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This paper presents a computational investigation of a range of morphological operations. These operations are first represented as morphological maps, or functions that take a stem as input and return an output with the operation applied (e.g., the ing-suffixation map takes the input ‘dɹɪŋk’ and returns ‘dɹɪŋk+ɪŋ’). Given such representations, eac...
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... Figure 1 illustrates the important difference between Dyirbal total reduplication (midi-midi) and the logically-possible but unattested palindrome pattern (midi-idim). From the perspective of a computational analysis, it will be important to establish that (at least some) reduplication constructions are unbounded, in the sense that they are usefully modeled by string-sets of the form {ww | w ∈ S} for some infinite set S. A partial reduplication construction, such as the Agta case above where an initial CVC sequence is copied, is obviously not unbounded in this sense, since -assuming a finite alphabet -there are only finitely-many CVC sequences (Chandlee and Heinz 2012). 2 But as observed by Clark and Yoshinaka (2014) and Chandlee (2017), even amongst total reduplication constructions we must take care to distinguish between unrestricted, productive total reduplication (which is unbounded in the 1 For clarity, we adopt a simplistic analysis here. When the bases start with a vowel, Agta copies the first VC sequence, as in uffu 'thigh' and uf-uffu 'thighs'. ...
This paper proposes a formal model of regular languages enriched with unbounded copying. We augment finite-state machinery with the ability to recognize copied strings by adding an unbounded memory buffer with a restricted form of first-in-first-out storage. The newly introduced computational device, finite-state buffered machines (FS-BMs), characterizes the class of regular languages and languages de-rived from them through a primitive copying operation. We name this language class regular copying languages (RCLs). We prove a pumping lemma and examine the closure properties of this language class. As suggested by previous literature (Gazdar and Pullum 1985, p.278), regular copying languages should approach the correct characteriza-tion of natural language word sets.
... Just like phonology, morphology has also been shown to be largely regular (Karttunen et al., 1992), most often subregular (Chandlee, 2017). 8 Since the expressivity of BMRSs is appropriately limited to at most regular functions -more specifically, to a strict sub-class called SUBSEQUENTIAL functions (Bhaskar et al., 2020) -we can therefore expect BMRSs to reliably characterize morphological processes. ...
This article analyzes stem allomorphy in Serbo-Croatian neuter noun inflection as morphological epenthesis. I demonstrate that consonant insertion in the inflection of Serbo-Croatian neuter nouns is a predictable, morphologically conditioned process, rather than an artifact of listed stem allomorphy. Furthermore, the process is not phonologically optimizing, and does not depend on phonological conditions such as vowel hiatus or illicit phonotactic structure. The present analysis includes the process in a wider, algorithmic interpretation of nominal inflection as logical transductions on strings, using Boolean Monadic Recursive Schemes (BMRSs).
BMRSs are appropriate for modeling morphological processes, as they can intensionally represent morphological substance and generalizations, much like theories of realizational morphology do, while retaining the computationally restrictive nature of such processes. A logical description is therefore offered of Serbo-Croatian neuter noun inflection, including the processes of stem-final consonant insertion and suffix-initial vowel fronting. The work presented here bears wider implications about the nature of morphophonological processes, and the interfaces of morphology with phonology and syntax.
... Sequential functions are of particular interest in phonology, which is a study of sound patterns and sound changes in natural languages. Heinz and Lai (2013); Chandlee (2014Chandlee ( , 2017; Chandlee and Heinz (2018) show that sequential functions can successfully model the majority of phonological processes, describing various types of sound alternations. The equivalent of letters in phonology are phonemes, which are the contrastive sound units within a language. ...
... This is because there are multiple definitions of ISL that are identical when considering string-to-string functions yet diverge when taking the step from strings to trees. Ji and Heinz (2020) take as their vantage point the presentation of ISL in terms of finitestate transducers in Chandlee (2017). Graf (2020), on the other hand, starts with the context-based definition used in Chandlee and Heinz (2018). ...
... Tree-based models are still rare in computational morphology, where morphological phenomena are usually modeled with finite-state machinery (Koskenniemi, 1983;Beesley and Karttunen, 2003;Roark and Sproat, 2007). From this perspective, morphological dependencies form regular string languages, and morphological processes can be computed by 1-way finite-state transducers. 1 In fact, many aspects of morphology are subregular over strings and fall within remarkably simple subclasses of regular string languages and finite-state transductions (Chandlee, 2014(Chandlee, , 2017Aksënova et al., 2016;. ...
... However, the Regular class is not learnable under various learning scenarios including identification in the limit from positive data, and the Probably Approximately Correct (PAC) framework (Gold 1967;Valiant 1984;de la Higuera 2010). Additionally, the range of distributions present in phonology and morphology that sit in the Regular region do not require the full complexity of Regular power (Heinz 2018;Chandlee 2017). For these reasons, phonological constraints are hypothesised to inhabit structured subclasses of the Regular languages, lumped under the term subregular (Heinz 2010a(Heinz , 2018. ...
... While this paper has so far focused on constraints, this work is easily extended to consider mappings between structures, expressed mathematically as Regular functions (Courcelle 1994;Courcelle and Engelfriet 2012;Filiot 2015;Engelfriet and Hoogeboom 2001). The notion of strict locality has been generalized to functions and shown to be relevant for natural language phonology and morphology (Chandlee 2014(Chandlee , 2017. These local functions have been model-theoretically characterized and extended to consider nonlinear structures in phonology (Chandlee and Jardine 2019; Strother-Garcia 2019). ...
We derive well-understood and well-studied subregular classes of formal languages purely from the computational perspective of algorithmic learning problems. We parameterise the learning problem along dimensions of representation and inference strategy. Of special interest are those classes of languages whose learning algorithms are necessarily not prohibitively expensive in space and time, since learners are often exposed to adverse conditions and sparse data. Learned natural language patterns are expected to be most like the patterns in these classes, an expectation supported by previous typological and linguistic research in phonology. A second result is that the learning algorithms presented here are completely agnostic to choice of linguistic representation. In the case of the subregular classes, the results fall out from traditional model-theoretic treatments of words and strings. The same learning algorithms, however, can be applied to model-theoretic treatments of other linguistic representations such as syntactic trees or autosegmental graphs, which opens a useful direction for future research.
... First of all, functions such as Opposite Tone Insertion (OTI) will apply solely at the tonal level, while segments can be undergoing other operations at the same time (recall that MT-FSTs can operate on some or all tapes simultaneously). Secondly, representing tones separately from segments make tonal processes local, and therefore all the alternations can be expresses with less powerful functions (Chandlee, 2017). Now that we presented the advantages of MT-FSTs, and the need for utilizing 2-way FSTs to model full reduplication, we combine those machines to account for all morphophonological pro- C and V are notational meta-symbols for consonants and vowels, resp.; T indicates the tone tape, S, the segmental tape, and O the output tape. ...
... Gazdar and Pullum (1985, 278) made the remark that 1 Total reduplication does not immediately guarantee unboundedness. When the set of bases is finite, i.e, {ww | w ∈ L} when L is finite, total reduplication can be squeezed in languages described by 1 way finite state machines (Chandlee, 2017), though doing so eventually leads to state explosion (Roark and Sproat, 2007;Dolatian and Heinz, 2020). Computationally, only total reduplication with infinite number of potential reduplicants is true unbounded copying. ...
... Crosslinguistically, most morphological processes are local across different domains (Embick 2010, Marantz 2013 and even in Semitic (Arad 2003, Kastner 2016), e.g. concatenative morphology or suffixation (Chandlee 2017). However, Semitic languages use non-concatenative templatic morphology or root-and-pattern morphology (RPM). ...
... They determine an output string for a given input string based only on contiguous substrings of bounded length (Chandlee 2014. Despite their reduced expressivity, they capture a striking majority of local segmental phonological and morphological maps (Chandlee 2017) and have been argued to provide a precise, well-defined notion of linguistic locality . ...
... There is little discussion on the locality or non-locality of Semitic template-filling. Chandlee (2017) shows that template-filling cannot be easily modeled with single-tape FSTs. Superficially, the fact that templatic morphology involves dis-contiguous units (interdigitation) implies that it is a non-local process. ...
This paper discusses the generative capacity required for Semitic root-and-pattern morphology. Finite-state methods effectively compute concatenative morpho-phonology, and can be restricted to Strictly Local functions. We extend these methods to consider non-concatenative morphology. We show that over such multi-input functions, Strict Locality is necessary and sufficient. We discuss some consequences of this generalization for linguistic theories of the morphological template.
... Within computational linguistics, reduplication has been a challenging process to model (Culy 1985;Sproat 1992;Roark and Sproat 2007;Hulden 2009a;Chandlee 2014Chandlee , 2017. Finite-state technology, as currently practiced, cannot adequately and elegantly describe many cases of productive reduplication, especially unbounded total reduplication. ...
... On one hand, Chandlee (2017) suggests that the inadequacy of 1-way FSTs for total reduplication is evidence for total reduplication being ontologically different from partial reduplication. There is some empirical support for this argument. ...
... To give more context, most morphological processes can be computed by 1-way finite state automata and transducers (Koskenniemi 1983;Beesley and Karttunen 2003). In fact, substantially less expressive subregular classes are capable of computing most of these morphological processes (Aksënova et al. 2016;Chandlee 2017). So far, these subclasses have been identified based on considerations of locality (ISL, OSL) and determinism (Seq, sequentiality). ...
This article describes a novel approach to the computational modeling of reduplication. Reduplication is often treated as a stumbling block within finite-state treatments of morphology because they cannot adequately capture the productivity of unbounded copying (total reduplication) and because they cannot describe bounded copying (partial reduplication) without a large increase in the number of states. We provide a comprehensive typology of reduplicative processes and show that an understudied type of finite-state machine, 2-way deterministic finite-state transducers (2-way D-FSTs), captures virtually all of them. Furthermore, the 2-way D-FSTs have few states, are in practice easy to design and debug, and are linguistically motivated in terms of the transducer’s origin semantics or segment alignment. Most of these processes, and their corresponding 2-way D-FSTs, are available in an online database of reduplication (RedTyp). We classify these 2- way D-FSTs according to the concatenation of known subclasses of regular relations and show that the majority fall into the Concatenated Output Strictly Local (C-OSL) class. Other cases require higher subclasses but are still definable by 2-way D-FSTs.
