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Building on recent work in subregular syntax, we argue that syntactic constraints are best understood as operating not over trees, but rather strings that track structural relations such as dominance and c-command. Even constraints that seem intrinsically tied to trees (e.g. constraints on tree tiers) can be reduced to such strings. We define serial constraints as an abstraction that decomposes string constraints into a context function (which associates nodes with strings) and a requirement function (which enforces constraints on these strings). We provide a general procedure for implementing serial constraints as deterministic tree automata. The construction reveals that the many types of constraints found in subregular syntax are variants of the same computational template. Our findings open up a string-based perspective on syntactic constraints and provide a new, very general approach to the automata-theoretic study of subregular complexity. 

We use the MG treebank of Torr (2017) to investigate the conjecture in Graf (2020) that category systems are ISL-2 inferrable. A category system is ISL-2 inferrable iff the category feature of every lexical item can be jointly inferred from phonological exponents of both the item itself and either its selecting head or the arguments it selects. If correct, this conjecture would greatly limit the overgeneration problem posed by subcategorization mechanisms. Our corpus study finds that the conjecture is largely borne out, with only a few exceptions attested in the corpus. However, we also observe that it holds even for features that aren't expected to be inferrable in this manner, and we demonstrate that inferrability can arise merely from language datasets displaying Zipfian distributions. We conclude that category systems in natural languages may well be ISL-2 inferrable, but that this could be due to extragrammatical factors. 

Even though languages can express a wide range of quantifiers, only a small number are ever realized as morphologically simplex determiners: every, no, some, and most. This is puzzling because I) most is much more complex than the other three, and II) quantifiers like an even number are simpler than most yet cannot belong to this class. Building on concepts from subregular complexity, I present a new way of measuring a quantifier’s complexity in terms of its verification pattern. The quantifiers every, no, some, and most all have strictly 2-local (SL-2) verification patterns, but quantifiers like an even number do not. This suggests that subregular complexity, and in particular strict locality, plays a crucial role for how much meaning can be packed into morphologically simplex expressions. 

Extending prior work in Graf (2018, 2020, 2022c), I show that movement is tier-based strictly local (TSL) even if one analyzes it as a transformation, i.e. a tree transduction from derivation trees to output trees. I define input strictly local (ISL) tree-to-tree transductions with (lexical) TSL tests as a tier-based extension of ISL tree-to-tree transductions. TSL tests allow us to attach each mover to all its landing sites. In general, this class of transductions fails to attach each mover to its final landing site to the exclusion of all its intermediate landing sites, which is crucial for producing output trees with the correct string yield. The problem is avoided, though, if syntax enforces a variant of the Ban on Improper Movement. Subregular complexity thus provides a novel motivation for core restrictions on movement while also shedding new light on the choice between copies and traces in syntax. 

Abstract Subregular linguistics is a fairly new approach that seeks a deeper understanding of language by combining the rigor of formal grammar with the empirical sophistication of theoretical linguistics. The approach started in phonology but has since branched out to morphology and even syntax, unearthing unexpected parallels between these three domains of language. In this paper, I argue based on these results that subregular linguistics has a lot to offer to both fields. Subregular linguistics may be the ideal conduit for knowledge transfer between these two communities. 

We fuse two recent strands of work in subregular linguistics—probabilistic tier projections (Mayer, 2021) and tier-based perspectives on movement (Graf, 2022a)—into a probabilistic model of syntax that makes it easy to add gradience to traditional, categorical analyses from the syntactic literature. As a case study, we test this model on experimental data from Sprouse et al. (2016) for a number of island effects in English. We show that the model correctly replicates the superadditive effects and gradience that have been observed in the psycholinguistic literature. 

Earlier work has shown that movement, which forms the backbone of Minimalist syntax, belongs in the subregular class of TSL-2 dependencies over trees. The central idea is that movement, albeit unbounded, boils down to local mother-daughter dependencies on a specific substructure called a tree tier. This reveals interesting parallels between syntax and phonology, but it also looks very different from the standard view of movement. One may wonder, then, whether the TSL-2 characterization is linguistically natural. I argue that this is indeed the case because TSL-2 furnishes a unified analysis of a variety of phenomena: multiple wh-movement, expletive constructions, the that-trace effect and the anti-that-trace effect, islands, and wh-agreement. In addition, TSL-2 explains the absence of many logically feasible yet unattested phenomena. Far from a mere mathematical curiosity, TSL-2 is a conceptually pleasing and empirically fertile characterization of movement. 

Based on a formal analysis of the operations Merge and Move, I provide a computational answer to the question why Move might be an integral part of language. The answer is rooted in the framework of subregular complexity, which reveals that Merge is most succinctly analyzed in terms of the formal class TSL. Any cognitive device that can handle this level of complexity also possesses sufficient resources for Move. In fact, Merge and Move are remarkably similar instances of TSL. Consequently, Move has little computational or conceptual cost attached to it and comes essentially for free in any grammar that expresses Merge as compactly as possible.