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We demonstrate a lower bound technique for linear decision lists, which are decision lists where the queries are arbitrary linear threshold functions. We use this technique to prove an explicit lower bound by showing that any linear decision list computing the function $MAJ circ XOR$ requires size $2^{0.18 n}$. This completely answers an open question of Tur{a}n and Vatan [FoCM97]. We also show that the spectral classes $PL_1, PL_infty$, and the polynomial threshold function classes $widehat{PT}_1, PT_1$, are incomparable to linear decision lists.
We consider the approximability of constraint satisfaction problems in the streaming setting. For every constraint satisfaction problem (CSP) on $n$ variables taking values in ${0,ldots,q-1}$, we prove that improving over the trivial approximability
We prove that a sufficiently strong parallel repetition theorem for a special case of multiplayer (multiprover) games implies super-linear lower bounds for multi-tape Turing machines with advice. To the best of our knowledge, this is the first connec
We prove a query complexity lower bound for $mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $mathsf{SBP}^A otsubset mathsf{QMA}^A$, resolving
Dawar and Wilsenach (ICALP 2020) introduce the model of symmetric arithmetic circuits and show an exponential separation between the sizes of symmetric circuits for computing the determinant and the permanent. The symmetry restriction is that the cir
In this paper we give lower bounds for the representation of real univariate polynomials as sums of powers of degree 1 polynomials. We present two families of polynomials of degree d such that the number of powers that are required in such a represen