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防衛省によりますと、日米地位協定では日本人従業員がアメリカ軍施設の外に銃を持ち出すことは認められておらず、銃刀法違反の疑いがあるということです。

Quoted from NHK Web News

Does it make any difference if I replace "認められておらず" with "認められず"?

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In short, ~は認められず is "~ is not allowed (, and...)", whereas ~は認められておらず is "~ has not been allowed (, and...)".

This (て)おらず is the negative form of (て)おり, which is a masu-stem of (て)おる, which is a variant of (て)いる. Therefore, this (て)おらず describes the lack of the continuation of a state.

As you may know, おる is basically a humble version of いる. But (て)おり and (て)おらず are exceptions, and they work as a neutral but stiffer equivalent of (て)いて and (て)いなくて, respectively.

See:

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