I consider the use of computational simulations in phonology, and the benefits and dangers of making abstractions, or failing to make abstractions. I argue that the potential of simulation studies is not yet realised as it could be.

A computational notion of locality, based on forbidden substructures of a fixed size, is applied to autosegmental representations, and tone-association patterns are argued to be local. This is significant for phonological theory, for two reasons. First, this notion of locality provides for an explicit theory of tonal well-formedness that is superior to previous explanations in that it makes clear, restrictive typological predictions. Second, it provides a clear path for understanding how these patterns can be learned. A brief survey of major tone-association patterns shows that association generalisations which are edge-based (Mende and Hausa), quality-specific (Kukuya) or positional (Northern Karanga Shona) are all local in this way. This is contrasted with previous explanations of the typology, which require global reference to the directionality of association, and can thus overgenerate.

Domains play an integral role in linguistic theories. This paper combines locality domains with current models of the computational complexity of phonology. The first result is that if a specific formalism – strictly piecewise grammars – is supplemented with a mechanism to enforce first-order definable domain restrictions, its power increases so much that it subsumes almost the full hierarchy of subregular languages. However, if domain restrictions are based on linguistically natural intervals, we instead obtain an empirically more adequate model. On the one hand, this model subsumes only those subregular classes that have been argued to be relevant for phonotactic generalisations. On the other hand, it excludes unnatural generalisations that involve counting or elaborate conditionals. It is also shown that strictly piecewise grammars with interval-based domains are theoretically learnable, unlike those with arbitrary, first-order domains.

This article presents a selection of methods to analyse, compare, verify and formally prove properties about phonological generalisations. Drawing from both well-known and recent results in the domains of model checking and automata theory, a useful methodology for automating the task of comparing analyses and inventing counterexamples is explored. The methods are illustrated by practical case studies that are intended to both resolve concrete issues and be representative of typical techniques and results.