We define and discuss symmetric subgroup membership problems and their properties, including a relation to the Decision DiffieHellman problem. We modify the Cramer-Shoup framework, so that we can derive a chosen ciphertext secure cryptosystem in the standard model from symmetric subgroup membership problems. We also discuss how chosen ciphertext secure hybrid cryptosystems based on a symmetric ...

We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. A more complete exposition can be found in 4]. Canonical bases for subalgebras of the commutative polynomial ring were introduced by Kapur and Madlener (see 2]), and independently by Robbiano and Sweedler ((5]). Some notes on the non-commutative case can be found in 3]. Using the la...

Leftist grammars were introduced by Motwani et al., who established the relationship between the complexity of the accessibility problem (or safety problem) for certain general protection systems and the membership problem for these grammars. The membership problem for leftist grammars is decidable. This implies the decidability of the accessibility problem. It is shown that the membership prob...

Macro tree transducers (mtts) are a useful formal model for XML query and transformation languages. In this paper one of the fundamental decision problems on translations, namely the “translation membership problem” is studied for mtts. For a fixed translation, the translation membership problem asks whether a given input/output pair is element of the translation. For call-by-name mtts this pro...

The maximal dimension of a commutative subalgebra of the Grassmann algebra is determined. It is shown that for any commutative subalgebra there exists an equidimensional commutative subalgebra spanned by monomials. It follows that the maximal dimension of a commutative subalgebra can be expressed in terms of the maximal size of an intersecting system of subsets of odd size in a finite set. 2010...

We show that the uniform membership problem of context-free tree grammars is PSPACE-complete. The proof of the upper bound is by construction of an equivalent pushdown tree automaton representable in polynomial space. With this technique, we can also give an alternative proof that the respective nonuniform membership problem is in NP. A corollary for uniform membership of "-free indexed grammar...

We consider the problem of proper learning a Boolean Halfspace with integer weights {0, 1, . . . , t} from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks n ) membership queries where the best lower bound for the number of membership queries is n [4]. In this paper we close this gap and give an adaptive proper learning algorithm with two rou...

We discuss various aspects of the noncommutative geometry a smooth subalgebra Toeplitz algebra. In particular, we study structure derivations on this subalgebra.