Tero Harju

Department of Mathematics

University of Turku, Finland

Regular languages have many different characterizations in terms of automata, congruences, semigroups etc. In this talk we have a look at the more recent result, obtained during the last two decades, namely characterizations using morphic compositions, equality sets and well ordered structures.

Lauri Karttunen

Palo Alto Research Center

Stanford University

A well-known phenomenon in Finnish prosody is the alternation of binary and ternary feet. In native Finnish words, the primary stress falls on the first syllable. Secondary stress generally falls on every second syllable: (vói.mis).(tè.li).(jòi.ta) 'gymnasts' creating a sequence of trochaic binary feet. However, secondary stress skips a light syllable that is followed by a heavy syllable. In (vói.mis.te).(lèm.me) 'we are doing gymnastics', the first foot is ternary, a dactyl.

Within the context of Optimality Theory (OT, Prince and Smolensky 1993), it has been argued that prosodic phenomena are best explained in terms of universal metric constraints. OT constraints can be violated; no word can satisfy all of them. A language-specific ranking of the constraints makes some violations less important than others. In her 1999 dissertation, A unified account of binary and ternary stress, Nine Elenbaas gives an analysis of Finnish in which the alternation between binary and ternary feet follows as a side effect of the ordering of two particular constraints, *Lapse and *(L'. H) The *Lapse constraint stipulates that an unstressed syllable must be adjacent to a stressed syllable or to word edge. The *(L'. H) constraint prohibits feet such as (tè.lem) where a light stressed syllable is followed by a heavy unstressed syllable. The latter constraint of course is outranked by the constraint that requires initial stress on the first syllable in Finnish regardless of the its weight. In his 2003 article on Finnish Noun Inflection, Paul Kiparsky gives essentially the same account of the binary/ternary alternation except that he replaces the *(L'.H) rule by a more general StressToWeight constraint.

Although OT constraints themselves can be expressed in finite-state terms, Optimality Theory as a whole is not a finite-state model if it involves unbounded counting of constraint violations (Frank and Satta 1998). With that limitation OT analyses can be modelled with finite-state tools. In this paper we will give a full computational implementation of the Elenbaas and Kiparsky analyses using the extended regular expression calculus from the 2003 Beesley & Karttunen book on Finite State Morphology. Surprisingly, it turns out that Elenbaas and Kiparsky both make some incorrect predictions. For example, according to their accounts a word such as kalasteleminen 'fishing' should begin with a ternary foot: (ká.las.te).(lè.mi).nen. The correct footing is (ká.las).(tè.le).(mì.nen). There may of course be some ranking of OT constraints under which the binary/ternary alternation in Finnish comes "for free". It does not emerge from the Elenbaas and Kiparsky analyses.

This case study illustrates a more general point: Optimality Theory is computationally difficult and OT theorists are much in the need of computational help.