His bicycle has a flat tire, he can't find the pump.
This is a run-on sentence. In order for this to be a complete sentence, you would have to add a semicolon between the two clauses, use a conjunction and a comma, or add a period and start a new sentence.
His bicycle has a flat tire; he can't find the pump.
His bicycle has a flat tire, and he can't find the pump.
His bicycle has a flat tire. He can't find the pump.
This sentence is not a compound or simple sentence because it isn't a complete sentence, and it is not a sentence fragment because it contains all the parts necessary to make a sentence, but uses a comma where it shouldn't.
