We study two group theoretic problems, Group Intersection and Double Coset Membership, in the setting of black-box groups, where Double Coset Membership generalizes a set of problems, including Group Membership, Group Factorization, and Coset Intersection. No polynomial-time classical algorithms are known for these problems. We show that for solvable groups, there exist efficient quantum algori...

This paper introduces a class of formal grammars made up by augmenting the formalism of context-free grammars with an explicit set-theoretic intersection operation. It is shown that conjunctive grammars can generate some important non-context-free language constructs, including those not in the intersection closure of context-free languages, and that they can provide very succinct descriptions ...

We express the Euler-Poincaré characteristic of a semi-algebraic set, which is the intersection of a non-singular complete intersection with two polynomial inequalities, in terms of the signatures of appropriate bilinear symmetric forms.