REGIONAL JET CREW PENETRATED P56 AIRSPACE AFTER TKOF AT DCA.

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ATC IRREGULARITY. NAV ERROR; TKOF; RESTR AIRSPACE DCA. WE TOOK OFF FROM DCA AT XA52Z AND IT WAS A NORMAL TKOF. IT WAS THE RWY 1 NOISE ABATEMENT PROC. WE FOLLOWED THE 328 DEG RADIAL OFF OF THE DCA VOR AND AFTER CLBING THROUGH APPROX 1700 FT; SELECTED FMS NAV AND THE COURSE WAS SHOWING THAT WE WERE L OF COURSE. WE NOTICED WE WERE OVER THE RIVER AS PRESCRIBED BY THE NOISE ABATEMENT PROC. I CHKED WITH FO IF HE COULD SEE THAT WE WERE CLR OF THE P56 AREA. AFTER HE SAID 'YES;' I STARTED A SHALLOW BANK TURN. ATC ADVISED US TO TURN L 270 DEGS IMMEDIATELY. WE DID SO IMMEDIATELY AND THEN AS WE WERE IN THE TURN TO 270 DEGS; ATC TOLD US TO ROLL OUT ON A NEW HDG OF 300 DEGS. WE WERE THEN ASKED TO CALL THE TWR WHEN WE GOT TO RDU. WE ALSO NOTICED ON THE FLT TO RDU THAT WE WERE GETTING INTERMITTENT MESSAGES STATING POS CORRECTING ON THE FMS. THIS OCCURRED AFTER BEING CLRED TO THE GORDONSVILLE VOR AND IT LASTED INTERMITTENTLY FOR ABOUT 5-7 MINS AND THEN CLRED ITSELF AND WE HAD NO FURTHER PROBS WITH THE FMS. UPON LNDG AT RDU I CALLED THE TWR AT DCA AND TALKED TO THE SUPVR. HE NOTIFIED US THAT WE HAD FLOWN INTO THE P56B AIRSPACE. I FOLLOWED UP WITH THE INFO HE REQUESTED AND HE ADVISED US THAT THE SECRET SVC WOULD BE IN TOUCH WITH US. WHEN WE ARRIVED IN RDU; WE WERE MET BY AN AGENT FROM THE SECRET SVC AND HE DEBRIEFED US IN RDU. SUPPLEMENTAL INFO FROM ACN 552715: UPON COMPLETING CLB CHKLIST AT APPROX 1700 FT AGL; WE SWITCHED TO FMS NAV AND RECEIVED INDICATION TO FLY R. CAPT ASKED ME TO CONFIRM WE WERE OVER POTOMAC RIVER. WE WERE OVER RIVER.