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The phrase "absence of a functioning" is correct and usable in written English.
It can be used in contexts where you are discussing the lack of something that is operational or effective, often in technical or formal writing.
Example: "The absence of a functioning system has led to significant delays in project completion."
Alternatives: "lack of an operational" or "nonexistence of a working".
Exact(52)
In the absence of a functioning national government, it's the only way to begin stabilizing parts of the country.
And in the absence of a functioning local government, the commercial radio station The Bay provided the main information hub.
The absence of a functioning public administration to enforce rules was also a key obstacle.
These outsiders exploited the absence of a functioning Somali state capable of protecting its coastal waters.
In the absence of a functioning financial system, the Federal Reserve announced plans this week to lend money to companies that cannot get credit in the free market.
The absence of a functioning jail means uncertainty over what to do with al-Shabaab members who are captured or who defect.
Similar(8)
But past presidents have found that when it comes to foreign interventions, it's very difficult to achieve and sustain military gains in the absence of a stable, functioning government and the institutions that go along with it.
In the absence of a fully functioning Iraqi police force or national intelligence service, agencies like the Army's Criminal Investigative Division and the Federal Bureau of Investigation have taken on a larger role.
In the absence of a properly functioning electricity demand side, well-designed capacity payment mechanisms hold more promise for signaling the value of capacity than non-CPM alternatives.
In order to determine the allowed sequences, in the absence of a function-based assay, we chose to first simultaneously randomize two different amino acid positions.
Unlike the PRKO mouse, however, the PRAKO mammary gland developed normally in the absence of PR-A function [ 29].
More suggestions(1)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com