The Use of Formal Language Theory in Studies of Artificial - CiteSeerX

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strings of the form given in the Out column surprising. If, on the other hand,subjects consistently fail to find strings of the form given in the Out columnsurprising after being familiarized to strings of the form given in the In column,this would be evidence that the target species is unable to distinguishpatterns of that level of complexity.[ Insert Table 2 here ]Table 2 summarizes the conclusions that can be drawn from such results.Recognize outcomes represent lower bounds on the species’ capacity. Theyindicate that the subject has at least the cognitive capabilities given in theCognitive significance column. Fail outcomes represent upper bounds, evidencethat the subject is limited in the way indicated in the Cognitive significancecolumn.6 ConclusionAcoustic pattern recognition or artificial language learning experiments providea powerful approach to understanding the ontogenetic and evolutionarybuilding blocks of the human language faculty, distinguishing what is sharedwith other species and what is uniquely human. To design experiments ofthis sort with highly interpretable results, one must be clear about a bewilderingarray of formal considerations. These include the cognitive capacitiesthat the experiment is designed to probe, the abstract structure of the classesof stringsets that those capabilities characterize, the structure of the stringsetsthe intended stringset may be confused with and what such confusion signifiesabout the capabilities of the subjects.The subregular hierarchy is a range of complexity classes that correspondto a range of cognitive capabilities that are, by virtue of the descriptive characteristicsof the classes, necessarily relevant to any faculty that processesaural stimuli solely as sequences of events. As such it provides a clear frameworkfor resolving these issues. We hope that our exposition of this hierarchywill facilitate continued experimentation of this type.Notes1 This work was undertaken while the first author was in residence at the Radcliffe Institutefor Advanced Study2 The authors would like to express their gratitude to Geoff Pullum for his extensive collaborationon this work and to Barbara Scholz and the referees for their helpful suggestions.3 The expression x|y denotes the property of y being an integral multiple of x.16
4 The expression |w| denotes the length of the string w—the number of symbols it contains.The expression |w| Adenotes the number of As it contains.5 These two examples are due to Geoffrey K. Pullum.6 Pumping lemmas establish certain types of closure properties of stringsets: if a stringsetincludes strings with length exceeding an arbitrary but fixed bound then it also includes stringsin which certain substrings are repeated arbitrarily many times. Shieber (1985) and Huybregts(1984) employed results of this sort to show that certain dialects of Swiss-German are notrepresentable as Context Free stringsets.7 These characterize the structure of stringsets in terms of the way in which certain relationson strings, which depend on the stringset, partition the set of all strings into equivalenceclasses.8 We provide concrete examples of what we mean by “nature of the information” as wesurvey a range of descriptive classes in the next section.9 It is easy to translate an SL k description into a k-expression defining the same stringset,so LT k is a strict superclass of SL k .10 Again, k-expressions can be easily translated into FO(+1) formulae; so FO(+1) is a strictsuperclass of LT.11 A Finite State automaton recognizes an FO(
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