, Volume 64, Issue 2, pp 279–294 | Cite as

Counting Paths in VPA Is Complete for #NC 1

  • Andreas Krebs
  • Nutan Limaye
  • Meena Mahajan


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.


Arithmetic Circuit Polynomial Size Boolean Circuit Input Alphabet Valid Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of TübingenTübingenGermany
  2. 2.Indian Institute of Technology BombayMumbaiIndia
  3. 3.The Institute of Mathematical SciencesChennaiIndia

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