Counting paths in VPA Is complete for #NC1

Authors:
Andreas Krebs;Nutan Limaye;Meena Mahajan
Affiliations:
University of Tübingen, Germany;Tata Institute of Fundamental Research, Mumbai, India;The Institute of Mathematical Sciences, Chennai, India
Venue:
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Year:
2010

Citing 14
Cited 0

The Boolean formula value problem is in ALOGTIME

STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Input-driven languages are in log n depth

Information Processing Letters
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1

Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Computing algebraic formulas using a constant number of registers

SIAM Journal on Computing
An optimal parallel algorithm for formula evaluation

SIAM Journal on Computing
Non-commutative arithmetic circuits: depth reduction and size lower bounds

Theoretical Computer Science
The Parallel Evaluation of General Arithmetic Expressions

Journal of the ACM (JACM)
Pebbling Moutain Ranges and its Application of DCFL-Recognition

Proceedings of the 7th Colloquium on Automata, Languages and Programming
Input-Driven Languages are Recognized in log n Space

Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
Nondeterministic NC1 Computation

CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Visibly pushdown languages

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Arithmetizing Classes Around $\textsf{NC}$1 and $\textsf{L}$

Theory of Computing Systems - Special Issue: Theoretical Aspects of Computer Science; Guest Editors: Wolgang Thomas and Pascal Weil
Arithmetizing classes around NC1and L

STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On the complexity of membership and counting in height-deterministic pushdown automata

CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We give a #NC1 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 ([9]). We also show that the problem is #NC1 hard. Our results show that the difference between #BWBP and #NC1 is captured exactly by the addition of a visible stack to a nondeterministic finite-state automata.