How Much Data Is Sufficient to Learn High-Performing Algorithms?
Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made available for the ...
Pure-Circuit: Tight Inapproximability for PPAD
The current state-of-the-art methods for showing inapproximability in PPAD arise from the ε-Generalized-Circuit (ε-GCircuit) problem. Rubinstein (2018) showed that there exists a small unknown constant ε for which ε-GCircuit is PPAD-hard, and subsequent ...
A Logical Approach to Type Soundness
Type soundness, which asserts that “well-typed programs cannot go wrong”, is widely viewed as the canonical theorem one must prove to establish that a type system is doing its job. It is commonly proved using the so-called syntactic approach (aka progress ...
A Generalized Method for Proving Polynomial Calculus Degree Lower Bounds
We study the problem of obtaining lower bounds for polynomial calculus (PC) and polynomial calculus resolution (PCR) on proof degree, and hence by [Impagliazzo et al. ’99] also on proof size. [Alekhnovich and Razborov ’03] established that if the clause-...
Transaction Fee Mechanism Design
Demand for blockchains such as Bitcoin and Ethereum is far larger than supply, necessitating a mechanism that selects a subset of transactions to include “on-chain” from the pool of all pending transactions. This paper investigates the problem of ...
Sparse Higher Order Čech Filtrations
For a finite set of balls of radius r, the k-fold cover is the space covered by at least k balls. Fixing the ball centers and varying the radius, we obtain a nested sequence of spaces that is called the k-fold filtration of the centers. For k = 1, the ...
The Bitcoin Backbone Protocol: Analysis and Applications
Bitcoin is the first and most popular decentralized cryptocurrency to date. In this work, we extract and analyze the core of the Bitcoin protocol, which we term the Bitcoin backbone, and prove three of its fundamental properties which we call Common ...