Abstract
This paper considers the satisfiability problem of symbolic heaps in separation logic with Presburger arithmetic and inductive definitions. First the system without any restrictions is proved to be undecidable. Secondly this paper proposes some syntactic restrictions for decidability. These restrictions are identified based on a new decidable subsystem of Presburger arithmetic with inductive definitions. In the subsystem of arithmetic, every inductively defined predicate represents an eventually periodic set and can be eliminated. The proposed system is quite general as it can handle the satisfiability of the arithmetical parts of fairly complex predicates such as sorted lists and AVL trees. Finally, we prove the decidability by presenting a decision procedure for symbolic heaps with the restricted inductive definitions and arithmetic.
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
Berdine, J., Calcagno, C., O’Hearn, P.W.: A decidable fragment of separation logic. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 97–109. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30538-5_9
Berdine, J., Calcagno, C., O’Hearn, P.W.: Symbolic execution with separation logic. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 52–68. Springer, Heidelberg (2005). doi:10.1007/11575467_5
Bozga, M., Iosif, R., Perarnau, S.: Quantitative separation logic and programs with lists. J. Autom. Reason. 45(2), 131–156 (2010)
Brotherston, J., Fuhs, C., Gorogiannis, N., Perez, J.N.: A decision procedure for satisfiability inseparation logic with inductive predicates. In: Proceedings of CSL-LICS 2014 (2014). Article 25
Chin, W.N., David, C., Nguyen, H.H., Qin, S.: Automated verification of shape, size and bag properties viauser-defined predicates in separation logic. Sci. Comput. Program. 77(9), 1006–1036 (2012)
Enderton, H.B.: A Mathematical Introduction to Logic, 2 edn. Academic Press (2000)
Iosif, R., Rogalewicz, A., Simacek, J.: The tree width of separation logic with recursive definitions. In: Bonacina, M.P. (ed.) CADE 2013. LNCS (LNAI), vol. 7898, pp. 21–38. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38574-2_2
Iosif, R., Rogalewicz, A., Vojnar, T.: Deciding entailments in inductive separation logic with tree automata. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 201–218. Springer, Heidelberg (2014). doi:10.1007/978-3-319-11936-6_15
Piskac, R., Wies, T., Zufferey, D.: Automating separation logic using SMT. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 773–789. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39799-8_54
Piskac, R., Wies, T., Zufferey, D.: Automating separation logic with trees and data. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 711–728. Springer, Heidelberg (2014). doi:10.1007/978-3-319-08867-9_47
Navarro Pérez, J.A., Rybalchenko, A.: Separation logic modulo theories. In: Shan, C. (ed.) APLAS 2013. LNCS, vol. 8301, pp. 90–106. Springer, Heidelberg (2013). doi:10.1007/978-3-319-03542-0_7
Reynolds, J.C.: Separation logic: a logic for shared mutable data structures. In: Proceedings of Seventeenth Annual IEEE Symposium on Logic in Computer Science (LICS2002), pp. 55–74 (2002)
Brotherston, J., Gorogiannis, N., Kanovich, M., Rowe, R.: Model checking for symbolic-heap separation logic with inductive predicates. In: Proceedings of POPL-43, pp. 84–96 (2016)
Acknowledgments
This work is partially supported by MoE Tier-2 grant MOE2013-T2-2-146.
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
Tatsuta, M., Le, Q.L., Chin, WN. (2016). Decision Procedure for Separation Logic with Inductive Definitions and Presburger Arithmetic. In: Igarashi, A. (eds) Programming Languages and Systems. APLAS 2016. Lecture Notes in Computer Science(), vol 10017. Springer, Cham. https://doi.org/10.1007/978-3-319-47958-3_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-47958-3_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47957-6
Online ISBN: 978-3-319-47958-3
eBook Packages: Computer ScienceComputer Science (R0)