Galois cohomology and some questions of the theory of algorithms

Let $G$ be an arbitrary linear algebraic group defined over an algebraic number field $K$, let $R$ be its solvable radical, let $S=G/R$, and let $\widetilde S$ be the simply connected covering group of $S$. The basic result of the paper asserts that whether any two Galois 1-cocycles in $Z_1(K,G)$ are cohomologous is algorithmically verifiable, if the “Hasse principle” holds for $\widetilde S$.
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