Abstract
By using the known lower and upper complexity bounds of the coverability problem for vass, we characterize the complexity of the classical backward algorithm for vass coverability, and provide optimal bounds on the size of the symbolic representation it computes.
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
Abdulla, P., Čerāns, K., Jonsson, B., Tsay, Y.: General Decidability Theorems for Infinite-State Systems. In: LICS 1996, pp. 313–321. IEEE Computer Society Press, Los Alamitos (1996)
Arnold, A., Latteux, M.: Recursivite et cones rationnels fermes par intersection. Calcolo 15, 381–394 (1978)
Delzanno, G., Raskin, J.-F.: Symbolic representation of upward-closed sets. In: Graf, S. (ed.) TACAS 2000. LNCS, vol. 1785, pp. 426–440. Springer, Heidelberg (2000)
Delzanno, G., Raskin, J.-F., Van Begin, L.: Attacking symbolic state explosion. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 298–310. Springer, Heidelberg (2001)
Dickson, L.E.: Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. American Journal of Mathematics 35, 413–422 (1913)
Esparza, J.: Decidability and Complexity of Petri Net Problems - An Introduction. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998)
Esparza, J., Nielsen, M.: Decidability issues for Petri nets - a survey. Journal of Informatik Processing and Cybernetics 30(3), 143–160 (1994)
Figueira, D., Figueira, S., Schmitz, S., Schnoebelen, P.: Ackermannian and primitive-recursive bounds with Dickson’s lemma. In: LICS 2011: Proc. 26th Annual IEEE Symp. on Logic in Computer Science, pp. 269–278. IEEE Computer Society Press, Los Alamitos (2011)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoretical Computer Science 256(1-2), 63–92 (2001)
Ganty, P., Majumdar, R.: Algorithmic verification of asynchronous programs. CoRR, abs/1011.0551 (2010)
Higman, G.: Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society (3) 2(7), 326–336 (1952)
Karp, R.M., Miller, R.E.: Parallel program schemata. Journal of Comput. Syst. Sci. 3(2), 147–195 (1969)
Lipton, R.: The Reachability Problem Requires Exponential Space. Technical Report 62, Yale University (1976)
Rackoff, C.: The Covering and Boundedness Problems for Vector Addition Systems. Theoretical Computer Science 6, 223–231 (1978)
Sen, K., Viswanathan, M.: Model checking multithreaded programs with asynchronous atomic methods. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 300–314. Springer, Heidelberg (2006)
Valk, R., Jantzen, M.: The residue of vector sets with applications to decidability problems in Petri nets. Acta Informatica 21, 643–674 (1985)
Yen, H.-C., Chen, C.-L.: On minimal elements of upward-closed sets. Theoretical Computer Science 410(24-25), 2442–2452 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bozzelli, L., Ganty, P. (2011). Complexity Analysis of the Backward Coverability Algorithm for VASS. In: Delzanno, G., Potapov, I. (eds) Reachability Problems. RP 2011. Lecture Notes in Computer Science, vol 6945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24288-5_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-24288-5_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24287-8
Online ISBN: 978-3-642-24288-5
eBook Packages: Computer ScienceComputer Science (R0)