Roger Federer and Andy Murray reached the semi-finals of the ATP’s Dubai Open on Thursday.

Federer, the Grand Slam record-holder from Switzerland, won for the 12th time in as many meetings with Mikhail Youzhny, the former world number eight from Russia.

His 6-3 6-4 success kept him on course for a record fifth title here.

Murray, the first British male since the 1930s to reach three Grand Slam finals, gained revenge 6-3 7-5 over Tomas Berdych, to whom he lost in their past three meetings, making it Murray’s best sequence in four attempts at the lucrative Middle East tournament.

The match ended in controversy as Berdych argued at length with the umpire over a Hawkeye decision when he had a point to break back for 6-6 in the final game

Murray’s appeal to the computer replay showed that the line judge’s call of fault had been wrong and that Murray’s unreturned serve had in fact been in.

But when the Scot was awarded the point, Berdych claimed the rally should have been replayed, arguing with Swedish umpire Mohamed Lahyani that the line judge’s call had interfered with his return of serve.

However TV replays showed that the out call came after Berdych had hit the ball, suggesting Lahyani’s decision may have been correct.

Murray went on to close the match out in that game, though he required six more rallies and seven match points altogether before doing it.

Berdych said he had been “shocked” by Lahyani’s decision.

“If we look at all the rule books we going to see that if it’s not a clear ace there is a repeat of point actually,” Berdych claimed.

“I have no idea what Mohamed did. He is the best referee on tour and I never had anything like that with him.”

Murray commented: “It’s a bad rule, and one that I have a big problem with.

“It comes down to kind of how the umpire sees it. You know, they don’t always see it the same way as the players do. Sometimes it goes your way; sometimes it doesn’t.”

Federer’s smooth and solid performance suggested that his fuller schedule so far during 2012 – having included Rotterdam and the Davis Cup – has helped make him match tight from the start of the week.

He established a break of serve in the fourth game of the first set, and the first game of the second, and consolidating the advantages right through.

“I played well on my service games,” added Federer, who went through both this match and his previous one with Feliciano Lopez of Spain without having dropped a service game.