Counting Paths in VPA Is Complete for #NC 1

Abstract

We give 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 and Ramachandran (SIAM J. Comput. 21:755–780, 1992). 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 automaton.