Finite monoids and the fine structure of NC1
Journal of the ACM (JACM)
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
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Computing with highly mixed states (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Circuits and expressions with nonassociative gates
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
Quantum automata and quantum grammars
Theoretical Computer Science
Quantum computation and quantum information
Quantum computation and quantum information
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
On Computational Power of Quantum Branching Programs
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
On the power of quantum finite state automata
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
1-way quantum finite automata: strengths, weaknesses and generalizations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Quantum branching programs and space-bounded nonuniform quantum complexity
Theoretical Computer Science
On the computational power of probabilistic and quantum branching program
Information and Computation
Computing with highly mixed states
Journal of the ACM (JACM)
On the computational power of probabilistic and quantum branching program
Information and Computation
Complexity of quantum uniform and nonuniform automata
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
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We prove upper and lower bounds on the power of quantum and stochastic branching programs of bounded width. We show any NC1 language can be accepted exactly by a width-2 quantum branching program of polynomial length, in contrast to the classical case where width 5 is necessary unless NC1 = ACC. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC1.