In dictionary/membership problem, we want to keep a set S of items with possibly some extra information associated with each one of them. (From now on, we denote the number of elements in S by n.) For the membership problem, the goal is to create a data structure that allows us to ask whether a given item x is in S or not. For a dictionary, the data structure should also return the infomation a...

Gain graphs are graphs in which each edge has a gain (a label from a group so that reversing the direction of an edge inverses the gain). In this paper we take a generalized view of gain graphs in which the label of an edge is related to the label of the reverse edge by an involution, i.e., an anti-automorphism of order at most two. Switching classes are equivalence classes of gain graphs under...

We introduce a combinatorial version of Stallings-Bestvina-Feighn-Dunwoody folding sequences. We then show how they are useful in analyzing the solvability of the uniform subgroup membership problem for fundamental groups of graphs of groups. Applications include coherent right-angled Artin groups and coherent solvable groups.

Given a monomial ideal I = 〈m1,m2, · · · ,mk〉 where mi are monomials and a polynomial f as an arithmetic circuit the Ideal Membership Problem is to test if f ∈ I . We study this problem and show the following results. (a) If the ideal I = 〈m1,m2, · · · ,mk〉 for a constant k then there is a randomized polynomial-time membership algorithm to test if f ∈ I . This result holds even for f given by a...

We introduce a model of one-way language acceptors (a variant of a checking stack automaton) and show the following decidability properties: 1. The deterministic version has a decidable membership problem but has an undecidable emptiness problem. 2. The nondeterministic version has an undecidable membership problem and emptiness problem. There are many models of accepting devices for which ther...

With the aim of applying Dokdo structure to BE-algebra, notions (weak) BE-subalgebra and BE-filter are introduced, their properties investigated. The relationship between weak BE-subalgebra, is established. conditions under which can be BE-filter,and condition explored. Characterizations provided.

We show that a number of natural membership problems for classes associated with finite semigroups are computationally difficult. In particular, we construct a 55-element semigroup S such that the finite membership problem for the variety of semigroups generated by S interprets the graph 3-colorability problem.

We study the problem of extending a state on an abelian C∗-subalgebra to a tracial state on the ambient C∗-algebra. We propose an approach that is well-suited to the case of regular inclusions, in which there is a large supply of normalizers of the subalgebra. Conditional expectations onto the subalgebra give natural extensions of a state to the ambient C∗-algebra; we prove that these extension...

‎In this paper‎, ‎we investigate the invariant elements of the dual mod $p$ Steenrod subalgebra ${mathcal{A}_p}^*$ under the conjugation map $chi$ and give bounds on the dimensions of $(chi-1)({mathcal{A}_p}^*)_d$‎, ‎where $({mathcal{A}_p}^*)_d$ is the dimension of ${mathcal{A}_p}^*$ in degree $d$‎.

Abstract The problem of finding generators the subalgebra invariants under action a group automorphisms finite-dimensional Lie algebra on its universal enveloping is reduced to homogeneous same acting symmetric tensor algebra. This process applied prove constructive Hilbert–Nagata Theorem (including degree bounds) for in nilpotent relatively free associative endowed with an induced by represent...