We identify the computational complexity of the satisfiability problem for FO, the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO has the finit...

We discuss two fundamental problems that arise in distributed systems. First, how to determine the order in which various events were executed. Second, how to obtain a consistent view of the system. To address the first problem, we describe different schemes that implement an abstract notion of time and can be used to order events in a distributed system. To address the second problem, we discu...

Secure Message Transmission (SMT) is a two-party cryptographic protocol by which the sender can securely and reliably transmit messages to receiver using multiple channels. An adversary corrupt subset of channels commit eavesdropping tampering attacks over In this work, we introduce game-theoretic security model for SMT in adversaries have some preferences execution. We define rational “timid” ...

Despite the presence of many famous examples, the precise interplay between basic hypergeometric series and modular forms remains a mystery. We consider this problem for canonical spaces of weight 3/2 harmonic Maass forms. Using recent work of Zwegers, we exhibit forms that have the property that their holomorphic parts arise from Lerch-type series, which in turn may be formulated in terms of t...

While it is called by many names and comes in different varieties, SScl is characterized by one basic problem: overproduction of collagen. Collagen is an important protein in the body that is a component of scar tissue, which allows injuries to heal. When too much collagen is deposited, however, a number of problems can arise, and this is the basic obstacle that must be faced in patients with S...