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Electronic Colloquium on Computational Complexity

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TR21-098 | 7th July 2021
Srikanth Srinivasan, S Venkitesh

On the Probabilistic Degree of an $n$-variate Boolean Function

Nisan and Szegedy (CC 1994) showed that any Boolean function $f:\{0,1\}^n\to\{0,1\}$ that depends on all its input variables, when represented as a real-valued multivariate polynomial $P(x_1,\ldots,x_n)$, has degree at least $\log n - O(\log \log n)$. This was improved to a tight $(\log n - O(1))$ bound by Chiarelli, Hatami ... more >>>


TR21-097 | 7th July 2021
Jacobo Toran, Florian Wörz

Number of Variables for Graph Identification and the Resolution of GI Formulas

We show that the number of variables and the quantifier depth needed to distinguish a pair of graphs by first-order logic sentences exactly match the complexity measures of clause width and positive depth needed to refute the corresponding graph isomorphism formula in propositional narrow resolution.

Using this connection, we ... more >>>


TR21-096 | 8th July 2021
Boaz Menuhin, Moni Naor

Keep That Card in Mind: Card Guessing with Limited Memory

A card guessing game is played between two players, Guesser and Dealer. At the beginning of the game, the Dealer holds a deck of $n$ cards (labeled $1, ..., n$). For $n$ turns, the Dealer draws a card from the deck, the Guesser guesses which card was drawn, and then ... more >>>



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