Rule-based approaches

Linear phonology

An utterance and the representations underlying that utterance are made up of a matrix of distinctive features with each column corresponding to a single segment.
Segments: bundles of unordered features
Utterances: ordered lists of segments
no tonal data discussed in this framework

Features have a place, like linear phonology, but segments do not.
Utterances: made up of several kinds of simultaneous levels
Two major theories
1. Metrical phonology (on stress and syllabification):i) relations of constituency and relative strength or prominence between contiguous prosodic unitsii) notation by a complex, binary-branching tree with labeled non-root nodes
2. Autosegmental phonology (tone, accent, and vowel harmony)i) abstracting out shared properties of possibly noncontiguous elements in an utteranceii) abstraction is mediated by a notation of simplex, n-ary branching trees, with the prosodic features of harmony or tone appearing on separate levels (tiers)iii) in short, the pieces of phonological representation (tones, segments, and features) are separate but coordinated by association lines

constraint-based approach by mapping the input and the output within the framework of generative grammar
the input is generally considered to be UG while the output is surface realization
major theoriesi) Containment theory (Prince and Smolensky, 1993/2002): Any SR output by GEN should include a representation of the UR as a subpart.ii) Correspondence theory (McCarthy and Prince, 1995)
advantages over rule-based theories:i) can predict the emergence of the unmarkedii) explanatory power of homogeneity of target/heterogeneity of process (e.g., rules applying different processes to the same target) thanks to the nature of factorial typology
disadvantages:opacity problems with regard to under application and over-application

opacity (McCarthy, 1999):i) underapplication (Generalization G plays an active role in language L, but there are surface forms of L that violate G)ii) overapplication (Generalization G shapes the surface form F, but the conditions that make G applicable are not visible in F)
feeding, counterfeiting, bleeding, and counter bleeding (https://linguistics.stackexchange.com/questions/6084/whats-the-difference-between-counterbleeding-bleeding-and-feeding)