you should learn to separate wishful thinking and facts; and go by facts.
1. yes they, meaning jihadi nuts, are connected with people of Pakistan. that is how they get support and recruit. they get recruits from the people using mullas and religion; they get money and training from Pak army. That is the unholy nexus that is at the root of all problems in Pakistan.
2. USA supported Pakistan in fighting off the soviet invasion of Afghanistan in order to SAVE Paksiatn from being taken over by communism from Soviet Russia and China. The way Pakistan executed that was to take money and weapons from the west (including Isreal!) to fight through the jihadi groups such as mujhideen. Where they made the mistake (intentionally) was they diverted a lot of these to intrude into India to cause terrorism in J&K. In that process they killed thousands of innocent people, corrupted and incited youth in the name of your religion; thus earned the name of terrorist state for your country! If you want more proof just look up what your own political leaders said about Kasab, Osama, DawoodIbrahim etc. It is not just your mullas, government leaders and military - even popular cricker such as Miandad and Imrah Khan openly support terrorists. Check photographs of Miandad kid marrying Dawood Ibrahim's kid. Or Imran Khan's statements about Taleban even as your army is doing the so called ZAB!
3. even you must be laughing when you say your army is doing the ZAB operation! they created funded and managed the terrorists - it has been proven with video and audio evidence (just google it). Ontop ofthat your ISI director Hamid Gul has accepted it in interviews. Now that the pressure from counntries from whom Pakistan receives financial support have threatened to stop giving money unless your country take some action, they started some operation. Even then nothing happened until West told them that if you don't do it, we will come in and do it.
So don't fool yourself thinking your army and government are somehow suddenly against the terrorists. Pakistan's ability to fool th worldin this regard no longer works.