From Pan¯ . inian Sandhi to Finite State Calculus

Malcolm D. Hyman∗ Max Planck Institute for the History of Science, Berlin

Abstract chapters (termed adhyaya¯ ). Conciseness (laghava¯ ) is a fundamental principle in Pan¯ . ini’s formulation of care- The most authoritative description of the mor- fully interrelated rules (Smith, 1992). Rules are either phophonemic rules that apply at word bound- operational (i. e. they specify a particular linguistic op- aries (external sandhi) in Sanskrit is by the eration, or karya¯ ) or interpretive (i. e. they define the great grammarian Pan¯ . ini (fl. 5th c. B. C. E.). scope of operational rules).2 Rules may be either oblig- These rules are stated formally in Pan¯ .ini’s atory or optional. grammar, the As..tadhy¯ ay¯ ¯ı ‘group of eight chap- A brief review of some well-known aspects of Pa-¯ ters’. The present paper summarizes Pan¯ ini’s . n.ini’s grammar is in order. The operational rules rel- handling of sandhi, his notational conventions, evant to sandhi specify that a substituend (sthanin¯ ) is and formal properties of his theory. An XML replaced by a substituens (ade¯ sa´ ) in a given context vocabulary for expressing Pan¯ . ini’s morpho- (Cardona, 1965b, 308). Rules are written using meta- phonemic rules is then introduced, in which linguistic case conventions, so that the substituend is his rules for sandhi have been expressed. Al- marked as genitive, the substituens as nominative, the though Pan¯ .ini’s notation potentially exceeds a left context as ablative (tasmat¯ ), and the right context finite state grammar in power, individual rules as locative (tasmin). For instance: do not rewrite their own output, and thus they may be automatically translated into a rule cas- 8.4.62 jhayo ho ’nyatarasyam¯ cade from which a finite state transducer can jhaY-ABL h-GEN optionally be compiled. This rule specifies that (optionally) a homogenous 1 Sandhi in Sanskrit sound replaces h when preceded by a sound termed jhaY — i. e. an oral stop (Sharma, 2003, 783–784). Sanskrit possesses a set of morphophonemic rules Pan¯ .ini uses abbreviatory labels (termed pratyah¯ ar¯ a) (both obligatory and optional) that apply at morpheme to describe phonological classes. These labels are and word boundaries (the latter are also termed pada interpreted in the context of an ancillary text of the boundaries). The former are called internal sandhi (< As..tadhy¯ ay¯ ¯ı, the Sivas´ utr¯ as, which enumerate a catalog sam. dhi ‘putting together’); the latter, external sandhi. of sounds (varn. asamamn¯ aya¯ ) in fourteen classes (Car- This paper only considers external sandhi. Sandhi rules dona, 1969, 6): involve processes such as assimilation and vowel coa- lescence. Some examples of external sandhi are: na 1. a i u N. 8. jh bh N˜ asti > nasti¯ ‘is not’, tat ca > tac ca ‘and this’, etat hi

1

> etad dhi ‘for this’, devas api > devo ’pi ‘also a god’. 2. r l K 9. gh d.h dh S. 3. e o N˙ 10. j b g d. d S´ 2 Sandhi in Pan¯ . ini’s grammar 4. ai au C 11. kh ph ch th th c t t V Pan¯ . ini’s As..tadhy¯ ay¯ ¯ı is a complete grammar of San- . . skrit, covering phonology, morphology, syntax, seman- 5. h y v r T. 12. k p Y tics, and even pragmatics. It contains about 4000 rules (termed sutr¯ a, literally ‘thread’), divided between eight 6. l N. 13. s´ s. s R ∗ This work has been supported by NSF grant IIS- 7. n˜ m n˙ n. n M 14. h L 0535207. Any opinions, findings, and conclusions or recom- mendations expressed are those of the author and do not nec- essarily reflect the views of the National Science Foundation. 2The traditional classification of rules is more fine- The paper has benefited from comments by Peter M. Scharf grained and comprises sam. jn˜a¯ (technical terms), paribhas¯. a¯ and by four anonymous referees. (interpretive rules), vidhi (operational rules), niyama (restric- 1The symbol ’ (avagraha) does not represent a phoneme tion rules), pratisedha (negation rules), atidesa´ (extension h i . but is an orthographic convention to indicate the prodelision rules), vibhas¯. a¯ (optional rules), nipatana¯ (ad hoc rules), adhi- of an initial a-. kar¯ a (heading rules) (Sharma, 1987, 89). The final items (indicated here by capital letters) are are specified as Perl-compatible regular expressions markers termed it ‘indicatory sound’ and are not con- (PCREs) (Wall et al., 2000).5 Sanskrit sounds are in- sidered to belong to the class. A pratyah¯ ar¯ a formed dicated in an encoding known as SLP1 (Sanskrit Li- from a sound and an it denotes all sounds in the se- brary Phonological 1) (Scharf and Hyman, 2007). An quence beginning with the specified sound and ending encoding such as Unicode is not used, since Unicode with the last sound before the it. Thus jhaY denotes the represents written characters rather than speech sounds class of all sounds from jh through p (before the it Y): (Unicode Consortium, 2006). The SLP1 encoding fa- jh, bh, gh, d. h, dh, j, b, g, d. , d, kh, ph, ch, .th, th, c .t, t, k, cilitates linguistic processing by representing each San- p (i. e. all oral stops).3 Sutra¯ 8.4.62, as printed above, skrit sound with a single symbol (see fig. 1).6 The use is by itself both elliptic and uninterpretable. Ellipses in of Unicode would be undesirable here, since (1) there sutras¯ are completed by supplying elements that occur would not be a one-to-one correspondence between in earlier sutras;¯ the device by which omitted elements character and sound, and (2) Sanskrit is commonly

can be inferred from preceding sutras¯ is termed anuvr¡ tti written in a number of different scripts (Devanagar¯ ¯ı, ‘recurrence’ (Sharma, 1987, 60). It will be noticed that Tamil, Romanization, etc.). no substituens is specified in 8.4.62; the substituens The following is the XML representation of sutra¯ savarnah. ‘homogenous sound-NOM’ (Cardona, 1965a) 8.3.23 mo ’nusvar¯ ah. , which specifies that a pada-final is supplied by anuvr¡ tti from sutra¯ 8.4.58 anusvar¯ asya m is replaced by the nasal sound anusvar¯ a (m. ) when yayi parasavarn. ah. . Still, the device of anuvr¡ tti is in- followed by a consonant (Sharma, 2003, 628): sufficient to specify the exact sound that must be in- light of the paribhas¯.a¯ ‘interpretive rule’ 1.1.50 sthane¯ ’ntaratamah, which specifies that a substituens must be This rule employs a syntactic extension used for . @(name) maximally similar (sc. in articulatory place and man- macros. The expression is replaced by the name ner) to the substituend (Sharma, 1987, 126). Thus the value of a defined macro . Macros are defined substituens in 8.4.62 will always be aspirated, since h with an XML element and may be defined (the substituend) is aspirated: e. g. vag¯ hasati (< vak¯ recursively. Macro expansion is performed immedi- hasati ‘a voice laughs’ by 8.2.39) > vag¯ ghasati.4 ately after parsing the XML file, before any further rcontext A second example further illustrates the principles processing. Here the attribute references @(wb) already discussed: two macros: is expanded to characters that indicate a word boundary, and @(hal) is expanded 8.4.63 sa´ s´ cho ’t.i to the characters representing the sounds of the pra- s´-GEN ch-NOM aT. -LOC tyah¯ ar¯ a haL (i. e. all consonants). Macros are a syn- tactic convenience that allows rules to be easier to Here jhayah. ‘jhaY-ABL’ and anyatarasyam¯ ‘option- read (and closer to Pan¯ .ini’s original formulation); one ally’ are supplied by anuvr¡ tti from the preceding sutra¯ might equally spell out in full all characters represent- (8.4.62). The rule specifies that (optionally) s´ is re- ing sounds in a phonological class. The square brackets placed by ch when it is preceded by an oral stop (jhaY) belong to the PCRE syntax and indicate that any char- and followed by a vowel or semivowel (aT). . acter contained between them should be matched; that Rules specific to external sandhi are found in the is, [abc] matches an a, b, or c. third quarter (pada¯ ) of the eighth adhyaya.¯ A num- In the target two additional syntactic facilities al- ber of rules are common to both internal and external low for rules to be expressed in a way that is close to sandhi, and rules relevant for external sandhi are also Pan¯ ini’s formulation. These facilities are termed map- found in the first pada¯ of the sixth adhyaya¯ and the . pings and functions. The following rule illustrates a fourth pada¯ of the eighth adhyaya.¯ mapping: 3 An XML encoding for Pan¯ inian rules tains an element , with required attributes 5So-called “regular expressions” in programming lan- source (the substituend) and target (the sub- guages such as Perl include extended features such as pattern stituens) and optional attributes lcontext (the left memory that exceed the power of regular languages (see 4); context) and rcontext (the right context). The for example, it is possible to write a regular expression §that values of source, lcontext, and rcontext matches the αα language, that is, the language of all redu- plicated strings. Thus PCREs are not, in the formal sense, 3The vowel a added after a consonant makes the pratya-¯ regular expressions at all. har¯ a pronounceable. 6Figure 1 is a simplified overview of SLP1. It does 4Note that Sanskrit h represents a voiced glottal fricative not show symbols for accents, certain nasalized sounds, or [¢ ]. sounds peculiar to the Vedic language.

£ £¥¤ ¦ § © ¨ a a¯ i § ¯ı u u¯ the pratyah¯ ar¯ a iK (a simple vowel other than a or a¯).

a A i I u U ik



 The macro is defined:

r r¯ l ¯l

f F x X



¤

 ¤ £¥¤¦ ¦ £¤ * e ai o au value="@(i)@(u)@(f)@(x)"

e E o O ref="A.1.1.71"/>

¦ ¦ ¤ ¦   k kh g gh n˙

k K g G N and depends on the macro definitions:

!" ¦ #  $% ¦ &'¦ ()¦ c ch j jh n˜

c C j J Y

 +  ,  -  . /0¦ * ref="A.1.1.69"/> t. t.h d. d.h n.

w W q Q R

¦ 34¦ 5  ¤ 67¦ 8¦ 12 ref="A.1.1.69"/> t th d dh n

t T d D n

9:¦ . ;: <¦ =)¦ >)¦ . ref="A.1.1.69"/> p ph b bh m

p P b B m ref="A.1.1.69"/>

¦ @  A0 B:¦ ? y r l v

y r l v The iK is stored in pattern memory, and the substituend

G

C0¦ . D:¦ EF¦  s´ s. s h (a-varn. a) is replaced by the output of calling the func- S z s h tion gunate on the stored iK. A function is defined * anusvara¯ = M; visarga = H with an element , which has as children one or more elements. These are context- Figure 1: A partial overview of the SLP1 encoding free rules that typically make use of mappings in the target. Thus gunate is defined:

This sutra¯ has been discussed earlier. The left context parentheses (part of PCRE syntax) specify that the con- stored in pattern memory are available for subsequent reference: the pattern matched by the first parenthe- sized group may be recalled with $1; the second, with Two mappings are invoked here: $2, etc. (only nine pattern memory variables are avail- in the target attribute. The rule specifies that an h, of a mapping, and input is the input symbol for the mapping. A mapping is defined with a el- ref="A.6.1.77"> The mapping guna maps simple vowels such as a- This mapping translates the voiced oral stops denoted varna (which includes short a and long a¯) to their guna ´ . . by the pratyah¯ ar¯ a jaS (j, b, g, d. , d) to the equivalent equivalent. The term gun. a is defined by the technical aspirated voiced oral stops denoted by the pratyah¯ ar¯ a rule (sam. jn˜a¯) (Sharma, 1987, 102) 1.1.2 aden˙ gun. ah. jhaS. (jh, bh, gh, d. h, dh). In the case that the input sym- ‘a and eN˙ [are] guna’ (the pratyah¯ ar¯ a eN˙ = e, o ). . { } bol to a mapping is not contained in from, the mapping The mapping semivowel maps those vowels that is equivalent to the identity function. possess homorganic semivowels to the corresponding Sutra¯ 6.1.87 ad¯ gun. ah. illustrates the use of a func- semivowels. The function gunate, if the input is a-,

tion: i-, or u-varn. a, outputs the corresponding gun. a vowel; ¡

ref="A.6.1.87"/> homorganic semivowel (either r or l). The domain of

¡ ¡ ¡ The source matches either short a or long a¯ (by the gunate is a, a,¯ i, ¯ı, u, u,¯ r¡ , r¯, l, l¯ and its range is a, { } { definition of the macro a), a word boundary, and then e, o, ar, al . } a regular grammar, all production rules have a single non-terminal on the left-hand side, and either a single terminal or a combination of a single non-terminal and a single terminal on the right-hand side. That is, all rules are of the form A a, A aB (for a right regular → → PSfrag replacements regular grammar), or A Ba (for a left regular gram- → context free mar), where A and B are single non-terminals, and a is context sensitive a single terminal (or ). A regular grammar is the least powerful type of grammar in the Chomsky hierarchy recursively enumerable (see fig. 2) (Chomsky, 1956). A context free grammar describes a context free language, a context sensitive Figure 2: The Chomsky hierarchy of languages (after grammar describes a context sensitive language, and Prusinkiewicz and Lindenmayer (1990, 3)) an unrestricted grammar describes a recursively enu- merable language. The hierarchy is characterized by proper inclusion, so that every regular language is con- text free, every context free language is context sensi- 4 Regular languages and regular tive, etc. (but not every context free language is regular, relations etc.). A regular grammar cannot describe a context free language such as anbn 1 n , which consists of the { | ≤ } First, it is necessary to define a regular language. Let Σ strings ab, aabb, aaabbb, aaaabbbb . . . (Kaplan and denote a finite alphabet and Σ denote Σ  (where { } ∪ { } Kay, 1994, 346).  is the empty string). e is a regular language where { } Since Pan¯ . inian external sandhi can be modeled using e Σ, and the empty language is a regular lan- ∈ ∅ finite state grammar, it is highly desirable to provide a guage. Given that L1, L2, and L are regular languages, finite state implementation, which is computationally additional regular languages may be defined by three efficient. Finite state machines are closed under com- operations (under which they are closed): concatena- position, and thus sandhi operations may be composed tion (L1 L2 = xy x L1, y L2), union (L1 L2), · { | ∈ ∈ i ∪ with other finite state operations to yield a single net- and Kleene closure (L∗ = ∞ L ) (Kaplan and Kay, ∪i=0 work. 1994, 338). Regular relations are defined in the same fashion. 6 From rewrite rules to regular An n-relation is a set whose members are ordered n- tuples (Beesley and Karttunen, 2003, 20). Then e grammars { } is a regular n-relation where e Σ . . . Σ ( ∈ × × ∅ A string rewriting system is a system that can trans- is also a regular n-relation). Given that R1, R2, and form a given string by means of rewrite rules. A rewrite R are regular n-relations, additional regular n-relations rule specifies that a substring x1. . . xn is replaced by may be defined by three operations (under which they a substring y . . . y : x . . . x y . . . y , where 1 m 1 n → 1 m are closed): n-way concatenation (R1 R2 = xy x x , y Σ (and Σ is a finite alphabet). Rewrite rules · { | ∈ i i ∈ R1, y R2), union (R1 R2), and n-way Kleene clo- used in phonology have the general form ∈ i ∪ sure (R∗ = ∞ R ). ∪i=0 φ ψ/λ ρ 5 Finite state automata and regular → grammars Such a rule specifies that φ is replaced by ψ when it is preceded by λ and followed by ρ. Tradition- A finite state automaton is a mathematical model that ally, the phonological component of a natural-language corresponds to a regular language or regular relation grammar has been conceived of as an ordered se- (Beesley and Karttunen, 2003, 44). A simple finite ries of rewrite rules (sometimes termed a cascade) state automaton corresponds to a regular language and W1, . . . , Wn (Chomsky and Halle, 1968, 20). Most is a quintuple S, Σ, δ, s0, F , where S is a finite set phonological rules, however, can be expressed as reg- h i of states, Σ the alphabet of the automaton, δ is a tran- ular relations (Beesley and Karttunen, 2003, 33). But  S sition function that maps S Σ to 2 , s0 S is a if a rewrite rule is allowed to rewrite a substring in- × ∈ single initial state, and F S is a set of final states troduced by an earlier application of the same rule, ⊆ (Aho et al., 1988, 114). A finite state automaton that the rewrite rule exceeds the power of regular relations corresponds to a regular relation is termed a finite state (Kaplan and Kay, 1994, 346). In practice, few such transducer (FST) and can be defined as a quintuple rules are posited by phonologists. Although certain S, Σ . . . Σ, δ, s0, F , with δ being a transition func- marginal morphophonological phenomena (such as ar- h × × i tion that maps S Σ . . . Σ to 2S (Kaplan and bitrary center embedding and unlimited reduplication) × × × Kay, 1994, 340). exceed finite state power, the vast majority of (mor- A regular (or finite) grammar describes a regular lan- pho)phonological processes may be expressed by reg- guage and is equivalent to a finite state automaton. In ular relations (Beesley and Karttunen, 2003, 419). e, o Since phonological rewrite rules can normally (with ? the provisos discussed above) be reexpressed as regular e, o , # relations, they may be modeled as finite state transduc- s0 s1 s2 ers (FSTs). FSTs are closed under composition; thus if ? e, o T1 and T2 are FSTs, application of the composed trans- ducer T T to a string S is equivalent to applying T ?, a:’ 1 ◦ 2 1 to S and applying T2 to the output of T1: Figure 3: An FST for sutra¯ 6.1.109 T T (S) = T (T (S)) 1 ◦ 2 2 1

So if a cascade of rewrite rules W1, . . . , Wn can be expressed as a series of FSTs T1, . . . , Tn, there is a n possible values, the rule is expanded into n rewrite single FST T that is a composition T . . . T and rules. Mappings and functions are automatically ap- 1 ◦ ◦ n is equivalent to the cascade W1, . . . , Wn (Kaplan and plied where they occur in ψ (the substituens). Kay, 1994, 364). G = T1 . . . Tn constitutes a regular The following cascade represents the four sutras¯ ex- ◦ ◦ grammar. Efficient algorithms are known for compil- emplified above: ing a cascade of rewrite rules into an FST (Mohri and Sproat, 1996). s $ / ( #) → | $ #u / a ( #)a → | 7 An FST for Pan¯ inian sandhi (a A)( #)(a A) a . | | | → (a A)( #)(i I) e The XML formalism for expressing Pan¯ inian rules in | | | → . (a A)( #)(u U) o 3 contains a number of devices; it is not immediately | | | → § (a A)( #)(f F) ar evident how rules employing these devices might be | | | → (a A)( #)(x X) al compiled into an FST. A rule compiler, however, is de- | | | → a ’ / (e o)( #) scribed here that translates Pan¯ .inian rules expressed in → | | the XML formalism into rewrite rules that can be au- Here the notation (x y z) expresses alternation; the rule | | tomatically compiled into an FST using standard algo- matches either x, or y, or z. The symbol represents rithms. a space character; the symbol # represents a boundary It is useful to begin with an instance of Pan¯ . inian that has been inserted by a rule. devo ’pi < devas api sandhi derivation of the string These rules may be efficiently compiled into FSTs. ‘also a god’. An FST encoding the final rule is shown in fig. 3. In FORM SU¯ TRA this transducer, s0 is the initial state and doubly-circled devas api states are the members of F , the set of final states. The deva$ api 8.2.66 graphical representation of the FST has been simpli- deva#u api 6.1.113 fied, so that symbols that are accepted on transition dev!(gunate(u)) api 6.1.87 from si to sj share an arc between si and sj (in this devo ’pi 6.1.109 case, the symbols are separated by commas). The nota- tion x : y indicates the symbols on the upper and lower Sutra¯ 8.2.66 replaces a pada-final s with rU (here sym- tapes of the transducer, respectively. If the transducer bolized by $). Sutra¯ 6.1.113 replaces pada-final rU reads input from the upper tape and writes output to the with u preceded by a boundary marker (#) when the lower tape, x : y indicates that if x is read on the up- next pada begins with a. Sutra¯ 6.1.87 has been dis- per tape, y is written on the lower tape. If the symbols cussed above. Sutra¯ 6.1.109 replaces pada-initial a on the upper and lower tapes are the same, a shorthand with avagraha (represented by ’ in SLP1) when the notation is used; thus x is equivalent to x : x. The spe- previous pada ends in the pratyah¯ ar¯ a eN˙ (i. e. e or o).7 cial symbol ? indicates that any symbol is matched on Although the PCREs in the XML format exceed the either the upper or lower tape. power of regular relations, and the implementation of Since it is possible to translate each rule in the above mappings and functions is not obvious in a regular cascade into an FST, and FSTs are closed under compo- grammar, the rule compiler mentioned above is able sition, it is possible to compose a single FST that imple- to produce a cascade of rewrite rules that may be ef- ments the portion of Pan¯ .ini’s sandhi represented by the ficiently compiled into an FST. A consequence of the rules in the cascade above. A compiler developed by rule compilation strategy is that a single Pan¯ .inian rule the author will be capable of compiling the entirety of may be represented as several rewrite rules. Where a Pan¯ .ini’s sandhi rules into a single FST. The FST is then rule makes use of pattern memory, which can contain converted to Java code using a toolkit written by the au- thor. Compilation of the generated source code yields 7Although avagraha is not a phoneme, it may be con- ceived of linguistically as a “trace” left after the deletion of binary code that may be run portably using any Java a-. For this reason, it is represented in the SLP1 phonological Virtual Machine (JVM) (Lindholm and Yellin, 1999). coding. Alternatively, for improved performance, the Java code may be compiled into native machine code using the strings (sequences of segments). As far as the com- GNU Compiler for Java (gcj). putational model is concerned, individual symbols are atomic, and no class relations between the symbols ex- 8 Implications ist. The goal in this study has been to develop an in- termediate representational structure, based on XML, While one of the guiding principles of Pan¯ ini’s gram- . that can faithfully encode some of the linguistically sig- mar is conciseness (laghava¯ ), a computational imple- nificant aspects of a portion of Pan¯ ini’s grammar (the mentation poses other demands, such as tractability and . rules involved in external sandhi) and at the same can efficiency. Pan¯ ini’s rules are formulated in terms of . be automatically translated into an efficient computa- classes based on distinctive features and must be con- tional implementation. strued with the aid of ‘interpretive’ (paribhas¯.a¯) rules, technical terms (sam. jn˜a¯), and other theoretical appara- 9 Appendix: core rules for external tus. However desirable the mathematical properties of a sandhi regular grammar may be, a grammar stated in such The following is a list of modeled vidhi rules (8.3.4: terms is at odds with Pan¯ .ini’s principles. Rather, it adhikar¯ a, 8.4.44: pratis.edha) for external sandhi. No

hearkens back to the vikar¯ a system employed by ear- account is taken here of pragr¡ hya rules that specify cer- lier linguistic thinkers, in which individual segments tain sounds as exempt from sandhi (since these rules are the target of specific rules (Cardona, 1965b, 311). refer to morphosyntactic categories). Various optional By way of contrast, Pan¯ .ini states a rule econom- rules are not listed. ically in terms of the sound classes enumerated in the Sivas´ utr¯ as. Thus 8.4.41 s..tuna¯ s..tuh. specifies the 6.1.73 che ca retroflexion of an s or dental stop either (1) before a 6.1.74 a¯nm˙ a¯no˙ sca´ pada-final -s. or (2) pada-finally before a .tU (i. e. a 6.1.132 etattadoh. sulopo ’koranansam˜ ase¯ hali retroflex stop). 8.2.66 sasajus.o ruh. With a little less economy, we can represent Pan¯ . ini’s 8.2.68 ahan rule by two rules in XML: 6.1.113 ato roraplutadaplute¯

lcontext="z[@(wb)]" 6.1.88 vr¡ ddhireci ref="A.8.4.41"/> 6.1.87 adgun¯ . ah. 6.1.77 iko yanaci 8.2.39 jhalam¯ . jaso´ ’nte The pratyah¯ ar¯ a tU stands for the dental stop series t, 8.3.4 anunasik¯ atpar¯ o ’nusvar¯ ah. { th, d, dh, n . We apply the retroflex mapping: 8.3.7 nasc´ havyapras´an¯ } 8.3.14 ro ri 8.3.19 lopah. s´akalyasya¯ The effect is to change a single phonological feature 8.3.20 oto gar¯ gyasya across an entire class; sounds with a dental place of 8.3.23 mo ’nusvar¯ ah. articulation (dantya) are replaced by sounds with a 8.3.31 si´ tuk retroflex articulation (mur¯ dhanya). In specifying such 8.3.32 namo˙ hrasvadaci¯ namun˙ . nityam 8.3.34 visarjan¯ıyasya sah a replacement, Pan¯ .ini makes use of the principle of . 8.3.35 sarpar´ e visarjan¯ıyah savarn¯ . ya ‘homogeneity of sounds’. So the substituend . chosen is that closest to the original—with respect to 8.3.40 namaspurasorgatyoh. 8.4.40 stoh scun´ a¯ scuh´ voice (ghos.avat / aghos.a), aspiration (mahapr¯ an¯ . a / . . 8.4.44 s´at¯ alpapran¯ . a), and nasality (sanun¯ asika¯ / niranunasika¯ ). Thus t t, th th, d d, and so on; yet Pan¯ ini does 8.4.41 s..tuna¯ s..tuh. → . → . → . . not need explicitly (and repetitively) to specify the ex- 8.4.45 yaro ’nunasik¯ e ’nunasik¯ o va¯ 8.4.53 jhalam¯ jasjha´ si´ act segments substituted. In this way, the As..tadhy¯ ay¯ ¯ı . avoids the bias (“segmentalism”) that places the linear 8.4.55 khari ca segment at the center of phonological theory—a bias 8.4.60 torli from which contemporary linguistics is beginning to 8.4.62 jhayo ho ’nyatarasyam¯ distance itself (Aronoff, 1992). 8.4.63 sa´ sc´ ho ’t.i The finite state approach discussed in this paper, 8.4.65 jharo jhari savarn. e however, is limited to describing the relations between References Rama Nath Sharma. 2003. The As..tadhy¯ ay¯ ¯ı of Pan¯ . ini, Vol. 6: English Translation of Adhyayas¯ Alfred V. Aho, Ravi Sethi, and Jeffrey D. Ullman. Seven and Eight with Sanskrit Text, Translitera- 1988. Compilers: Principles, Techniques, and tion, Word-Boundary, Anuvr.tti, Vr.tti, Explanatory Tools. Addison-Wesley, Reading, MA. Notes, Derivational History of Examples, and In- dices. Munshiram Manoharlal, New Delhi. Mark Aronoff. 1992. Segmentalism in linguistics: The alphabetic basis of phonological theory. In Pamela Henry Smith. 1992. Brevity in Pan¯ . ini. Journal of Downing, Susan D. Lima, and Michael Noonan, ed- Indian Philosophy, 20:133–147. itors, The Linguistics of Literacy, volume 21 of Ty- pological Studies in Language, pages 71–82. John Unicode Consortium. 2006. The Unicode Standard, Benjamins, Amsterdam. Version 5.0. Addison-Wesley, Boston. Larry Wall, Tom Christiansen, and John Orwant. 2000. Kenneth R. Beesley and Lauri Karttunen. 2003. Finite Programming Perl. O’Reilly, Sebastapol, CA, 3d State Morphology. CSLI, Stanford, CA. edition. Akshar Bharati, Vineet Chaitanya, and Rajeev Sangal. 1996. Natural Language Processing: A Paninian Perspective. Prentice-Hall of India, New Delhi.

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