Abstract. The factorisation problem is to construct the specification of a submodule X when the specifications of the system and all submodules but X are given. It is usually described by the equation P [ X e Q where P and X are submodules of system Q, I is a composition operator, and & is the equivalence criterion. In this paper we use a finite state machine (FSM) model consistent with CCS and study two factorisation problems: P III X-Q and P III X ~ Q, where Ill is a derived CCS composition operator, -and ~ represent strong and observational equivalences. Algorithms are presented and proved correct to find the most general specification of submodule X for P III X -Q with Q r-deterministic and for P III X--~ Q with Q deterministic. Conditions on the submachines of the most general solutions that remain solutions to P III X Q (P I1[ X ~ Q) are given. This paper extends and is based on the work of M. W. Shields.
We investigate homogeneous geodesics in a class of homogeneous spaces G/K called generalized C-spaces. We give necessary conditions so that a G-invariant metric on G/K is a g.o. metric.
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