponding successor state). If the given formula is Until-free or Release-free, the Büchi automaton can be obtained directly in this manner. For a general formula, the construction is more involved: an additional component will be needed for each formula that helps us to identify the set of accepting states. Notably, our construction is an on-the-fly construction, which starts with the given formula and explores successor states according to the normal forms. We implement our construction and compare the tool with SPOT [3]. The comparision results are very encouraging and show our construction is quite innovative.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Babiak, T., Křetínský, M., Řehák, V., Strejček, J.: LTL to Büchi Automata Translation: Fast and More Deterministic. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 95–109. Springer, Heidelberg (2012)
Daniele, M., Giunchiglia, F., Vardi, M.Y.: Improved Automata Generation for Linear Temporal Logic. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. CAV, pp. 249–260. Springer, Heidelberg (1999)
Duret-Lutz, A., Poitrenaud, D.: SPOT: an extensible model checking library using transition-based generalized Büchi automata In. In: The IEEE Computer Society’s 12th Annual International Symposium, pp. 76–83 (2004)
Etessami, K., Holzmann, G.J.: Optimizing Büchi Automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 153–167. Springer, Heidelberg (2000)
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)
Gerth, R., Peled, D., Vardi, M.Y., Wolper, P.: Simple on-the-fly automatic verification of linear temporal logic. In: PSTV, pp. 3–18 (1995)
Giannakopoulou, D., Lerda, F.: From States to Transitions: Improving Translation of LTL Formulae to Büchi Automata. In: Peled, D.A., Vardi, M.Y. (eds.) FORTE 2002. LNCS, vol. 2529, pp. 308–326. Springer, Heidelberg (2002)
Li, J., Pu, G., Zhang, L., Wang, Z., He, J., Larsen, K.G.: On the Relationship between LTL Normal Forms and Buechi Automata. CoRR (2012)
Rozier, K.Y., Vardi, M.Y.: LTL satisfiability checking. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 149–167. Springer, Heidelberg (2007)
Sebastiani, R., Tonetta, S.: “More Deterministic” vs. “Smaller” Büchi Automata for Efficient LTL Model Checking. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, pp. 126–140. Springer, Heidelberg (2003)
Somenzi, F., Bloem, R.: Efficient Büchi Automata from LTL Formulae. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 248–263. Springer, Heidelberg (2000)
Tauriainen, H., Heljanko, K.: Testing LTL formula translation into Büchi automata. STTT 4(1), 57–70 (2002)
Vardi, M.Y.: An Automata-Theoretic Approach to Linear Temporal Logic. In: Banff Higher Order Workshop, pp. 238–266 (1995)
Vardi, M.Y., Wolper, P.: An Automata-Theoretic Approach to Automatic Program Verification. In: LICS, pp. 332–344 (1986)
Couvreur, J.-M.: On-the-fly verification of linear temporal logic. In: Wing, J.M., Woodcock, J. (eds.) FM 1999. LNCS, vol. 1708, pp. 253–271. Springer, Heidelberg (1999)
Bryant, R.E.: Graph-Based Algorithms for Boolean Function Manipulation. IEEE Trans. Computers, 677–691 (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Li, J., Pu, G., Zhang, L., Wang, Z., He, J., Guldstrand Larsen, K. (2013). On the Relationship between LTL Normal Forms and Büchi Automata. In: Liu, Z., Woodcock, J., Zhu, H. (eds) Theories of Programming and Formal Methods. Lecture Notes in Computer Science, vol 8051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39698-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-39698-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39697-7
Online ISBN: 978-3-642-39698-4
eBook Packages: Computer ScienceComputer Science (R0)