We need a language to read a book, and that affects our thought process, as we start thinking like the author and behave in a manner we perceive from the books. Like how someone speaks under the influence of alcohol, books n authors too influence.
Sawdust that is created from cutting natural wood is safe for your compost no matter what kind of tree the wood comes from. Just make sure the wood has not been treated with any chemicals. Another option with sawdust is to try mixing it in with potting soil.
However, it may not be a good idea to use charcoal ashes, such as those from grills. Compost with charcoal can have chemical residue from the additives in the charcoal. These chemicals can be harmful to plants, especially when used in large amounts.