Abstract
We adapt hypergraph rewriting system to a generalization of Vector Addition Systems with States (VASS) that we call vector addition systems with pairs (VASP). We give rewriting systems and strategies, that allow us to obtain reachability equivalence results between some classes of VASP and VASS. Reachability for the later is well known be equivalent to reachability in Petri nets. VASP generalize also Branching Extension of VASS (BVASS) for which it is unknown if they are more expressive than VASS. We consider here a more restricted notion of reachability for VASP than that for BVASS. However the reachability decision problem corresponding is already equivalent to decidability of the provability in Multiplicative and Exponential Linear Logic (MELL), a question left open for more than 20 years.
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
Preview
Unable to display preview. Download preview PDF.
References
Brázdil, T., Jancar, P., Kucera, A.: Reachability games on extended vector addition systems with states. CoRR (2010) abs/1002.2557
de Groote, P., Guillaume, B., Salvati, S.: Vector addition tree automata. In: LICS, pp. 64–73. IEEE Computer Society, Los Alamitos (2004)
Demri, S., Jurdzinski, M., Lachish, O., Lazic, R.: The covering and boundedness problems for branching vector addition systems. In: Kannan, R., Kumar, K.N. (eds.) FSTTCS. LIPIcs, vol. 4, pp. 181–192 (2009)
Esparza, J., Nielsen, M.: Decidability issues for petri nets - a survey. Bulletin of the EATCS 52, 244–262 (1994)
Gallo, G., Longo, G., Pallottino, S.: Directed hypergraphs and applications. Discrete Applied Mathematics 42(2), 177–201 (1993)
Ginsburg, S., Spanier, E.H.: Semigroups, presburger formulas, and languages. Pacific Journal of Mathematic 16(2), 285–296 (1966)
Ginzburg, A., Yoeli, M.: Vector addition systems and regular languages. J. Comput. Syst. Sci. 20(3), 277–284 (1980)
Girard, J.-Y.: Linear logic. Theor. Comput. Sci. 50, 1–102 (1987)
Hopcroft, J.E., Pansiot, J.-J.: On the reachability problem for 5-dimensional vector addition systems. TCS 8, 135–159 (1979)
Karp, R.M., Miller, R.E.: Parallel program schemata. J. Comput. Syst. Sci. 3(2), 147–195 (1969)
Kosaraju, S.R.: Decidability of reachability in vector addition systems (preliminary version). In: STOC, pp. 267–281. ACM, New York (1982)
Lambert, J.-L.: A structure to decide reachability in petri nets. Theor. Comput. Sci. 99(1), 79–104 (1992)
Mayr, E.W.: An algorithm for the general petri net reachability problem. SIAM J. Comput. 13(3), 441–460 (1984)
Müller, H.: The reachability problem for vas. In: Rozenberg, G., Genrich, H.J., Roucairol, G. (eds.) APN 1984. LNCS, vol. 188, pp. 376–391. Springer, Heidelberg (1985)
Parikh, R.: On context-free languages. J. ACM 13(4), 570–581 (1966)
Plump, D.: Termination of graph rewriting is undecidable. Fundam. Inform. 33(2), 201–209 (1998)
Reutenauer, C.: Aspects Mathématiques des Réseaux de Pétri. Masson (1989)
Verma, K.N., Goubault-Larrecq, J.: Karp-miller trees for a branching extension of vass. Discrete Mathematics & Theoretical Computer Science 7(1), 217–230 (2005)
Verma, K.N., Goubault-Larrecq, J.: Alternating two-way ac-tree automata. Inf. Comput. 205(6), 817–869 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jacobé de Naurois, P., Mogbil, V. (2010). Rewriting Systems for Reachability in Vector Addition Systems with Pairs. In: Kučera, A., Potapov, I. (eds) Reachability Problems. RP 2010. Lecture Notes in Computer Science, vol 6227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15349-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-15349-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15348-8
Online ISBN: 978-3-642-15349-5
eBook Packages: Computer ScienceComputer Science (R0)