[This is adapted from part of paper I’m working on with Charles Reiss.]

Assimilation is a key notion for many phonological theories, and there are even intimations of it in the Prague School. Hyman provides an early formalization: he defines it as the insertion of a feature specification αF on a segment immediately adjacent to another segment specified αF.

(1) Assimilation schemata (after Hyman 1975: 159):
X → {αF} / __ [αF]
X → {αF} / [αF] __

In autosegmental phonology, assimilation is instead conceptualized as the sharing (rather than the “copying”) of feature specification via the insertion of association lines and phonological tiers provide a more general notion of adjacent, but the basic notion remains the same.

Substance-free phonology (SFP) also makes use of these “Greek letter” coefficients to express segmental identity (or non-identity) between features on various segments. What SFP denies is that there is any need to recognize or formalize notions like assimilation (or dissimilation) in the first place, because SFP rejects the notion of formal markedness. Yes, there are rules that cause an obstruent to agree in voicing with an obstruent to its immediate right, or which delete a glide between identical vowels, or which raise mid vowels before high vowels, and SFP can easily express such rules. However, there are also rules which raise mid vowels before low vowels, before nasals, or before a word boundary. The following principle expresses this position in general terms:

(2) Substance-freeness of structural change: featural specifications changed by rule application need not be present in the rule’s structural environment.

This principle is a claim that proposed phonological rules need not “make sense” in featural terms. It holds that the whatness of a rule, what feature is being added to a segment, is logically independent of the whereness, the triggering environment. This in turn echos Chomsky & Halle’s (1968:428) claim that “the phonological component requires wide latitude in the freedom to change features.” Note that principle (2) is not itself an axiom of SFP, but rather something which is not part of the theory.

References

Chomsky, N. and Halle, M. 1968. The Sound Pattern of English. Harper & Row.
Hyman, L. M. 1975. Phonology: Theory and Analysis. Holt, Rinehart and
Winston.