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## computational complexity OnlineFirst articles

29.09.2018

### Lower Bounds and PIT for Non-commutative Arithmetic Circuits with Restricted Parse Trees

We investigate the power of Non-commutative Arithmetic Circuits, which compute polynomials over the free non-commutative polynomial ring $${\mathbb{F}\langle{x_1,\ldots,x_N\rangle}}$$ F ⟨ x 1 , … , x N ⟩ , where variables do not commute. We …

29.09.2018

### Asymptotic tensor rank of graph tensors: beyond matrix multiplication

We present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on k vertices. For $${k \geq 4}$$ k ≥ 4 , we show that the exponent per edge is at most 0.77 …

20.08.2018

### On the Relationship Between Statistical Zero-Knowledge and Statistical Randomized Encodings

Statistical Zero-knowledge proofs (Goldwasser et al. in SICOMP: SIAM J Comput, 1989) allow a computationally unbounded server to convince a computationally limited client that an input x is in a language $${\Pi}$$ Π without revealing any …

04.06.2018

### On semiring complexity of Schur polynomials

Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that semiring complexity of a Schur polynomial $${s_\lambda(x_1,\dots,x_k)}$$ s λ ( x 1 , ⋯ , x k ) labeled …

24.05.2018

### An adaptivity hierarchy theorem for property testing

Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of adaptive testing algorithms, wherein each query may be determined by the answers …

## Aktuelle Ausgaben

### Über diese Zeitschrift

computational complexity presents outstanding research in computational complexity. Its subject is at the interface between mathematics and theoretical computer science, with a clear mathematical profile and strictly mathematical format.

The central topics are:

Models of computation, complexity bounds (with particular emphasis on lower bounds), complexity classes, trade-off results

• for sequential and parallel computation
• for "general" (Boolean) and "structured" computation (e.g. decision trees, arithmetic circuits)
• for deterministic, probabilistic, and nondeterministic computation
• worst case and average case

Specific areas of concentration include:

• Structure of complexity classes (reductions, relativization questions, degrees, derandomization)
• Algebraic complexity (bilinear complexity, computations for polynomials, groups, algebras, and representations)
• Interactive proofs, pseudorandom generation, and randomness extraction

Complexity issues in:

• cryptography
• learning theory
• number theory
• logic (complexity of logical theories, cost of decision procedures)
• combinatorial optimization and approximate solutions
• distributed computing
• property testing

Bibliographic Data
comput. complex.
First published in 1991
1 volume per year, 4 issues per volume
approx. 800 pages per volume
Format: 15.5 x 23.5 cm
ISSN 1016-3328 (print)
ISSN 1420-8954 (electronic)

AMS Mathematical Citation Quotient (MCQ): 0.30 (2015)

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