AN ACR LTT CREW CROSSED AN ACTIVE RWY WITHOUT CLRNC.

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WE ARRIVED AT SYR ARPT AT XA58 PM ON A SCHEDULED PAX FLT. WE WERE ABOUT TO DEPART ON OUR FINAL LEG OF A 3 DAY TRIP. THE PREVIOUS NIGHT WAS A REDUCED REST OVERNIGHT AND WE WERE NOW INTO OUR 11TH HR OF DUTY TIME. WE WERE ABOUT TO COMPLETE OUR 10TH HR OF FLT TIME OF THE TRIP. AT XE00; AFTER A 3 HR LAYOVER; WE WERE GIVEN A DELAY INTO BOSTON WITH AN UPDATE TIME OF XF00. FROM XE00 TO XF00 I SLEPT UNCOMFORTABLY IN THE ACFT AS I WAS EXTREMELY FATIGUED AND WE HAVE NO CREW LOUNGE TO REST IN. AT XF00 I AWOKE AND CALLED CLRNC TO FIND OUT WE WERE RELEASED. AT XF11 WE WERE PULLING OUT OF THE CHOCKS; CLRED TO TAXI TO RWY 28 (I WAS STILL GROGGY). DURING MY TAXI; MY FO INFORMED ME WE WERE CLRED TO CROSS ALL RWYS. THEN HE BRIEFED THE FLT ATTENDANT TO PREPARE FOR DEP. HE RETURNED TO THE LOOP TO COMPLETE THE BEFORE TKOF CHKLIST. WHILE PERFORMING THE CHKLIST; WE TAXIED ACROSS RWY 28 TO RWY 32. THE CTLR ASKED US IF WE KNEW WE HAD CROSSED THE ACTIVE RWY. I TOLD HIM WE WERE NOT AWARE AND GAVE MY APOLOGIES. CONTRIBUTING FACTORS WERE FATIGUE AND STRESS TO MAKE UP TIME FOR THE DELAY RECEIVED. SUPPLEMENTAL INFO FROM ACN 245351: WHILE TAXIING TO THE RWY; CLRED FOR TKOF; PF FAILED TO TURN L AND PROCEEDED ACROSS ACTIVE RWY. NO ACFT WERE IN ATA DURING EVENT. I; AS PNF; WAS 'HEADS DOWN' ACCOMPLISHING BEFORE TKOF TASKS AND CHKLISTS.