We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluat...
The LLL algorithm is a well-known and widely used lattice basis reduction algorithm. In many applications, its speed is critical. Parallel computing can improve speed. However, th...
We present the state of the art solvers of the Shortest and Closest Lattice Vector Problems in the Euclidean norm. We recall the three main families of algorithms for these problem...
The existence of optimal algorithms is not known for any decision problem in NP \ P. We consider the problem of testing the membership in the image of an injective function. We co...
Edward A. Hirsch, Dmitry Itsykson, Valeria Nikolae...
Set of lecture notes for the algorithms classes required for all computer science undergraduate and graduate students at the University of Illinois, Urbana-Champaign.