We give a function h : {0, 1} → {0, 1} such that every deMorgan formula of size n3−o(1)/r2 agrees with h on at most a fraction of 1 2 + 2 −Ω(r) of the inputs. This improves the previous average-case lower bound of Komargodski and Raz (STOC, 2013). Our technical contributions include a theorem that shows that the “expected shrinkage” result of H̊astad (SIAM J. Comput., 1998) actually holds with v...

The first two sections are largely based on the first two lectures by Oded Regev, course ”Lattices in Computer Science, Fall 2004. The third part is somewhat based on the paper by Oded Regev and Daniele Micciancio Worst-case to Average-case Reductions based on Gaussian Measures, SIAM Journal on Computing 37(1) pp. 267-302, 2007. and to a larger extent on the paper by O. Goldreich, S. Goldwasser...

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One of the key steps in Network-on-Chip-based design is spatial mapping of cores and routing of the communication between those cores. Known solutions to the mapping and routing problems first map cores onto a topology and then route communication, using separate and possibly conflicting objective functions. In this paper, we present a unified single-objective algorithm, called Unified MApping,...

The problem we are dealing with is the following: find two sequences an and bn such that the average of the first bn triangular numbers (starting with the triangular number 1) is still a triangular number, precisely the an-th triangular number. We get also some side results: for instance one of the sequence instrumental to finding the asked for sequences turns out to be a bisection of the seque...

The research field of networked systems has burgeoned during the last years attracting the attention of outstanding mathematicians, computer scientists and electrical engineers. This is due in no small part to the recent technological advances in communication and computation and to the miniaturization of electronic components which have made large groups of embedded systems, such as sensors an...