On Boundedness Problems for Pushdown Vector Addition Systems
We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems. The question of the boundedness of the reachability set for this model can be refined into two decision problems that ask if infinitely many counter values or stack configurations are reachable, respectively. Counter boundedness seems to be the more intricate problem. We show decidability in exponential time for one-dimensional systems. The proof is via a small witness property derived from an analysis of derivation trees of grammar-controlled vector addition systems.
KeywordsProduction Rule Coverability Problem Exponential Time Parse Tree Reachability Problem
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- 1.Ball, T., Majumdar, R., Millstein, T.D., Rajamani, S.K.: Automatic predicate abstraction of C programs. In: PLDI, pp. 203–213 (2001)Google Scholar
- 3.Dassow, J., Pun, G., Salomaa, A.: Grammars with controlled derivations. In: Handbook of Formal Languages, pp. 101–154 (1997)Google Scholar
- 6.Kosaraju, S.R.: Decidability of reachability in vector addition systems (preliminary version). In: STOC, pp. 267–281 (1982)Google Scholar
- 7.Lazic, R.: The reachability problem for vector addition systems with a stack is not elementary. CoRR abs/1310.1767 (2013)Google Scholar
- 8.Leroux, J., Praveen, M., Sutre, G.: Hyper-ackermannian bounds for pushdown vector addition systems. In: CSL/LICS (2014)Google Scholar
- 9.Leroux, J., Schmitz, S.: Demystifying reachability in vector addition systems. In: LICS (2015)Google Scholar
- 11.Lipton, R.J.: The reachability problem requires exponential space. Tech. Rep. 63, Yale University (January 1976)Google Scholar
- 12.Mayr, E.W.: An algorithm for the general Petri net reachability problem. In: STOC. pp. 238–246 (1981)Google Scholar