The Boolean formula value problem is in ALOGTIME
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
An optimal parallel algorithm for formula evaluation
SIAM Journal on Computing
Nondeterministic NC1 computation
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
The complexity of matrix rank and feasible systems of linear equations
Computational Complexity
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
The complexity of two problems on arithmetic circuits
Theoretical Computer Science
Read-once polynomial identity testing
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Arithmetic Circuits: A Chasm at Depth Four
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Counting classes and the fine structure between NC1 and L
Theoretical Computer Science
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On Enumerating Monomials and Other Combinatorial Structures by Polynomial Interpolation
Theory of Computing Systems
Monomials, multilinearity and identity testing in simple read-restricted circuits
Theoretical Computer Science
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We study the problem of testing if the polynomial computed by an arithmetic circuit is identically zero (ACIT). We give a deterministic polynomial time algorithm for this problem when the inputs are read-twice formulas. This algorithm also computes the MLIN predicate, testing if the input circuit computes a multilinear polynomial. We further study two related computational problems on arithmetic circuits. Given an arithmetic circuit C, 1) ZMC: test if a given monomial in C has zero coefficient or not, and 2) MonCount: compute the number of monomials in C. These problems were introduced by Fournier, Malod and Mengel [STACS 2012], and shown to characterize various levels of the counting hierarchy (CH). We address the above problems on read-restricted arithmetic circuits and branching programs. We prove several complexity characterizations for the above problems on these restricted classes of arithmetic circuits.