The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.

Introduction. If d is a positive square-free integer let Id be the ring of integers in Q(\Jd). Id is a Euclidean domain if d = 1, 2, 3, 7, 11. The groups PSL2(/d) = Fd over these Euclidean rings have recently been investigated. Methods for generating presentations as well as actual presentations were given in [2], [3] and [8], while these groups were shown to be describable in terms of generali...

In many geographical applications there is a need to model spatial phenomena not simply by sharp objects but rather through indeterminate or vague concepts. To support such applications we present a model of vague regions which covers and extends previous approaches. The formal framework is based on a general exact model of spatial data types. On the one hand, this simplifies the definition of ...

Abstract Classical sets are used commonly to consider reliability. Because of the uncertainty in data (which considered present paper) classical fail describe reliability accurately. Uncertainty leads fluctuation actual situation structure. Fuzzy logic method attempts test system with benefit membership function. Within this context, specific problems reasoning-based approaches studied, explore...