Before revision:  We first provide an alternate  proof to show that vanilla Transformers are Turing-complete and then we prove that Transformers with  positional masking and without any positional encoding are also Turing-complete.
After revision:  We first provide an alternate proof to show that vanilla Transformers are Turing-complete and then we prove that Transformers with only positional masking and without any positional encoding are also Turing-complete.