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Lower Bounds Against Circuits with Modular Gates

By theoryapp Posted on December 27, 2020 Posted in Theory Tagged with acc circuit, circuit lower bound

The modular gate MODm, for any integer \(m\), outputs 0 if the sum of its inputs is 0 modulo \(m\), and outputs 1 otherwise. An ACC[m] circuit is a circuit with NOT gates and unbounded fan-in AND, OR, and MODm …

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Combinatorial Design and Pseudorandom Generator

By theoryapp Posted on December 26, 2020 Posted in Theory Tagged with chernoff bound, combinatorial design, pseudorandom generator

For a set of size \(l\), choose \(m\) subsets each of size \(n\) such that each pair of subsets has intersection size at most \(d\). This gives a combinatorial design with parameters \((m,l,n,d)\). That is, we have \(I_1,\ldots, I_m \subseteq …

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Embed Google Maps Image and Street View

By theoryapp Posted on December 24, 2020 Posted in Web Tagged with google maps, street view

Google Maps APIs provide easy ways to embed maps images. The following are static map image, satellite image and street view image of “Lincoln Memorial”. Static Maps API supports map images with custom styles, markers, satellite maps. The following is …

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Time and Space Complexity Class

By theoryapp Posted on December 20, 2020 Posted in Theory

Robust classes are those such that no reasonable changes to the model of computation should change the class; capable of classifying interesting problems. Examples \(\mathsf{L}\) (contains Formula Value, integer multiplication and division), \(\mathsf{P}\) (contains circuit value, linear programming, max flow), …

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