Algorithms to test open set condition for self-similar set related to P.V. numbers

Fix a P.V. number $λ^{-1}>1.$ Given $\mathbf{p}=(p_{1},\cdots,p_{m})\in \mathbb{N}^{m}$, $\mathbf{b}=(b_{1},\cdots,b_{m})\in \mathbb{Q^{m}$, for the self-similar set $E_{\mathbf{p},\mathbf{b}}=\cup_{i=1}^{m}(λ^{p_{i}}E_{\mathbf{p},\mathbf{b}}+b_{i})$ we find an efficient algorithm to test whether $E_{\mathbf{p},\mathbf{b}}$ satisfies the open set condition (strong separation condition) or not.

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