In [33], Ferdinand de Saussure proposes the idea of ``sign,'' which is composed of ``signifier'' and ``signified.'' He stresses that the signifier and the signified are as inseparable as the two sides of a piece of paper. In this sense, ``signs'' are atomic, since they are not further dividable. ``Sign'' consists of the centerpiece of semiotics and captures a crucial characteristic of language. For the sake of argument, let us try to ``force'' this view into a modern computational framework.
For a computer scientist who is accustomed to an analytic way of thinking, a dichotomy of ``signifier'' and ``signified'' seems to invite further analysis. Indeed, when it comes to the question of the ``meaning'' of a symbol, modern computer scientists (including computational linguists) tend to go deeper into the ``signified.'' For example, a naive ontology can be developed to represent the ``signified'' as a set of non-linguistic concepts. Specifically, in a computational implementation, the relation between ``signifier'' and ``signified'' is slot-filler or container-content.
In a computational model, these ``non-linguistic'' concepts of fillers or contents are entities implemented in a formal computer language engineered by human experts. In practice, a concept very often (perhaps always) turns out to be a composite concept and can be further analyzed. A computational linguist who is constrained by limited computational resources has to know when the analysis should come to a stop. In most cases, it is taken as a practical question -- it depends on the capacity of computational resources, the complexity of the domain of discourse, etc. These constrains result in a limited set of primitive concepts that are at the very bottom of the representation scheme. In any case, these primitives are linguistic objects embodied in a formal programming language. Moreover, the abstract embodiments are atomic, since they are not analyzed further. They are frames (because they are symbols) but also fillers. As far as the atomicity of these primitives is concerned, the ``slot-filler'' picture is remarkably similar to the original idea of the inseparability of ``signifier'' and ``signified.''
Note that the way with which we arrive at this conclusion is independent of the kind of computation used. This conclusion is equally valid in a quantum computational framework.