56 research outputs found
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Questioning to Resolve Transduction Problems
Elgot & Mezei (1965) show that non-deterministic regular functions (NDRFs) are compositions ρ ⚬ λ of two contradirectional subsequential functions (SSQs), where λ is unbounded lookahead for ρ. Such decompositions facilitate the identification of processes that require supra-SSQ expressivity. We use concepts adapted from decision theory to outline a set of necessary and sufficient properties for a composition ρ ⚬ λ to define a non-SSQ NDRF . These conditions define a set of functions between the IF-WDRFs (McCollum et al. 2018, Hao & Andersson 2019) and proper NDRFs, organized in terms of a precise notion of the degree of lookahead that λ provides for ρ
Modelling human choices: MADeM and decision‑making
Research supported by FAPESP 2015/50122-0 and DFG-GRTK 1740/2. RP and AR are also part of the Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant (2013/07699-0). RP is supported by a FAPESP scholarship (2013/25667-8). ACR is partially supported by a CNPq fellowship (grant 306251/2014-0)
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Functional pressures and linguistic typology
The explanation of linguistic variation and change is one of the central questions in the language sciences. Functional explanations focus on how the needs and abilities of language users shape the distribution of linguistic structures that typically conventionalize -- e.g. structures that are harder to perceive or learn accurately are less likely to conventionalize accurately. Perceptibility effects are common sound patterns that seem closely related to the relative confusability of different speech sound sequences. One class of explanations -- purely phonological accounts --have assumed speakers (implicitly) know how confusability varies as a function of immediately adjacent sounds, and that this is a rich enough description of confusability to explain perceptibility effects. Chapter 2 shows that the perceptibility of tokens of any given sound in American English systematically varies based on a listener's incrementally-adjusted expectations about what the speaker intends to say, and shows that this variation is significantly greater than variation due to immediately adjacent sounds. To derive this result, I present a computational psycholinguistic model of word recognition and apply it to experimental confusability data and a transcribed lexicon of 10^4 words. I conclude that purely phonological accounts of perceptibility effects need to be more complicated and less modular than currently appreciated. Chapter 3 applies the same word recognition model and novel information-theoretic measures of confusability to two conversational corpora and shows that words that are more contextually confusable are lengthened in contexts where they are more confusable, and shortened where they are less so. This is a crucial step towards a linking hypothesis between the realtime perceptibility of different speech sound sequences and conventionalized perceptibility effects. Chapter 4 considers morphology. Prior research has observed an inverse relation between morphological complexity and demographic variables like speech community size and proportion of adult learners. Recent work has hypothesized that higher complexity may be helpful to child learners, and that populations with differing demographics constitute environments with different 'selection pressures' for language variants to 'evolve' in. I argue that mathematical formulations of Darwinian evolution suggest a more likely explanation: 'neutral' change caused by random fluctuations in variant frequency ('drift') is much more powerful in small populations and can easily overwhelm selection relative to large populations
Recommended from our members
Functional pressures and linguistic typology
The explanation of linguistic variation and change is one of the central questions in the language sciences. Functional explanations focus on how the needs and abilities of language users shape the distribution of linguistic structures that typically conventionalize -- e.g. structures that are harder to perceive or learn accurately are less likely to conventionalize accurately. Perceptibility effects are common sound patterns that seem closely related to the relative confusability of different speech sound sequences. One class of explanations -- purely phonological accounts --have assumed speakers (implicitly) know how confusability varies as a function of immediately adjacent sounds, and that this is a rich enough description of confusability to explain perceptibility effects. Chapter 2 shows that the perceptibility of tokens of any given sound in American English systematically varies based on a listener's incrementally-adjusted expectations about what the speaker intends to say, and shows that this variation is significantly greater than variation due to immediately adjacent sounds. To derive this result, I present a computational psycholinguistic model of word recognition and apply it to experimental confusability data and a transcribed lexicon of 10^4 words. I conclude that purely phonological accounts of perceptibility effects need to be more complicated and less modular than currently appreciated. Chapter 3 applies the same word recognition model and novel information-theoretic measures of confusability to two conversational corpora and shows that words that are more contextually confusable are lengthened in contexts where they are more confusable, and shortened where they are less so. This is a crucial step towards a linking hypothesis between the realtime perceptibility of different speech sound sequences and conventionalized perceptibility effects. Chapter 4 considers morphology. Prior research has observed an inverse relation between morphological complexity and demographic variables like speech community size and proportion of adult learners. Recent work has hypothesized that higher complexity may be helpful to child learners, and that populations with differing demographics constitute environments with different 'selection pressures' for language variants to 'evolve' in. I argue that mathematical formulations of Darwinian evolution suggest a more likely explanation: 'neutral' change caused by random fluctuations in variant frequency ('drift') is much more powerful in small populations and can easily overwhelm selection relative to large populations
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Weak determinism and the computational consequences of interaction
Abstract:
Recent work has claimed that (non-tonal) phonological patterns are subregular (Heinz 2011a,b, 2018; Heinz and Idsardi 2013), occupying a delimited proper subregion of the regular functions—the weakly deterministic (WD) functions (Heinz and Lai 2013; Jardine 2016). Whether or not it is correct (McCollum et al. 2020a), this claim can only be properly assessed given a complete and accurate definition of WD functions. We propose such a definition in this article, patching unintended holes in Heinz and Lai’s (2013) original definition that we argue have led to the incorrect classification of some phonological patterns as WD. We start from the observation that WD patterns share a property that we call unbounded semiambience, modeled after the analogous observation by Jardine (2016) about non-deterministic (ND) patterns and their unbounded circumambience. Both ND and WD functions can be broken down into compositions of deterministic (subsequential) functions (Elgot and Mezei 1965; Heinz and Lai 2013) that read an input string from opposite directions; we show that WD functions are those for which these deterministic composands do not interact in a way that is familiar from the theoretical phonology literature. To underscore how this concept of interaction neatly separates the WD class of functions from the strictly more expressive ND class, we provide analyses of the vowel harmony patterns of two Eastern Nilotic languages, Maasai and Turkana, using bimachines, an automaton type that represents unbounded bidirectional dependencies explicitly. These analyses make clear that there is interaction between deterministic composands when (and only when) the output of a given input element of a string is simultaneously dependent on information from both the left and the right: ND functions are those that involve interaction, while WD functions are those that do not
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On the proper treatment of weak determinism: Subsequentiality and simultaneous application in phonological maps
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