Counting paths in VPA is complete for #NC1

Andreas Krebs Universitat Tubingen Wilhelm-Schickard-Inst. fur Informatik Arbeitsbereich Theoretische Informa
Thursday, 8 Jul 2010 (all day)
A-212 (STCS Seminar Room)
We prove a $\\#$NC$^1$ upper bound for the problem of counting accepting paths in any fixed visibly pushdown automaton. Our algorithm involves a non-trivial adaptation of the arithmetic formula evaluation algorithm of Buss, Cook, Gupta, Ramachandran. We also show that the problem is $\\#$NC$^1$ hard. Our results show that the difference between $\\#$BWBP and $\\#$NC$^1$ is captured exactly by the addition of a visible stack to a nondeterministic finite-state automata.

To appear in proceedings of the 16th International Computing and Combinatorics Conference COCOON, 19-21 July, 2010, Vietnam. (Andreas Krebs (University of Tubingen, Germany), Nutan Limaye (TIFR, Mumbai), Meena Mahajan (Institute of mathematical sciences, Chennai)