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The phrase "a complete specification of" is correct and usable in written English.
It can be used when discussing detailed descriptions or requirements of a product, system, or process.
Example: "The engineer provided a complete specification of the new software features to ensure all team members understood the project requirements."
Alternatives: "a thorough description of" or "a detailed outline of".
Exact(24)
In this paper, we propose an approach and a domain-specific language (DSL), named IIS⁎CFuncLang, aimed at enabling a complete specification of application-specific functionalities at the PIM level.
By design, the methods target specific feature of the dynamic system and do not require a complete specification of the time-series evolution.
See http://nifti.nimh.nih.gov for a complete specification of this file format.
The CellBuilder can write a hoc file that contains a complete specification of geometry and biophysics.
A complete specification of the Clark-Jacob library in CAPSL is available at http://www.cs.sri.com/millen/capsl/].
But in a complete specification of these consonants the relative amplitudes of the formants also have to be given, because they are not completely predictable.
Similar(35)
For convenience, a complete specification is provided in Section 1 of the supplementary document The Simplest Quantified Modal Logic.
The notion of a platform as a precise and complete specification of the computational environment that a piece of software relies on is of particular importance for software preservation.
The second main component of a class predictor is complete specification of the mathematical function that will provide a predicted class label for any given expression vector.
A link leads to the complete specification of the model in OWL-DL.
His design for the Automatic Computing Engine (ACE) was the first complete specification of an electronic stored-program all-purpose digital computer.
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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