AN MD83 AT BOS IS CLRED TO TAXI VIA KILO; SIERRA; HOLD SHORT OF RWY 4L; EXPECT RWY 9. AS TAXI BEGINS FO NOTICES THE ACARS MALFUNCTION AND CHANGES TO #2 RADIO TO RECEIVE CLOSEOUT NUMBERS. CAPT TAXIES ONTO TXWY S AND CONTINUES ACROSS RWY 4L TO RWY 9.

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DURING TAXI FOR DEP; AN INITIAL TAXI CLRNC WAS RECEIVED OF 'TAXI VIA KILO; SIERRA; HOLD SHORT OF 4L; EXPECT RWY 9.' THE FO READ BACK THE CLRNC; WHICH I THEN ACKNOWLEDGED. AFTER CLRING L AND R; I BEGAN TO TAXI. THE FO THEN DISCOVERED THE ACARS PRINTER HAD MALFUNCTIONED; AND SWITCHED TO THE NO 2 RADIO TO OBTAIN CLOSEOUT DATA FROM THE COMPANY. I CONTINUED TO MONITOR ATC. AT TXWY SIERRA; I CLRED L AND R; ILLUMINATED THE ACFT AND MADE THE TURN ONTO SIERRA; WHICH THEN TOOK ME ACROSS RWY 4L. THREE QUARTERS OF THE WAY ACROSS RWY 4L; GND STATED; 'I SEE YOU ARE CROSSING RWY 4L; CONTACT THE TWR ON 128.8.' ON INITIAL CONTACT WITH THE LOCAL CTLR; SHE REPLIED; 'WHAT WAS YOUR LAST CLRNC?' I RESPONDED; 'KILO; SIERRA; HOLD SHORT OF RWY 9;' WHICH WAS IN FACT WHAT I THOUGHT OUR CLRNC WAS AT THAT POINT IN TIME. WE THEN WERE ASKED TO CALL THE TWR ON OUR ARRIVAL AT OUR DESTINATION. UPON DISCUSSION WITH THE FO AND TWR MANAGER; I REALIZED THAT WE WERE TO HOLD SHORT OF RWY 4L AND EXPECT RWY 9. THERE HAD BEEN NO CONFLICT WITH ANY OTHER ACFT; AND IT HAD NOT CAUSED ANY REDIRECTION OF TFC. I BELIEVE CONTRIBUTING FACTORS TO THIS RWY INCURSION ARE AS FOLLOWS. FIRST; THE ATIS HAD BROADCAST THE RWYS IN USE TO BE RWY 4R AND 9. RWY 4L WAS NOT CURRENTLY IN USE. THIS WAS FIXED IN THE BACK OF MY MIND. SECONDLY; THE FO HAD LEFT THE ATC FREQ. WHILE HE CORRECTLY REMEMBERED OUR INITIAL TAXI CLRNC; HE THOUGHT I HAD RECEIVED FURTHER CLRNC WHILE HE WAS OFF THE ATC FREQ; AND DID NOT CHALLENGE ME THEREFORE; WHEN I BEGAN TO CROSS RWY 4L. THE FO WAS ALSO VERY NEW; AND MAY HAVE BEEN HESITANT TO CHALLENGE OR QUESTION MY ACTION. OTHER FACTORS WERE THAT TXWY SIERRA IS VERY SHORT WHERE IT JOINS RWY 4L FROM KILO; SO THAT IN ORDER TO TURN ONTO SIERRA WITH A LARGE ACFT ENTAILS MOVING ONTO RWY 4L. LASTLY; I COULD SEE ANOTHER ACFT TAXIING ACROSS THE APCH END OF RWY 4L DOWNFIELD ON HIS WAY TO RWY 9. THESE THINGS ALL MOVED ME TO THINK OUR CLRNC HAD BEEN TO CROSS RWY 4L AND HOLD SHORT OF RWY 9 ON SIERRA. I THINK A BETTER PHRASEOLOGY FOR THE ORIGINAL CLRNC SHOULD HAVE BEEN; 'TAXI VIA KILO; HOLD SHORT OF RWY 4L AT SIERRA;' INSTEAD OF TAXI VIA KILO; SIERRA; HOLD SHORT OF RWY 4L; DUE TO THE VERY SMALL SECTION OF TXWY AT THE INTERSECTION. IN THE FUTURE I WILL VERBALLY VERIFY WITH THE FO ANY RWY CROSSING BEFORE CROSSING IT. SUPPLEMENTAL INFO FROM ACN 510002: WHEN I HEARD 'SWITCH TO 128.8.' I THEN REALIZED THAT WE WERE CROSSING RWY 4L; AND THOUGHT THAT THE CAPTAIN WAS GIVEN CLRNC TO CROSS RWY 4L PRIOR TO ME HEARING THE FREQ CHANGE. WHEN THE TWR TOLD US TO COPY A NUMBER AND CALL IT AT OUR DESTINATION; THE CAPTAIN THEN HAD ME CONFIRM WHAT THE CLRNC WAS; AND I SAID IT WAS KILO; SIERRA; HOLD SHORT OF RWY 4L. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT HE CALLED THE TWR AND DISCUSSED THE PROB. THERE WILL BE NO ACTION TAKEN. RPTR FEELS HE HAS LEARNED TO QUESTION HIMSELF AND FO PRIOR TO CROSSING ANY RWY TO ASSURE THEY HAVE CLRNC. SINCE THERE WAS NO CONFLICTING TFC AND HE KNEW RWY 4L WAS NOT IN USE WHICH HE FEELS MAY HAVE GIVEN HIM A FALSE SENSE OF THE CLRNC BEING TO RWY 9. THE SHORT DISTANCE ON TXWY S IS ALSO A CONTRIBUTING FACTOR AS THE HOLD SHORT LINE IS AT THE BEGINNING OF THE TXWY. THE ACARS BEING OTS WAS THE ADDED PROB WHICH TOOK THE FO OUT OF THE LOOP.