Is it true that any language that can be accepted by a polynomial time alternating Turing machine with existential and universal states can be accepted by a polynomial time alternating Turing machine with only existential and negating states?It is known that any language that can be accepted by an alternating Turing machine with existential, universal, and negating states can be accepted by an alternating Turing machine with only existential and universal states. 
Polynomial time alternating Turing machines with only existential and negating states
complexity theory