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\title{Informatics in P{\=a}\d{n}ini's Grammar }
\author[Amba Kulkarni]{Amba Kulkarni}
\institute[IIAS Shimla]{IIAS Shimla \\ \vspace{1cm}
}
\date{\small {20th March 2017}}
\begin{document}
\maketitle
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\begin{frame}{Outline}
\frametitle{Outline}
\tableofcontents[hideallsubsections]
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\begin{frame}
\begin{quote}
The mathematical method is characteristic of much of Western philosophy whereas the grammatical method is characteristic of much of Indian philosophy.
\end{quote}
Daniel H H Ingalls, `Comparison of Indian and Western Philosophy', Journal of Oriental Research, (2),1954.
\end{frame}
\begin{frame}
%\section{Introduction}
%\subsection{Informatics}
\frametitle{Informatics}
Etymology: Informatics\\
\begin{itemize}
\item German:Informatik
\item French:Informatique
\end{itemize}
\pause
\begin{block}{}
{\bf Informat}ion + auto{\bf matique} $\Rightarrow$ informatique \\
Informatics: Science of Automatic processing of Information\\
Information coding device: Language\\
\end{block}
\pause
Computational Linguistics $\subset$ Informatics\\
\pause
\begin{block}{}
The First Formal system of Grammar: P{\=a}\d{n}ini's A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}
\end{block}
\end{frame}

\begin{frame}
\frametitle{P{\=a}\d{n}ini's A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}
%\subsection{P{\=a}\d{n}ini's A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}

\begin{itemize}
\item Circa 500 B.C.E.
\item Extant Grammar of the then prevalent Sanskrit Language
\item Around 4000 sutras\footnote{\color{magenta}alp{\=a}k\d{s}aram\color{black}(concise) \color{magenta}asandigdham\color{black}(unambiguous) \color{magenta}s{\=a}ravat\color{black}(contains essence) \color{magenta}vi\'{s}vatomukham\color{black}(general) \textbar \\\color{magenta}astobham\color{black}(continuous) \color{magenta}anavadyam\color{black}(without flaw) \color{magenta}ca s{\=u}tra\d{h} s{\=u}travido vidu\d{h}\color{black} \textbar \textbar(v{\=a}yu pur{\=a}\d{n}a)}(aphorism)
\item 8 chapters 4 sections each
\end{itemize}
%% Add relevant part from Staal's article on Euclid and Panini
\end{frame}

\begin{frame}
\frametitle{A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i} .. contd}
 It is admired for its
\begin{itemize}
\item simplicity
\item completeness of the descriptive coverage
\item rigorous consistency in the use of meta language
\item intricate system of conventions governing rule application and rule interaction
\item richness in various aspects of informatics
\end{itemize}
\end{frame}
\begin{frame}
\begin{quote}
One of the greatest monuments of human intelligence (Bloomfield) is only
beginning to claim its rightful position in linguistics. Many of the
insights of Panini's grammar still remain to be recaptured, but those
that are already understood constitute a major theoretical contribution.
\end{quote}

Paul Kiparsky, Emeritus Prof. Stanford University\\
`The encyclopedia of Language  and Linguistics', Asher, pp 2923.

\end{frame}
\begin{frame}
\begin{quote}
Panini, then, was not an ancient and nebulous precursor of a science in
which everything has since been done better, but a distant colleague of
genius from whom linguists are still able to learn.

\end{quote}
\begin{quote}
Prof. Fritz Staal\\
P{\=a}\d{n}ini , `Encyclopedia of Languge and Linguistics', Vol-6, Page no: 2917; Ed: Asher
\end{quote}
\end{frame}
\begin{frame}
%\begin{quote}
%... he(Panini) could devise an extremely compact data representation for
%a very rich grammatical formalisation. This applies not only to the pratyaharas, but also in general to his exception control structure, which is strongly evocative of object-oriented programming.
%\end{quote}
%-- Prof. G\'erard Huet, Inria, France (personal communiation with Prof. Vineet Chaitanya)

\begin{quote}
Not only Panini was by far the first linguist in recorded history, but I
claim he was the first informaticien, 24 centuries before computers came into
existence.
\end{quote} 
-- Prof. G\'erard Huet, Computer Scientist, Inria, Paris, in the Inaugural Speech at the First International Sanskrit Computational Linguistics Symposium, Paris, 29th october, 2007

\end{frame}

\begin{frame}
\frametitle{Informatics in A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}

From informatics point of view,\\
the importance of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i} is two fold, 
\begin{itemize}
\item The Structure of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}
\item Method of Analysis of Sanskrit Language
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}
\section{Structure of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}
A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i} consists of around 4000 aphorisms with some ancillary texts.
\begin{itemize}
\item \'{s}ivas{\=u}tras (special order of the phonemes)
\item dh{\=a}tup{\=a}\d{t}ha (list of verbal roots)
\item ga\d{n}ap{\=a}\d{t}ha (various sets of nouns)
\item li\.{n}g{\=a}nu\d{s}{\=a}sanam (system for deciding the gender)
\item u\d{n}{\=a}di s{\=u}tras (?) (special rules)
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{{\it \'{s}ivas\=utr{\=a}\d{n}i}}
\subsection{{\it \'{s}ivas\=utr{\=a}\d{n}i}}
Normal Arrangement of Alphabet \\
\vspace{0.5cm}
\begin{tabular}{l l}
\hline
\color{magenta}Vowels \color{black}& {\it a \={a} i \={\i} u \={u} \d{r}  \d{\={r}} \d{l} e ai o au a\d{m} a\d{h} }\\
\hline \hline
\end{tabular}\\
\begin{tabular}{l l l l l l}
\color{magenta}Velar  \color{black}& {\it ka }& {\it kha }& {\it ga }& {\it gha }& {\it \'{n}a }\\
\color{magenta}Palatal  \color{black}& {\it ca }& {\it cha }& {\it ja }& {\it jha }& {\it \~{n}a }\\
\color{magenta}Retroflex  \color{black}& {\it \d{t}a }& {\it \d{t}ha }& {\it \d{d}a }& {\it \d{d}ha }& {\it \d{n}a}\\
\color{magenta}Dental  \color{black}& {\it ta }& {\it tha }& {\it da }& {\it dha }& {\it na}\\
\color{magenta}Labiel  \color{black}& {\it pa }& {\it pha }& {\it ba }& {\it bha }& {\it ma}\\
\hline \hline 
\end{tabular}\\
\begin{tabular}{l l}
\color{magenta}semi-vowel  \color{black}& {\it ya ra la va }\\
\color{magenta}Fricative  \color{black}& {\it \'{s}a \d{s}a sa ha }\\
\hline
\end{tabular}
\end{frame}

\begin{frame}
\frametitle{ \'{s}ivas\=utr{\=a}\d{n}i}
P{\=a}\d{n}ini required several(42) subsets of this
alphabet to describe various operations.
\end{frame}

\begin{frame}
\frametitle{\'{s}ivas\=utr{\=a}\d{n}i}
Some of these subsets: \\
\vspace{0.5cm}
	All vowels \\
	All consonants \\
	All vowels + semivowels + nasals \\
	The voiceless stops  \\
	stops and sibilants \\
	Any of {\it ba ga \d{d}a da} \\
        Any of {\it bha gha \d{d}ha dha} \\
        Any of {\it ya va ra la \~na ma \.na \d{n}a na ma jha bha} \\ ....
\end{frame}

\begin{frame}
\frametitle{ \'{s}ivas\=utr{\=a}\d{n}i}
It is not advisable to give 42 names to these sets.  \\
It will be difficult to memorize the association. \\
\vspace{1cm}

These are Partially ordered sets. \\
\vspace{1cm}

P{\=a}\d{n}ini arranged them linearly in the form of 14 ShivasUtras.
\end{frame}
\begin{frame}
\frametitle{ \'{s}ivas\=utr{\=a}\d{n}i}
\begin{columns}
\begin{column}{0.1\textwidth}
1\\
2\\
3\\
4\\
5\\
6\\
7\\
8\\
9\\
10\\
11\\
12\\
13\\
14\\
\end{column}
\begin{column}{0.9\textwidth}
\begin{center}
\color{blue}{\it a i u \color{red}(\d{N})}\\
\color{blue}{\it \d{r} \d{l}\color{red}(K)}\\
\color{blue}{\it e o \color{red}(\.N) }\\
\color{blue}{\it ai au \color{red}(C) }\\
\color{blue}{\it ha ya va ra\color{red} (\d{T}) }\\
\color{blue}{\it la \color{red}(\d{N})}\\
\color{blue}{\it \~na ma \.na \d{n}a na \color{red}(M) }\\
\color{blue}{\it jha bha\color{red}(\~N) }\\
\color{blue}{\it gha \d{d}ha dha \color{red}(\d{S})}\\
\color{blue}{\it ja ba ga \d{d}a da \color{red}(\'{S}) }\\
\color{blue}{\it kha pha cha \d{t}ha tha ca \d{t}a ta \color{red}(V)}\\
\color{blue}{\it ka pa \color{red}(Y)}\\
\color{blue}{\it \'{sa} \d{sa} s \color{red}(R)}\\
\color{blue}{\it ha \color{red}(L)}\\
\end{center}
\end{column}
\end{columns}
\end{frame}

\begin{frame}
\frametitle{ \'{s}ivas\=utr{\=a}\d{n}i}
Justification of this arrangement is  \\
attempted independently by  \\
\vspace{0.5cm}
Cardona (on historical grounds) \\
Stall (linguistically) \\
Kiparsky (logically) \\
and Petersen (mathematically) \\
\vspace{0.5cm}
Petersen (2008) proved that the arrangement is optimal.\\
And is one among the 12 000 000 possibilities.\\
\end{frame}
\begin{frame}
\frametitle{ \'{s}ivas\=utr{\=a}\d{n}i}
The set {\it khar}
\begin{columns}
\begin{column}{0.1\textwidth}
1\\
2\\
3\\
4\\
5\\
6\\
7\\
8\\
9\\
10\\
11\\
12\\
13\\
14\\
\end{column}
\begin{column}{0.9\textwidth}
\begin{center}
\color{blue}{\it a i u \color{red}(\d{N})}\\
\color{blue}{\it \d{r} \d{l}\color{red}(K)}\\
\color{blue}{\it e o \color{red}(\.N) }\\
\color{blue}{\it ai au \color{red}(C) }\\
\color{blue}{\it ha ya va ra\color{red} (\d{T}) }\\
\color{blue}{\it la \color{red}(\d{N})}\\
\color{blue}{\it \~na ma \.na \d{n}a na \color{red}(M) }\\
\color{blue}{\it jha bha\color{red}(\~N) }\\
\color{blue}{\it gha \d{d}ha dha \color{red}(\d{S})}\\
\color{blue}{\it ja ba ga \d{d}a da \color{red}(\'{S}) }\\
\color{black}{\it kha pha cha \d{t}ha tha ca \d{t}a ta \color{red}(V)}\\
\color{black}{\it ka pa \color{red}(Y)}\\
\color{black}{\it \'{sa} \d{sa} s \color{red}(R)}\\
\color{blue}{\it ha \color{red}(L)}\\
\end{center}
\end{column}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{ \'{s}ivas\=utr{\=a}\d{n}i}
\begin{columns}
\begin{column}{0.1\textwidth}
1\\
2\\
3\\
4\\
5\\
6\\
7\\
8\\
9\\
10\\
11\\
12\\
13\\
14\\
\end{column}
\begin{column}{0.9\textwidth}
\begin{center}
\color{blue}{\it a i u \color{red}(\d{N})}\\
\color{blue}{\it \{\d{r} \d{l}\}\color{red}(K)}\\
\color{blue}{\it \{\{e o\} \color{red}(\.N) }\\
\color{blue}{\it \{ai au\}\} \color{red}(C) }\\
\color{blue}{\it ha ya va ra\color{red} (\d{T}) }\\
\color{blue}{\it la \color{red}(\d{N})}\\
\color{blue}{\it \~na ma \{\.na \d{n}a na\} \color{red}(M) }\\
\color{blue}{\it jha bha\color{red}(\~N) }\\
\color{blue}{\it \{gha \d{d}ha dha\} \color{red}(\d{S})}\\
\color{blue}{\it ja \{ba ga \d{d}a da\} \color{red}(\'{S}) }\\
\color{blue}{\it \{kha pha\} \{cha \d{t}ha tha\} \{ca \d{t}a ta\} \color{red}(V)}\\
\color{blue}{\it \{ka pa\} \color{red}(Y)}\\
\color{blue}{\it \{\'{sa} \d{sa} s\} \color{red}(R)}\\
\color{blue}{\it ha \color{red}(L)}\\
\end{center}
\end{column}
\end{columns}
2! * 2! * 2! * 2! * 3! * 3! * 4! * 2! * 3! * 3! * 2! * 3! $\approx$ 12 000 000
\end{frame}
\begin{frame}
\frametitle{ \'{s}ivas\=utr{\=a}\d{n}i}
Given a set of Partially Ordered Sets,  \\
\vspace{0.25cm}
Now it is possible to tell \\
\vspace{0.25cm}
Whether the elements are  \\
\vspace{0.25cm}
\'{S}ivas{\=u}tra encodable or not. \\
\vspace{0.25cm}
Weibke Petersen(2008) \\
\end{frame}
\begin{frame}
\frametitle{Structure of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}
A) The First Formal Grammar\\
\vspace{1cm}
a) A Formal Grammar is written in a Formal Language.\\
b) The Formal language has well-defined Syntax.\\
\vspace{1cm}

A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i} is written in Sanskrit.\\
The syntax as well as the programme are intermixed in the same piece of work.

\end{frame}
\begin{frame}
\frametitle{Formal Grammar}
%Backus Naur Form (BNF)\\
%
%A BNF specification is a set of derivation rules, written as\\
%\vspace{0.25cm}
%$<$symbol$>$ ::= Expression \\
%\begin{itemize}
%\item $<$symbol$>$ is a nonterminal
%\item Expression consists of one or more sequences of symbols separated by \textbar'
%\item Symbols that never appear on a left side are terminals
%\item Symbols that appear on a left side are non-terminals
%\item '::=' means that the symbol on the left is replaced with the
%expression on the right.
%\end{itemize}
$ G = ( N, \Sigma, P, S ) $
\begin{itemize}
\item $N$ : A finite set of Non-terminals
\item $S$: The Start Symbol $ \in N$
\item $\Sigma$: A finite set of Terminals
\item $P$: Production rules, of the type\\
$(\Sigma \cup N)*N(\Sigma \cup N)* \rightarrow (\Sigma \cup N)*$
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{Syntax of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}
\subsection{Syntax of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}
Example 1
\begin{tabular}{rl}
{\it padam}\color{blue} (word)\color{black} ::= & {\it subantam}\color{blue} (nominal form)\color{black}\\
\textbar & {\it ti\.nantam}\color{blue} (verbal form)\color{black}\\  \color{red}({supti\.nantam padam} 1.4.14)\color{black}\\
;&\\
{\it subantam} \color{blue}(nominal form)\color{black}::= & {\it pr{\=a}tipadikam} \color{blue}(nom stem)\color{black}\color{magenta} {\it sup}\color{blue} (nom suff)\color{black}\\
{\it pr{\=a}tipadikam}\color{blue} (nominal stem)\color{black}::= & {\it k\d{r}t} \color{blue} (noun derived from a verb)\color{black}\\\color{red}({\it k\d{r}ttaddhitasam{\=a}s{\=a}\'{s}ca} 1.2.46)\color{black}\\
\textbar & {\it taddhita}\color{blue} (noun derived from a noun)\color{black}\\
\textbar & {\it sam{\=a}sa}\color{blue} (compound)\color{black}\\
\textbar & \color{magenta}underived\_{pr{\=a}tipadikam}\color{blue} (nominal stem)\color{black}\color{black}\\
;&\\
{\it sam{\=a}sa}\color{blue} (compound)\color{black}::= & {\it alaukika vigraha\d{h}}\color{blue} (Intermediate ling exp)\color{black}\\
;&\\
{\it alaukika vigraha\d{h}}::= & \color{magenta}{\it pr{\=a}tipadikam} {\it sup} {\it pr{\=a}tipadikam} {\it sup}\color{black} \\\color{red}({\it saha sup{\=a}} 2.1.4)\color{black}\\
;&\\
\end{tabular}
\end{frame}

\begin{frame}
\frametitle{Syntax of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}
\subsection{Syntax of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}

\begin{tabular}{rl}
A ::= & B\\
\textbar& C\\
;&\\
B ::= & D \color{magenta}E\color{black}\\
D ::= & F\\
\textbar & G\\
\textbar & H\\
\textbar & \color{magenta}I\color{black}\\
;&\\
H ::= & J\\
;&\\
J ::= & \color{magenta}K `+' L M `+' N\color{black}\\
;&\\
\end{tabular}
\end{frame}

\begin{frame}
\frametitle{Syntax of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}
Example 2:\\
\color{magenta} iko ya\d{n}aci (6.1.77)\\
\vspace{0.5cm}
ik\{6\} ya\d{n}\{1\} ac\{7\}\\
\vspace{0.5cm}
\pause
\begin{itemize}
\item \color{magenta}{tasmin iti nirdi\d{s}\d{t}e p{\=u}rvasya} (1.1.65)\color{black}\\
A word ending in locative case indicates `of the preeceding'.
\item \color{magenta}{\it \d{s}a\d{s}\d{t}h{\=\i} sth{\=a}neyog{\=a}} (1.1.48)\color{black}\\
A word in genitive case undergoes change.
\end{itemize}
\pause
{\it ik}\{6\} {\it ac}\{7\} ::= {\it ya\d{n}}\{1\} {\it ac}\{7\}\color{black}\\
\pause
\{i,u,\d{r},\d{l}\} \{a,i,u,\d{r},\d{l},e,o,ai,au\} $\rightarrow$ \{y,v,r,l\} \{a,i,u,\d{r},\d{l},e,o,ai,au\}\\
\end{frame}
\begin{frame}
\frametitle{Syntax of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}}
\begin{itemize}
\item \color{magenta}{tasmin iti nirdi\d{s}\d{t}e p{\=u}rvasya} (1.1.65)\color{black}\\
A word ending in locative case indicates `of the preceeding'.
\item \color{magenta}{tasm{\=a}t iti uttarasya} (1.1.66)\color{black}\\
A word ending in ablative case indicates `of the following'.
\item \color{magenta}{\it \d{s}a\d{s}\d{t}h{\=\i} sth{\=a}neyog{\=a}} (1.1.48)\color{black}\\
A word in genitive case undergoes change.
\end{itemize}
W\{5\} \color{blue}W\{6\}\color{black} W\{7\} ::= W\{5\} \color{blue}W\{1\}\color{black} W\{7\}\\
\vspace{0.5cm}
Ingermann observed that the s{\=u}tras of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}
have the same structure as that of BNF and suggested to rename `Backus Naur Form' as `P{\=a}\d{n}ini Backus Naur Form' (1967 ACM Communications). \\
\vspace{1cm}
\end{frame}

\begin{frame}
\frametitle{{\it Anuv\d{r}tti} }
\subsection{{\it Anuv\d{r}tti} }

{\bf Distributivity in Mathematics:}\\
a * (b + c) = a * b + a * c \\
\vspace{0.5cm}

{\bf Distributivity in Languages:}\\
\vspace{0.5cm}
{\it John goes home.}\\
{\it John eats fruits.}\\
\vspace{0.25cm}
{\it John goes home and eats fruits}\\
\vspace{0.5cm}

Or simply, \\
{\it John goes home},\\
{\it eats fruits}.
\end{frame}

\begin{frame}
\frametitle{{\it Anuv\d{r}tti}}
Consider the following s{\=u}tras:\\
\vspace{0.5cm}
\begin{itemize}
\item \textit{\it upade\'{s}e ac anun{\=a}sik it} 1.3.2
\item \textit{\it hal antyam} 1.3.3
\item \textit{\it na vibhaktau tusm{\=a}\d{h}} 1.3.4
\item \textit{\it {\=a}di\d{h} \~ni\d{t}u\d{d}av{\=a}\d{h}} 1.3.5
\item \textit{\it \d{s}a\d{h} pratyayasya} 1.3.6
\item \textit{\it cu\d{t}{\=u}} 1.3.7
\item \textit{\it la\d{s}aku ataddhite} 1.3.8
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{{\it Anuv\d{r}tti} }
\begin{center}
\begin{longenum}
\item \textit{\it \color{black}upade\'{s}e it}
   \begin{longenum}
   \item \textit{\it \color{magenta}ac anun{\=a}sik (=it)}
   \item \textit{\it \color{magenta}hal antyam}
     \begin{longenum}
       \item \textit{\it \color{blue}na vibhaktau tusm{\=a}\d{h} (=it)}
     \end{longenum}
   \item \textit{\it \color{magenta}{\=a}di\d{h}}
      \begin{longenum}
      \item \textit{\it \color{blue}\~ni\d{t}u\d{d}av{\=a}\d{h} (=it)}
      \item \textit{\it \color{blue}pratyayasya}
         \begin{longenum}
         \item \textit{\it \color{red}\d{s}a\d{h} (=it)}
         \item \textit{\it \color{red}cu\d{t}{\=u} (=it)}
         \item \textit{\it \color{red}la\'{s}aku (=it) ataddhite}
         \end{longenum}
      \end{longenum}
   \end{longenum}
\end{longenum}
\end{center}
\end{frame}

\begin{frame}
\frametitle{{\it Anuv\d{r}tti} }
\begin{center}
\begin{longenum}
\item \textit{\it \color{red}upade\'{s}e} (\color{black} a \color{black})  \textit{\it \color{red}it} (\color{black} c\color{black})
   \begin{longenum}
   \item \textit{\it \color{magenta}ac anun{\=a}sik} \color{black}( = it)(b\color{black}) 
   \item \textit{\it \color{magenta}hal antyam} (\color{black} d\color{black})
     \begin{longenum}
       \item \textit{\it \color{blue}na vibhaktau tusm{\=a}\d{h}(=it)} (\color{black} e\color{black}) 
     \end{longenum}
   \item \textit{\it \color{magenta}{\=a}di\d{h}} (\color{black} f\color{black})
      \begin{longenum}
      \item \textit{\it \color{blue}\~ni\d{t}u\d{d}av{\=a}\d{h} (=it)} (\color{black} g\color{black}) 
      \item \textit{\it \color{blue}pratyayasya} (\color{black} h\color{black})
         \begin{longenum}
         \item \textit{\it \color{red}\d{s}a\d{h}(=it)} (\color{black} i\color{black}) 
         \item \textit{\it \color{red}cu\d{t}{\=u} (=it)} (\color{black} j\color{black}) 
         \item \textit{\it \color{red}la\'{s}aku (=it) ataddhite} (\color{black} k\color{black})
         \end{longenum}
      \end{longenum}
   \end{longenum}
\end{longenum}
\end{center}
\end{frame}

\begin{frame}
\frametitle{{\it Anuv\d{r}tti} }
\begin{center}
\begin{longenum}
\item {\bf a} {\bf c}
   \begin{longenum}
   \item {\bf b} 
   \item {\bf d}
       \begin{longenum}
       \item {\bf e}
       \end{longenum}
   \item {\bf f}
      \begin{longenum}
      \item {\bf g}
      \item {\bf h}
         \begin{longenum}
         \item {\bf i}
         \item {\bf j}
         \item {\bf k}
         \end{longenum}
      \end{longenum}
   \end{longenum}
\end{longenum}
\end{center}
a (b + de + f [ g + h \{ i + j + k \} ] ) c
\end{frame}

\begin{frame}
\frametitle{{\it Anuv\d{r}tti\d{h}} }
No Proper Nesting; {\it ma\d{n}d{\=u}ka pluti\d{h}} \\
\vspace{0.5cm}

\begin{itemize}
\item 1.1.1 \color{red} {\it v\d{r}ddhi\d{h} } \color{black} {\it {\=a}daic}
\item 1.1.2 {\it ade\.n} \color{blue} {\it gu\d{n}a\d{h}} \color{black}
\item 1.1.3 {\it ika\d{h}} \color{red} {\it gu\d{n}av\d{r}ddh{\=\i}} (\color{red}{\it v\d{r}ddhi\d{h} } \color{blue}{\it gu\d{n}a\d{h}}\color{black})
\end{itemize}

\end{frame}

\begin{frame}
\frametitle{{\it Anuv\d{r}tti\d{h}} }
Maximum advantage of features of Natural Language:\\
\vspace{1cm}
How are the complete phrases reconstructed?\\
\vspace{1cm}
{\it {\=a}k{\=a}\.nk\d{s}{\=a}\d{h} } (Expectancy): Major role in deciding the {\it anuv\d{r}tti} (Bhate)\\
\end{frame}

\begin{frame}
\frametitle{{\it Anuv\d{r}tti\d{h}} }
Example of borrowing from as many as 12 s{\=u}tras

\vspace{0.5cm}
Original s{\=u}tra: 
3-3-65 {\it kva\d{n}a\d{h} v{\=\i}\d{n}{\=a}y{\=a}m ca }

After {\it Anuv\d{r}tti}:
\color{blue}pratyaya\d{h} \color{red}para\d{h} ca (\color{blue}{\=a}dyud{\=a}tta\d{h} ca \color{red}dh{\=a}to\d{h} \color{blue}k\d{r}t \color{red}kriy{\=a}rth{\=a}y{\=a}m \color{blue}bh{\=a}ve \color{red}akartari ca k{\=a}rake saj\~n{\=a}y{\=a}m) \color{blue}ap \color{red}upasarge \color{blue}v{\=a} \color{red}nau \color{black}\\
\end{frame}

\begin{frame}
\frametitle{{\it Anuv\d{r}tti\d{h}} }
Some Statistics:\\
\vspace{0.25cm}

\begin{tabular}{ll}
Total S{\=u}tras &	(3,984)  4,000 \\
Total Words & (7,007) 7,000    \\
Total Words after repeating the words with anuv\d{r}tti& 40,000 \\
Compression due to anuv\d{r}tti&   (40,000/7,000 $\approx$)       1/6 \\
In terms of byte size, compression&      1/3 \\
\end{tabular}

\vspace{0.5cm}

Significant from Oral Tradition.\\
The time to memorise the s{\=u}tras grows exponentially.\\
With anuv\d{r}tti, a student can memorise the complete A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i} in about only 6 months!
\end{frame}


\begin{frame}
\frametitle{Ordering of the rules}
\subsection{Ordering of the rules}
\begin{itemize}
%\item Sa\~nj{\=a} triggers the rules\\
%{\it sam{\=a}s{\=a}nta\d{h}}, {\it dvandve}, {\it avyay{\=\i}bh{\=a}ve}, {\it uttarapade}, {\it sa\d{m}hit{\=a}y{\=a}m} , ..
\item {\it p{\=u}rvatra asiddham} (8.2.1)
\item {\it asiddhavat atra {\=a}bh{\=a}t} (6.4.22)
\item {\it \d{s}atvatukorasiddha\d{h}} (6.1.83)
\end{itemize}
\end{frame}

\begin{frame}
\frametitle{Ordering of the rules}
\begin{itemize}
\item {\it asiddhavat atra {\=a}bh{\=a}t} (6.4.22)
\begin{itemize}
\item {\it hujhulbhyo\d{h} herdhi\d{h}} (6.4.101)
\item {\it \'{s}{\=a}hau} (6.435)
\end{itemize}
\end{itemize}

\vspace{0.5cm}
6.4.101: {\it \'{s}{\=a}s} + {\it hi} $\rightarrow$ {\it \'{s}{\=a}s}  \color{red} {\it dhi} \color{black}\\
6.4.35: {\it \'{s}{\=a}s} + {\it hi}$\rightarrow$ \color{red} {\it \'{s}{\=a}} \color{black} + {\it hi}\\

\vspace{0.5cm}
Application of one rule blocks the application of the other.\\
Both the rules need to be applied.
\vspace{0.5cm}

{\it asiddhavat atra {\=a}bh{\=a}t} (6.4.22) $\rightarrow$ Parallel Computing
\end{frame}

%\begin{frame}
%\frametitle{Ordering of the rules}
%Instead of a rule as \\
%R: a b $\rightarrow$ c d\\
%\vspace{0.5cm}
%P{\=a}\d{n}ini states it as a combination of two rules:\\
%\vspace{0.5cm}
%
%$R_{1}$: a b $\rightarrow$ c b\\
%$R_{2}$: a b $\rightarrow$ a d\\
%\vspace{0.5cm}
%
%Implications:
%\begin{itemize}
%\item Brevity\\
%Instead of $n_1$ * $n_2$ rules, only $n_1$ + $n_2$ rules are needed.
%\item Parallel Computing
%\end{itemize}

%\end{frame}

\begin{frame}
\frametitle{Conflict Resolution}
\subsection{Conflict Resolution}

Programming Languages
\begin{itemize}
\item Longest match
\item Precedence Rules
\end{itemize}

\vspace{1cm}
A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i}
\begin{itemize}
\item {\it viprati\d{s}edhe para\d{m} k{\=a}ryam} (1.4.2)
\end{itemize}

\end{frame}
\begin{frame}
\includegraphics[scale=0.25]{model_ash.jpg}
\end{frame}

\begin{frame}
\frametitle{Modularity}
\subsection{Modularity}
The rules related to a particular task are grouped together. \\
For example,\\
consider the following s{\=u}tras which identify sounds used as markers
(\textit{anubandha}).
\begin{itemize}
\item \textit{\it upade\'{s}e ac anun{\=a}sik it} 1.3.2
\item \textit{\it hal antyam} 1.3.3
\item \textit{\it na vibhaktau tusm{\=a}\d{h}} 1.3.4
\item \textit{\it {\=a}di\d{h} \~ni\d{t}\d{d}av{\=a}\d{h}} 1.3.5
\item \textit{\it \d{s}a\d{h} pratyayasya} 1.3.6
\item \textit{\it cu\d{t}{\=u}} 1.3.7
\item \textit{\it la\d{s}aku ataddhite} 1.3.8
\end{itemize}

\end{frame}
%\begin{frame}
%\frametitle{Modularity}
%If we take into account the recurrence (\textit{anuv\d{r}tti}) of terms
%from preceding s{\=u}tras, the rules may be rewritten (indicating the
%anuv\d{r}tti by indentation) as
%\begin{center}
%\begin{longenum}
%\item \textit{\it upade\'{s}e it}
%   \begin{longenum}
%   \item \textit{\it ac anun{\=a}sik} 1.3.2
%   \item \textit{\it hal antyam} 1.3.3
%      \begin{longenum}
%      \item \textit{\it na vibhaktau tusm{\=a}\d{h}} 1.3.4
%      \end{longenum}
%   \item \textit{\it {\=a}di\d{h}}
%      \begin{longenum}
%      \item \textit{\it \~ni\d{t}\d{d}av{\=a}\d{h}} 1.3.5
%      \item \textit{\it pratyayasya}
%         \begin{longenum}
%         \item \textit{\it \d{s}a\d{h}} 1.3.6
%         \item \textit{\it cut{\=u} } 1.3.7
%         \item \textit{\it la\'{s}aku ataddhite} 1.3.8
%         \end{longenum}
%      \end{longenum}
%   \end{longenum}
%\end{longenum}
%\end{center}
%
%Translation of this set of rules into a simple algorithm will show the
%parallel between P\={a}\d{n}ini's s{\=u}tras and a computer algorithm.
%
%\end{frame}

\begin{frame}
\frametitle{Features of A\d{s}\d{t}{\=a}dhy{\=a}y{\=\i} .. contd}
Object Oriented Programming:\\
\vspace{1cm}
Encapsulation of data with the (markers to the) functions\\
Bhaj + (gh)a(\~n): In the presence of gh, j $\rightarrow$ g\\

\vspace{1cm}
Inheritance: \\
\vspace{1cm}

Multiple inheritance $\rightarrow$ arranged as a linear inheritance \\

derivational suffixes, deriving a noun from a noun (Taddhita pratyaya)\\
(Ashwini Deo 2007)
\end{frame}

\begin{frame}
\frametitle{Analysis of Sanskrit Language}
\section{Analysis of Sanskrit Language}

P{\=a}\d{n}ini paid utmost attention to the dynamics of Information flow while analysing Sanskrit.
\vspace{1cm}

We cite 3 s{\=u}tras to highlight this point.
\begin{itemize}
\item anabhihite(1.3.1)  ({\it Where} is the information Coded)
\item svatantra\d{h} kart{\=a} (1.4.54)  ({\it How much} information is coded) 
\item sam{\=a}nakart\d{r}kayo\d{h} p{\=u}rvak{\=a}le (3.4.21) ({\it How} is the information coded)
\end{itemize}
\end{frame}

\begin{frame}
anabhihite (Where is the information coded?)
\begin{itemize}
\item Skt: r{\=a}ma\d{h} r{\=a}va\d{n}am hanti.\\
Gloss: Rama\{nom\} Ravana\{acc\} kill\{3p sg pres\}\\
Eng: Rama killed Ravana.\\

\item Skt: r{\=a}me\d{n}a r{\=a}va\d{n}a\d{h} hata\d{h}.\\
Gloss: Rama\{inst\} Ravana\{nom\} kill\{3p sg past pl\}\\
Eng: Ravana was killed by Rama.
\end{itemize}
\end{frame}

\begin{frame}
svatantra\d{h} kart{\=a} (1.4.54)  ({\it How much} information is coded) 
\begin{itemize}
\item {\bf John} opened the door with a key.
\item {\bf This key} opened the door.
\item {\bf The wind} opened the door.
\item {\bf The door} opened.
\end{itemize}
\pause
\begin{itemize}
\item {\bf John} opened the door with a key. \color{red} Agent \color{black}
\item {\bf This key} opened the door. \color{red} Instrument \color{black}
\item {\bf The wind} opened the door. \color{red} Cause \color{black}
\item {\bf The door} opened. \color{red} goal \color{black}
\end{itemize}

In P{\=a}\d{n}inian Framework, all of them are {\bf kart{\=a}}!
\end{frame}

\begin{frame}
Greatness of \textit{P\={a}\d{n}ini} lies in\\
identifying \color{blue}EXACTLY HOW MUCH \color{black}\\
information is coded in a language string.\\

$\Rightarrow$
Upper Bound for the possible Analysis\\
using only a language string and grammar.\\

\end{frame}
\begin{frame}
We can extract precisely only that information which can be decoded from the 
language string `without any requirement of additional knowledge'.\\
\vspace{0.5cm}
Analogy: \\
We can not do high quality work with low quality energy.\\

\end{frame}
\begin{frame}
\begin{center}
{\it Dhanyav{\=a}da\d{h}}\\
{Thank you for your attention}
\end{center}
\end{frame}
\end{document}