Final answer:
The characteristic not required for statehood is their own written language. States are defined by population, borders, and sovereignty, not by having a unique written language.
Step-by-step explanation:
The characteristic of a state that does NOT apply is d) Their own written language. A state is defined by having a population, regardless of its size, recognized borders, and sovereignty, which allows it to decide on its own domestic and foreign policies without the oversight of other nations. Having a written language is not a prerequisite for statehood as states can and do exist with multiple languages or use a common language shared with other states.