Vegetarian Restarant

Question

If an unsupervised restaurant advertises and claims itself to be a vegetarian restaurant (ie- no meat products) can one rely that in fact there are no meat products being used? The specific scenario I am referring to involved a pita restaurant with a unreliable hashgacha. If the restaurant is representing itself to be vegetarian, does halacha allow me to assume that it is? Also, is there a bishul akum problem regarding falafel balls? If there is not a bishul akum problem, and they are being served in a vegetarian restaurant, I would like partake. Thank you for this tremendous service that you are providing. Erica