Selective <inline-formula> <tex-math notation="TeX">$\ell_{1}$</tex-math></inline-formula> Minimization for Sparse Recovery

On Approximate Horn Formula Minimization

The minimization problem for Horn formulas is to find a Horn formula equivalent to a given Horn formula, using a minimum number of clauses. A 2 1−ǫ(n)-inapproximability result is proven, which is the first inapproximability result for this problem. We also consider several other versions of Horn minimization. The more general version which allows for the introduction of new variables is known t...

The Complexity of Boolean Formula Minimization

The Minimum Equivalent Expression problem is a natural optimization problem in the second level of the Polynomial-Time Hierarchy. It has long been conjectured to be Σ2 -complete and indeed appears as an open problem in Garey and Johnson [GJ79]. The depth-2 variant was only shown to be Σ2 -complete in 1998 [Uma98], and even resolving the complexity of the depth-3 version has been mentioned as a ...

The Complexity of SPP Formula Minimization

Circuit minimization is a useful procedure in the field of logic synthesis. Recently, it was proven that the minimization of (∨,∧,¬) formulae is hard for the second level of the polynomial hierarchy [BU08]. The complexity of minimizing more specialized formula models was left open, however. One model used in logic synthesis is a three-level model in which the third level is composed of parity g...

Formula Layout Formula Layout

Both the quality of the results of TEX s formula layout algorithm and the complexity of its description in the TEXbook are hard to beat The algorithm is verbally described as an imperative program with very complex control ow and complicated manipulations of the data structures representing formulae In a forthcoming textbook we describe TEX s formula layout algorithm as a functional program tra...

Math 254a: the Analytic Class Number Formula, and Dirichlet Characters