ACFT Y IS GIVEN A CLRNC TO CROSS THE RWY AS ACFT X IS TAKING OFF.

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I WAS WORKING GND CTL. I HAD 2 GLF4 ACFT AND A CL60 TAXIING FOR DEP TO RWY 9L FROM FBO. TAXI RTE: TXWY E CROSS RWY 31 TXWY F CROSS RWY 9L TXWY C TO RWY 9L. I HAD PREVIOUSLY TAXIED A COMMUTER TO RWY 13 FOR DEP. WHEN I PLACED THE COMMUTER'S DEP STRIP IN THE LCL CTL STRIP BAY; I INFORMED LCL AND CAB COORDINATOR (SUPVR) THAT I NEEDED TO CROSS THE DEP END OF RWY 13; 3 TIMES. I ANSWERED A FEW MORE CALLS THEN HEARD LCL SAY 'YOU'RE GOOD FOR RWY 13.' I TOOK THAT AS APPROVAL TO CROSS RWY 13 DEP END AND ISSUED CLRNCS TO CROSS RWY 13 WITH THE 2 GLF4'S AND THE CL60. LCL TOLD ME TO 'STOP THAT GUY;' POINTING AT THE FIRST GLF4. I LOOKED AND SAW THE BE02 THAT HAD DEPARTED; AND THE NOSE OF THE GLF4 APPEARED TO BE ON THE RWY. 2 ISSUES I FEEL CONTRIBUTED TO THIS ERROR: 1) WHEN WORKING GND CTL AND HAVING A LCL CTLR APPROVE MY REQUEST TO CROSS AN ACTIVE RWY WITHOUT USING THE PHRASEOLOGY 'CROSS;' I'VE ALWAYS QUESTIONED THE COORD. I BROKE MY OWN RULE AND DID NOT AFFECT POSITIVE COORD FOR THE RWY XING. 2) AT PBI; ACFT PARKED AT THE FBO'S HAVE TO CROSS 2 ACTIVE RWYS; REGARDLESS OF RTE; TO GET TO RWY 9L. RWY INCURSIONS WILL PROBABLY CONTINUE WITH THIS TAXI FLOW.