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Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

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TR18-040 | 21st February 2018
Marshall Ball, Dana Dachman-Soled, Siyao Guo, Tal Malkin, Li-Yang Tan

Non-Malleable Codes for Small-Depth Circuits

We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by small-depth circuits. For constant-depth circuits of polynomial size (i.e.~$\mathsf{AC^0}$ tampering functions), our codes have codeword length $n = k^{1+o(1)}$ for a $k$-bit message. This is an exponential improvement of the previous best construction due to Chattopadhyay ... more >>>

TR18-039 | 23rd February 2018
Md Lutfar Rahman, Thomas Watson

Complexity of Unordered CNF Games

The classic TQBF problem is to determine who has a winning strategy in a game played on a given CNF formula, where the two players alternate turns picking truth values for the variables in a given order, and the winner is determined by whether the CNF gets satisfied. We study ... more >>>

TR18-038 | 21st February 2018
Nathanael Fijalkow, Guillaume Lagarde, Pierre Ohlmann

Tight Bounds using Hankel Matrix for Arithmetic Circuits with Unique Parse Trees

This paper studies lower bounds for arithmetic circuits computing (non-commutative) polynomials. Our conceptual contribution is an exact correspondence between circuits and weighted automata: algebraic branching programs are captured by weighted automata over words, and circuits with unique parse trees by weighted automata over trees.

The key notion for understanding the ... more >>>

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ISSN 1433-8092 | Imprint