A B737 FLT CREW; TAXIING FOR TKOF AT SJC; CROSSED RWY 30R WITHOUT CLRNC.

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ON TAXI OUT; GND CLRED US TO (FROM GATE XX) 'MAKE A R ON TXWY H; CROSS TXWY Y AND BACK-TAXI ON RWY 30R UNTIL I ADVISE WHEN TO TURN OFF.' AS WE BACK TAXIED ON RWY 30R; GND ADVISED US TO 'TURN L ON NEXT INTXN TAXI ON TXWY Y AND HOLD SHORT OF RWY 30R.' THE CAPT COMPLIED WHEN WE GOT TO TXWY B HE KEPT TAXIING TO CROSS RWY 30R. I SAID; 'HEY WHERE ARE YOU GOING?' HE RESPONDED BY SAYING 'WHEN YOU'RE CLRED TO RWY 30L; YOU'RE CLRED ALL THE WAY.' I SAID OK AND QUESTIONED IF WE WERE CLRED TO RWY 30L OR RWY 30R. I THEN THOUGHT I MUST HAVE HEARD WRONG. ON THE OTHER SIDE OF TXWY B AND HOLDING SHORT OF RWY 30L; TWR ASKED IF WE CROSSED RWY 30R. I ANSWERED YES. HE CLRED US FOR TKOF ON RWY 30L. WE ASKED IF WE SHOULD CONTACT HIM. HE REPLIED NO. I FEEL I SHOULD HAVE BEEN MORE INQUISITIVE IN THE CAPT'S DECISION. IT NEVER HURTS TO ASK GND FOR VERIFICATION. SUPPLEMENTAL INFO FROM ACN 541971: WHILE TAXIING TO RWY 30L FOR DEP AT SJC; I CROSSED RWY 30R. TWR CALLED AND ASKED IF WE JUST CROSSED RWY 30R. I SAID YES AND THAT I THOUGHT GND HAD CLRED US TO RWY 30L. APCHING RWY 30R; THE FO QUESTIONED ME ABOUT ENTERING. I THOUGHT HE WAS ASKING IF IT WAS OK TO CROSS RWY 30R ON THE WAY TO RWY 30L. HE WAS REALLY ASKING IF WE HAD BEEN CLRED 'ON TO HOLD' AND HE MISSED IT. I TOLD HIM WE WERE CLRED; THINKING IT WAS LIKE EARLIER; WHEN WE CROSSED TXWY Y. IN THE FUTURE; I'LL PAY EVEN MORE ATTN TO CLRNCS. I'LL REPEAT ALL HOLD SHORT INSTRUCTIONS OUT LOUD AND USE MY TECHNIQUES EVERY TIME. I WILL STOP RATHER THAN SLOW DOWN IF EITHER PLT HAS A QUESTION ABOUT OUR CLRNC. I'LL ASK THE CTLR TO REPEAT THE INSTRUCTIONS IF THEY ARE SO LENGTHY OR COMPLICATED THAT WE'RE NOT ABSOLUTELY SURE OF THE CTLR'S INTENTIONS.