Abstract
Interpreting temporal logics on finite traces has specific use in many fields, and it attracts more and more attention in recent years. Foundation formulas (FL for short) is the core part of PSL, which has once been an industrial standard of specification language accepted by IEEE, and has now been adopted in SystemVerilog. We in this paper present a variant of FL, called FL\(^{res}\), whose semantics is defined w.r.t. finite words. In comparison to the original FL, the only syntactic restriction is that the “length-matching and” operator cannot appear in the first argument when doing concatenation. This restriction in syntax would not change the expressiveness, whereas could gain a much succinct automata based decision procedure. Namely, an FL\(^{res}\) formula \(\varphi \) can be equivalently transformed into a 2-way (or, stuttering) alternating finite automaton with \(\mathcal {O}(|\varphi |)\) states. Subsequently, one can convert it to a 1-way nondeterministic finite automaton with \(2^{\mathcal {O}(|\varphi |)}\) states.
Supported by NSFC under grant Nos 61872371, 61802415, and U19A2062.
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
Similar content being viewed by others
Notes
- 1.
Because, SERE and RE are the same in expressiveness. Our logic uses a restricted version of SERE, whereas it subsumes standard RE.
- 2.
For example, the language of \( \left( a^+ \& \& (a^+;b)\right) ;b^+\) is empty, whereas \( (a^+;b^+) \& \& (a^+;b;b^+)\) matches abb.
- 3.
We assume \(Q_1\cap Q_2=\emptyset \) in the sequel. Otherwise, just need a systematic state renaming.
References
Accellera: Accellera property languages reference manual, June 2004. http://www.eda.org/vfv/docs/PSL-v1.1.pdf
Birget, J.C.: State-complexity of finite-state devices, state compressibility and incompressibility. Math. Syst. Theory 26(3), 237–269 (1993)
Bustan, D., Fisman, D., Havlicek, J.: Automata construction for PSL. Technical Report MCS05-04, IBM Haifa Research Lab, May 2005
Cimatti, A., Roveri, M., Semprini, S., Tonetta, S.: From PSL to NBA: a modular symbolic encoding. In: FMCAD 2006 (2006)
Cimatti, A., Roveri, M., Tonetta, S.: Symbolic compilation of PSL. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 27(10), 1737–1750 (2008)
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982). https://doi.org/10.1007/BFb0025774
Eisner, C., Fisman, D.: A Practical Introduction to PSL. Springer, New York (2006). https://doi.org/10.1007/978-0-387-36123-9
De Giacomo, G., Vardi, M.: Linear temporal logic and linear dynamic logic on finite traces. In: IJCAI 2013, pp. 2000–2007. AAAI Press (2013)
De Giacomo, G., Vardi, M.: Synthesis for LTL and IDL on finite traces. In: IJCAI 2015, pp. 1558–1564. AAAI Press (2015)
IEEE Computer Society and IEEE Standards Association Corporate Advisory Group: IEEE standard for SystemVerilog – unified hardware design, specification, and verification language, December 2017
Jin, N., Shen, C.: Dynamic verifying the properties of the simple subset of PSL. In: 1st IEEE Symposium of Theoretical Aspects on Software Engineering, pp. 173–182. IEEE Society (2007)
Li, J., Rozier, K.Y., Pu, G., Zhang, Y., Vardi, M.Y.: SAT-based explicit LTL\(_f\) satisfiability checking. CoRR, abs/1811.03176 (2018)
Li, J., Zhang, L., Pu, G., Vardi, M.Y., He, J.: LTL\(_f\) satisfiability checking. In: ECAI 2014, volume 263 of Frontiers in Artificial Intelligence and Applications, pp. 513–518. IOS Press (2014)
Li, J., Zhu, S., Pu, G., Zhang, L., Vardi, M.Y.: SAT-based explicit LTL reasoning and its application to satisfiability checking. Formal Methods Syst. Des. 54(2), 164–190 (2019)
Löding, C.: Optimal bounds for transformations of \(\Omega \)-automata. In: Rangan, C.P., Raman, V., Ramanujam, R. (eds.) FSTTCS 1999. LNCS, vol. 1738, pp. 97–109. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-46691-6_8
Muller, D.E., Schupp, P.E.: Alternating automata on infinite trees. Theoret. Comput. Sci. 54, 267–276 (1987)
Pnueli, A.: The temporal logic of programs. In: Proceedings of 18th IEEE Symposium on Foundation of Computer Science (FOCS 1977), pp. 46–57. IEEE Computer Society (1977)
Ruah, S., Fisman, D., Ben-David, S.: Automata construction for on-the-fly model checking PSL safety simple subset. Technical Report H0234, IBM Haifa Research Lab, April 2005
Wolper, P.: Temporal logic can be more expressive. Inf. Control 56(1–2), 72–99 (1983)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Liu, W., Yin, L., Li, T. (2020). Compiling FL\(^{res}\) on Finite Words. In: Pang, J., Zhang, L. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2020. Lecture Notes in Computer Science(), vol 12153. Springer, Cham. https://doi.org/10.1007/978-3-030-62822-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-62822-2_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-62821-5
Online ISBN: 978-3-030-62822-2
eBook Packages: Computer ScienceComputer Science (R0)