FINITE STATE PROCESSING OF SYSTEMS

Dafydd Gibbon

(U Bielefeld)

ABSTRACT as floating tones and compound tones. Floating tones are not associated with , but are po- It is suggested in this paper that two-level stulated to explain appparent irregularities in pho- morphology theory (Kay, Koskenniemi) can be ex- netic patterning in terms of regular tended to include morphological tone. This exten- properties. sion treats phonological features as I/O tapes for Finite State Transducers in a parallel sequential The tone sandhi rules define how tones affect incrementation (PSI) architecture; phonological their neighbours. The example to be treated here is processes (e.g. assimilation) are seen as variants of a kind of tonal assimilation known as tonal sprea- an elementary unification operation over feature ding in which low tones are phonetically raised tapes (linear unification phonology, LUP). The following a high tone or, more frequently, high phenomena analysed are with tones are lowered after a low tone, either to the tone-spreading (horizontal assimilation), down- level of the low tone (total ) or to a mid step, , , upsweep in two West Afri- level (partial downstep). The newly defined tone is can languages, Tem (Togo) and Baule (C6te then the reference point for following tones. d'Ivoire). It is shown that an FST acccount leads to more insightful definitions of the basic pheno- The latter kind of assimilation produces a cha- mena than other approaches (e.g. phonological racteristic perceptual, and experimentally measu- rules or metrical systems). rable, effect known as tone terracing. Tone se- quences are realized at a fairly high level at the beginning of a sequence, and at certain well- 1. Descriptive context defined points the whole pitch appears "to be downstepped to a new level. The process may The topic of this paper is tone sandhi in two be iterated several times. It is often represented in West African tone languages and suitable formal the literature in the following way (partial down- models for it. The languages investigated are Tern step); it can be seen that a later high tone may be (Gur/Voltaic family, Togo) and Baule (Akan fami- as high as or lower than an earlier low tone: ly, C6te d'Ivoire). Tone languages of other types, in particular the Sino-Tibetan languages, will not be discussed.

The specific concern of this paper is with the way in which certain quite well-known morpho- phonological (lexical) tone patterns are realized in hhhllhhllhh sequence in terms of phonetic pitch patterns. There are three interacting factors involved: i. tone-text In particular, it will be seen that the two ter- association rules; ii. tone-sandhi rules; iii. phone- raced tone languages, Tem and Baule, involve si- tic interpretation rules. milar processes in detail and have similar basic FST architectures, but differ systematically at cer- Tone-text association rules are concerned with tain well-defined points involving sandhi generali- the association of tones with syllables (primary ty, and scope of sandhi context. associations and a form of tone spreading) as well

291 Detailed phonetic interpretation involves pitch mappings between abstract and concrete phonolo- patterns between neighbouring tones of the same gical and phonetic levels of representation. FST type within terraces. These are processses of systems are conceptually bidirectional; they may downdrift (neighbouring tones fall) or upsweep easily be processed in either direction with the (neighbouring tones, usually high tones, rise). same finite state mechanism; the problem of the They will not be dealt with here. recoverability of underlying structure (short of am- biguity through genuine neutralization) loses its importance. 2. Theoretical context The idea of formulating prosodic patterns in The view is developing, based on work by Kay English in FS terms was originated and and Kaplan, Koskenniemi, Church, and others, developed by Pierrehumbert (1980), though FS that in phonology it is sufficient to use finite state intonation models had been developed much ear- transducers which are not allowed to apply to their lier by 't Hart and others for DutcL intonation. own output. Kay and Kaplan have shown that it is These existing FS intonation descriptions are possible to reduce conventional, so-called straightforward finite state automata (FSAs; for "context-sensitive" phonological rules to finite- Dutch, probabilistic FSAs). The problem of map- state relations, and to apply the FSTs thus pro- ping such patterns at one level on to patterns at duced in sequential order (Kay 1986). another, the traditional problem in descriptive lin- guistics as well as in computational parsing and Koskenniemi developed a somewhat different translation, has not been formulated in finite state concept for Finnish morphology, in which the terms for this domain. This mapping question is a FSTs operate as parallel filters over the input: they different one from the question of recognition, and must all agree in their output. A careful analysis the finite state devices required for an answer to also shows that Church's allophonic parser, in his the question are different. Additionally, the tone actual implementation using matrix operations to language application constitutes a different domain. simulate bottom up chart parsing, can also be seen as a system of parallel finite state filters. The PSI The input and output languages for FSTs are (Parallel Sequential Incrementation) system of pro- both regular sets (Type 3 languages). FSTs have sodic analysis being developed by myself in the various interesting properties which are in part DFG Forschergruppe "Koh~renz" in Bielefeid in- similar to those of FSAs. The reversibility property corporates a similar concept of FSTs used as a pa- shown in the simulations is one of the most inter- rallel filter bank (Gibbon & al. 1986). esting. Any FST which is deterministic in one di- rection is not necessarily deterministic in the other, The context within descriptive phonology is as the neutralization facts in Tern and Baule show. that of theories which postulate interreelated but Furthermore, it is not true for FSTs, as it is for structurally autonomous parallel levels of organi- FSAs, that for any non--deterministic FST there is zation in phonology. The four major classical di- a deterministic one which is weakly equivalent re- rections in this area are traditional intonation ana- lative to the input language. This only holds if the lysis (surveyed and developed in Gibbon 1976), paired input and output symbols are interpreted Firthian "prosodic phonology", Pike's simul- as compound (relational) input symbols, and the taneous hierarchies, and the non-linear (autoseg- input and output tapes are seen as a single tape of mental and metrical) phonologies of the last thir- pairs. This is an abstraction which formally redu- teen years. ces FSTs to FSAs. Kay has suggested this perspec- tive on FSTs as an explication for relations be- Parallel FST systems are used in order to ex- tween linguistic levels, where FSTs define relations plicate both traditional phonological rules, so long between linguistic levels of representation in an as they do not apply to their own output, and also, essentially declarative fashion, though with a pro- with appropriate synchronization measures, the cedural interpretation. For a slightly different FST parallel tiers which figure in autosegmental phono- definition cf. Aho & Ullman (1972). In current logy, the mappings between these tiers, and the computational theories of language (FUG, GPSG,

292 LFG), the standard treatment for concord restric- Reverse: tion, to which phonological assimilation and neu- tralization may be compared, is in terms of a class INs (LC LC LC LC) of operations related to unification. The situation OUTs t (L L L L) in autosegmental phonology is simpler than in syn- IN: (HC H H) tax, in that each feature or tier can be modelled by OUTt 1 (H H H) 2 (H H L) a finite state device. The elementary unification operator required is, correspondingly, restricted to INJ (LC !H H) OUT1 % (L H H) non-recursive, adjacent feature specification on a 2 (L H L) given tier, as in the present analysis. In a INs (LC!HHLC) non--parallel architecture, the operation would be OUTs 1 (LHHeL) 2 (LHLL) embedded in a more complex, perhaps context-free-style, context. IN= (LC !H LC} OUTs t (L H ~L)

INs (LC LC LC !H) OUT: 1 (L L L H) 3.The Tern and Baule data IN= (LC fH H !H) OUT: 1 (L H L H) The essential tonal properties of Tern are: IN~ (LC ~H H LC !H) downstep, downdrift, phonetically constant OUT: t (L H L L H) (non-terraced) low tone, high tone spreading over IN= (LC !H H !H H) a following low; only terracing and sandhi are OUT: 1 (LHLHH} dealt with here. The Tern data and the inter-level 2 (LHLHL) relations are taken from Tchagbale (1984). The INI (LC 'H H LC !H H LC) following shows a simulation using a bidirectional OUT - l (L H L L H H =L) 2 (L H L L H L L) FST interpreter, with runs in each direction. INs (LC !H H !H H H) 0UT: 1 (LHLHHH) Forward: 2 (LHLHHL)

INi (L L L L) [NI (HC H !H H LC) OUT: 1 (LC LC LC LC) OUT: 1 (H L H H ~L) 2 (H L H L L} INs (H H H} OUTt 1 (HC H H)

INi (L H H) OUTI 1 (LC !H H)

IN: (L H L L) OUTs I (LC !H H LC} The essential tonal properties of Baule are: INt (L H ~L} partial or total downstep (style-determined), up- 0UT2 1 (LC !H LC) step, upsweep, downdrift, tone spreading of both IN= (L L L H} low and high over the first tone of an appositely OUT= X (LC LC LC !H) specified sequence, compound tone. Again, only IN= (L H L H) terracing and sanditi are dealt with. The Baule OUTz I (LC !H H !H) sandhi data are from Ahoua (1987a), simulated by INs (LHLLH) the same interpreter, with an FST designed for OUT: 1 (LC !H H LC !H) Baule. IN: (LHLHH} OUT: I (LC !H H !H H}

INs (L H L L H L L} OUT: 1 (LC !H H LC !H H LC)

IN: (L H L H H H) OUT: 1 (LC !H H !H H H)

INm (HLHLL) OUTs 1 (HC H !H H LC)

293 Forward: Reverse:

INs (HC H L L L) INu (H L L L L) OUT: t (H L L L L) OUTs I (HC H L L L) INz (HC H L) INs (H L L) OUT: 1 (H H L) OUT: 1 (HC H L) 2 (H L L)

IN: (L H L L) IN: (LC !H H L) OUT~ l (LC !H H L) OUTs I 4L H L L)

IN: (L L L H L L L) INs (LC L L !H H L L) OUT: 1 (LC L L !H H L L) OUT: I (L L L H L L L) 2 (L L H H L L L) IN: (L H H H H) OUT: I (LC L !H H H) IN: (LC L !H H H) OUT: 1 (L H H H H) IN: (H L H H H H) OUTs 1 (HC L L ~H H H} IN: (HC L L !H H H) OUT: 1 (H L H H H H) IN: (L L L L H L) OUT: 1 (LC L L L !H L) IN: (LC L L L !H L) OUT: 1 (L L L L H L) IN: (L H H) 2 (LLLHHL) OUT: 1 (LC L 'H) IN: (LC L ! H} INs (L H L H} OUT: I (L L H) OUT: I 4LC ~H L !H) 2 (L H H)

(L H L H L) INs (LC !H L !H) OUTI 1 (LC ~H L ~H L) OUTs 1 (L H L H)

IN: (L H L L H) IN: ¢LC !H L !H L) OUT~ I (LC !H H L !H) OUTI I (L H L H L)

IN: (L H) INs (LC !H H L !H) OUT: 1 (LC !H) OUT: 1 (L H L L H)

INz (H H) IN~ (LC !H) OUT: I (HC H) 0UTz 1 (L H)

IN: (L L) INi (HC H) OUT: 1 (LC L) OUT: 1 (H H)

IN: (H L) IN: (LC L) OUT: 1 (HC L) OUT: 1 (L L)

IN: (HC L) OUT" 1 (H L)

The underlying morphophonological tones are annotated as follows:

L = low H = high *L = low with an additional morphological feature (Tem only).

294 The surface phonetic tones are:

LC = low constant (in Baule, only initial) iH,h HC = high constant (only initial) H = high relative to currently defined level L = low relative to currently defined level H,hc L,h (Bade) L,I !H = mid (=downstepped high) tone. H, The simulations show the properties of the tone sandhi systems of Tern and Bade very clearly, in particular the contextual dependencies (sandhi). H, :h The reverse (recognition) simulations show the ef- fects of tone neutralization: in the reverse direc- L,I tion, non-deterministic analyses are required,

which means in the present context that more than H,I one underlying form may be found.

The tone systems of Tern and Baule can be seen to differ in several important respects, which L,Ic are summarized in the transition network represen- tations given in Figures 1 and 2, respectively.

H,h ic Figure 2: The Bade FST

Another interesting point pertains to local vs. global pitch relations. The relations described here are clearly local, if they are formalizable in finite state terms. But this is not to say that there L,h is not a global factor involved in addition to these local factors. On the contrary, Ahoua(1987b) has demonstrated the presence of global intonational factors in Baule which are superimposed on the local tonal relations and partly suppress them in fast speech styles.

4.Conclusion

Figure 1: The Tem FST It is immediately obvious that the transition diagramme representations show similar iterative cyclical processes for Tem and for Bade; the Bau- le system has an "inner" and an "outer" cycle, which may be accessed and left at well-defined points. At corresponding points in the diagrammes,

295 both systems show "epicycles", i.e. transitions In current non-linear approaches in descrip- which start and end at the same node, and the tone tive phonology it is not clear that the basic assimilation transitions also occur at similar points explicanda-types of iteration or , the cha- in the systems relative to the epicycles. racter of terracing as a particular kind of iteration or oscillation, and the relative complexity of dif- The suggested interpretation for these interre- ferent tone systems - are captured by the nota- lated iterative process types, three in Tem and five tion, in contrast to the clarity and immediate inter- in Baule, is that they are immediately plausible pretability of the FST model. In one current model explications for the concept of linguistic rhythm (Clements, communicated by Ahoua), complex and interlocking rhythmic patternings. This is the constructive definitions are given; they may be same explicandum, fundamentally, as in metrical characterized in terms of conventional parsing phonology, but it is associated here with the claim techniques as follows: that an explicit concept of iteration is a more ade- quate expl:.~'ation for rhythm than a tree-based, i. analyze the input suing into "islands" implicitly context-free notation, which is not only which define the borders between tone ter- over-powerful but also ill-suited to the problem, races; or traditional phonological rules, whose formal ii. proceed "bottom up" to make constituents properties are unclear. (feet, in general to the left) of these is- lands; The formal properties of Tem and Baule as ter- iii. proceed either bottom up or top down to raced tone languages can be defined in terms of create a right-branching tree over these the topology of the FST transition diagrammes: constituents. iv. (implicit) perform tonal assimilation on the i. The fundamental notion of "terrace" or left--most tone on each left branch. "tonal unit" is defined as one cycle (iteration, oscillation) between ma- This is an unnecessarily complex system, whose jor nodes of the system. formal properties (context-free? bottom up? ii. A major node is a node which has unlike right-left'?) are not clear. input symbols on non-epicyclic input and output transitions and can also be a final A complete evaluation of different approaches node. will clearly require prior elaboration of the iii. Terrace-internal monotone sequences are tone-text association rules and the phonetic inter- defined as epicycles; in Baule, epicyclic pretation rules. The former will follow the prin- sequences start not on the second but on ciples laid down in Goldsmith's well -- formedness the third item of the sequence, and a condition on tone alignment, which also point to non-epicyclic sub-system is required. the applicability of FST systems. iv. Stepping and spreading occurs on any non-epicyclic transition leaving a ma- In summary, the prospects for a comprehensive jor node; in languages with downstep only FST based account of morphophonological tone (Tem), this only applies to high tones, in phenomena appear to be good. The prospects are those with downstep and upstep, upstep all the more interesting in view of the develop- occurs with low tones in these positions. ments in FS morphology and phonology over the past four years, suggesting that an overall model These definitions show that the FST formalism for all aspects of sublexical processing may be fea- is not just another "notational variant", but pre- sible using an overall parallel sequential incremen- cise, highly suggestive, and useful in that it is a tation (PSI) architecture with FST components for formally clear and simple system with well-un- inter-level mapping. It may be predicted with derstood computational properties which make it some hope of success that components which are easy to implement tools for testing the consistency and completeness of a given description.

296 more powerful than Finite State will turn out to be Tchagbale, Z. 1984. T.D. de Linguistique: exerci- unnecessary, at least for the sublexical domain, ces et corriges. Institut de Linguistique Appli- even outside the conventional area of Western qude, Universitd Nationale de European languages. C6te-d'Ivoire, Abidjan, No. 103.

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