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
Two applications of inductive counting for complementation problems
SIAM Journal on Computing
Complexity theory of parallel time and hardware
Information and Computation
Boolean circuits versus arithmetic circuits
Information and Computation
Properties that characterize LOGCFL
Journal of Computer and System Sciences
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
An optimal parallel algorithm for formula evaluation
SIAM Journal on Computing
Bounded-width polynomial-size Boolean formulas compute exactly those functions in AC0
Information Processing Letters
Unambiguous auxiliary pushdown automata and semi-unbounded fan-in circuits
Information and Computation
Computational Complexity
Non-commutative arithmetic circuits: depth reduction and size lower bounds
Theoretical Computer Science
Nondeterministic NC1 computation
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Characterizations of Pushdown Machines in Terms of Time-Bounded Computers
Journal of the ACM (JACM)
On the Tape Complexity of Deterministic Context-Free Languages
Journal of the ACM (JACM)
On TC0, AC0, and arithmetic circuits
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Pebbling Moutain Ranges and its Application of DCFL-Recognition
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Proceedings of the 16th Conference on Foundations of Software Technology and Theoretical Computer Science
Input-Driven Languages are Recognized in log n Space
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
Hierarchies of Circuit Classes that are Closed Under Complement
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Deterministic CFL's are accepted simultaneously in polynomial time and log squared space
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Arithmetic Circuits, Syntactic Multilinearity, and the Limitations of Skew Formulae
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
On Lower Bounds for Constant Width Arithmetic Circuits
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
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
Counting paths in VPA Is complete for #NC1
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
On the complexity of membership and counting in height-deterministic pushdown automata
Journal of Automata, Languages and Combinatorics
Resource Trade-offs in Syntactically Multilinear Arithmetic Circuits
Computational Complexity
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The parallel complexity class NC1 has many equivalent models such as bounded width branching programs. Caussinus et.al[10] considered arithmetizations of two of these classes, #NC1 and #BWBP. We further this study to include arithmetization of other classes. In particular, we show that counting paths in branching programs over visibly pushdown automata has the same power as #BWBP, while counting proof-trees in logarithmic width formulae has the same power as #NC1. We also consider polynomial-degree restrictions of SCi, denoted sSCi, and show that the Boolean class sSC1 lies between NC1 and L, whereas sSC0 equals NC1. On the other hand, #sSC0 contains #BWBP and is contained in FL, and #sSC1 contains #NC1 and is in SC2. We also investigate some closure properties of the newly defined arithmetic classes.