Computing and classifying reduplication with 2-way finite-state transducers

Abstract

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 2way 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.

Learning Repetition, but not Syllable Reversal

“…Recently, a series of papers by Dolatian and Heinz have investigated the typological space of reduplicative processes as well as the formal models of reduplication in the framework of FLT. Dolatian & Heinz (2020) develop their own complexity hierarchy of subclasses of 2-way Finite State Transducers (2-way FSTs) which they use to model the copying function. Finite State Transducers describe functions or relations between two sets (while grammars in the Chomsky hierarchy describe sets).…”

Finite-state Model of Shupamem Reduplication

“…Figure 1 illustrates a deterministic 2-way FST that reduplicates ká 'fry.IMP'; readers are referred to Dolatian and Heinz (2020) for formal definitions. The key difference between deterministic 1-way FSTs and deterministic 2-way FSTs are the addition of the 'direction' parameters {+1, 0, −1} on the transitions which tell the FST to advance to the next symbol on the input tape (+1), stay on the same symbol (0), or return to the previous symbol (-1).…”

“…We define Deterministic 2-Way n, m Multitape FST (2-way (n, m) MT FST for short) for n, m ∈ N by synthesizing the definitions of Dolatian and Heinz (2020) and Dolatian and Rawski (2020b); n, m refer to the number of input tapes and output tapes, respectively. A Deterministic 2-Way n, m Multitape FST is a six-tuple (Q,…”

“…unique because the sequence of configurations is determined deterministically. If the computation of a 2-way MT-FST T halts on some input #» w (perhaps because a subsequent configuration does not exist), then we say T is undefined on #» w. The 2-way FSTs studied by Dolatian and Heinz (2020) are 2-way 1,1 MT FST. The n-MT-FSTs studied by Dolatian and Rawski (2020b) are 2-way n,1 MT FST where none of the transitions contain the −1 direction.…”

“…Total reduplication, on the other hand, is the only known morphophonological process that cannot be modelled with 1-way FSTs because the number of copied elements, in principle, has no upper bound. Dolatian and Heinz (2020) address this challenge with 2way FSTs, which can move back and forth on the input tape, producing a faithful copy of a string.…”