Kindly guide me

i came across a signage "No smoking permitted in this area". I understand there are many ways to convey the same message such as "Smoking not permitted in this area" or "NO smoking area" etc. In my estimation the said message is incorrect as "No" and "permitted" are used together. Permitted or not permitted but no smoking permitted tantamounts to negating "NO" by placing permitted.

Regards,

Tahir Khan