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A polynomial time isomorphism test for a class of groups, properly containing the class of abelian groups, is presented. Isomorphism testing of group presentations for (a subclass of) the same class of groups is shown to be (graph) isomorphism complete. These seem to be the first known isomorphism complete problems in group theory. Subexponential tests are presented as well for rings and algebras.
A basic question in the area of asynchronous computation is: Given a synchronization problem, what synchronization primitives are needed for a solution? This paper is directed toward answering this question by characterizing the "behavior" of synchronization systems incorporating PV, PV multiple, PV chunk and PV general synchronization primitives.
It is an open problem, suggested by Papert and McNaughton, to find a decision procedure for determining whether a regular event is locally testable. In this paper we provide a partial solution, giving two effectively decidable conditions, one necessary and one sufficient, for local testability. Our proofs are for the most part algebraic, using machine decompositions and semigroup theory.
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