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

nize non-Finite-State stringsets does not imply that the physical mechanismsthey employ must have access to a store of unbounded size. The mechanismsmay implement an algorithm which, in principle, requires unbounded storagewhich fails on sufficiently long or sufficiently complicated inputs. Or wouldif it ever encountered such.4.6 Beyond Finite StateThe ability to recognize stringsets that are not Finite State implies discriminatingbetween strings on the basis of information about the string the size ofwhich depends on the length of the string—being able to count to values thatare proportional to the length of the string, for example. The weakest classof the Chomsky hierarchy which properly extends the class of Finite Statestringsets is the class of context free stringsets, those that can be generatedby context free grammars. But there are many ways of utilizing amounts ofinformation that depend on the length of the string that do not provide theability to recognize context free stringsets in general. The single counter thatsuffices to recognize A n B n can also recognize sets of well-nested brackets(the single bracket Dyck stringsets, D 1 ), but it does not suffice to recognizeD 2 , the two bracket Dyck stringsets, for example. There are, in fact, multiplehierarchies which partition the context free stringsets just as the sub-regularhierarchy partitions the Finite State stringsets. Experiments that are intendedto differentiate abilities beyond the Finite State will need to be based on formalanalyses of this territory similar to the analysis of the sub-regular hierarchywe have provided here.5 Recognition experiments[ Table 1 goes here ]Tables 1 and 2 summarize the conclusions that can be drawn about thecognitive capabilities of the subjects given the results of recognition experimentsbased on the sub-regular hierarchy.To test the recognition capabilities of a species relative to these classesone could use experiments based on patterns such as those given in the Examplecolumn of Table 1. Species with the ability to recognize patterns of thatsort, having been familiarized to strings of the form given in the In column,should generally find novel strings of that form unsurprising while finding15