Sharpened lower bounds for cut elimination

Sharpened lower bounds for cut elimination

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our results remove the constant of proportionality, giving an exponential stack of...

Corrected upper bounds for free-cut elimination

Free-cut elimination allows cut elimination to be carried out in the presence of non-logical axioms. Formulas in a proof are anchored provided they originate in a non-logical axiom or non-logical inference. This paper corrects and strengthens earlier upper bounds on the size of free-cut elimination. The correction requires that the notion of a free-cut be modified so that a cut formula is ancho...

Streaming Lower Bounds for Approximating MAX-CUT

We consider the problem of estimating the value of max cut in a graph in the streaming model of computation. At one extreme, there is a trivial 2-approximation for this problem that uses only O(log n) space, namely, count the number of edges and output half of this value as the estimate for max cut value. On the other extreme, if one allows Õ(n) space, then a near-optimal solution to the max cu...

Lower Bounds for Elimination via Weak Regularity

We consider the problem of elimination in communication complexity, that was first raised by Ambainis et al. [1] and later studied by Beimel et al. [4] for its connection to the famous direct sum question. In this problem, let f : {0, 1} → {0, 1} be any boolean function. Alice and Bob get k inputs x1, . . . , xk and y1, . . . , yk respectively, with xi, yi ∈ {0, 1}. They want to output a k-bit ...

Some Lower Bounds for Estrada Index