The document describes a system for converting Arabic numbers to their Yoruba lexical equivalents. It discusses Yoruba numerals and their derivation using addition, subtraction and multiplication. A computational model is presented using pushdown automata to capture the number conversion. The system was implemented in Python and evaluated using Mean Opinion Score testing. Examples of number conversions like 19679 are provided to demonstrate the system.

1. A Number to Yor`b´ Text Transcription System
u a
Akinad´ Olugb´nga Ol´w´l´
e e . a ae
and
e ı . eu ı `a ı
Od´job´ Od´t´nj´ Aj`d´
. . .
Computer Sci. & Engr. Department
Ob´f´mi Aw´l´w` University, Il´-If`
ae. oo o
. . e e .
AGIS 2011 Conference, Addis
Ababa, Ethiopia
01 December, 2011

2. Presentation Outline
Introduction
Numbers and Numerals
Normalisation of Numbers for TTS
Objectives
The Yor`b´ numeral system
u a
The Yor`b´ numeral generation
u a
methodology
Software Implementation
Evaluation
Overview
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3. Numbers and Numerals
Number is an abstract concept that is represented by symbols
within a numeral system.
A Numeral system is concerned with the written representation of
spoken positive whole numbers.
The Hindu-Arabic numeral has being adopted as a universally
acceptable representation for numbers and mathematical
expressions.
The Hindu-Arabic numeral has ten symbols i.e. 0, 1, 2, 3, 4, 5, 6,
7, 8 and 9
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4. Numbers and Numerals
Numbers can take different formats, Which include
` ` a
Cardinal Numbers: 3, 10, Eta, Ew´
. .
` . ta, ` . w`´
Ordinal Numbers: 3rd , 10th, Ike Ike aa
Monetary Value: $300, Naira M´w`´
e aa
.
Phone Numbers: 234802234****
Percentage: 10%, ` a m´`w´ n´ u og´run
Id´ ee a ın´ . o
.. .
The Yor`b´ has many dialects with varying linguistic variation
u a
(Fabunmi, 2010). But they can all communicate using the
Standard Yor`b´ (SY).
u a
So, our focus is to develop a system that can convert cardinal
numbers to their SY lexical forms.
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5. Normalisation of Numbers for TTS
Text normalisation is one of the important steps in high level
speech synthesis.
Numbers, abbreviations, symbols etc are converted into their
lexical (textual) equivalence.
Normalisation of numbers is thus an important stage in this step.
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6. Objectives
To specify and design a computational model to capture the
conversion of numbers to their Standard Yor`b´ (SY) lexical
u a
equivalence
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7. Objectives
To specify and design a computational model to capture the
conversion of numbers to their Standard Yor`b´ (SY) lexical
u a
equivalence
To implement a software for the number to SY text transcription
model designed above
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8. Objectives
To specify and design a computational model to capture the
conversion of numbers to their Standard Yor`b´ (SY) lexical
u a
equivalence
To implement a software for the number to SY text transcription
model designed above
To evaluate the system implemented
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9. The Yor`b´ numeral system
u a
Yor`b´ numerals is Vigesimal ie based on 20. *(Ekundayo, 1975),
u a
(Zaslavsky, 2000), (Longe, 2009)
The Yoruba has 16 lexicons which serves as the basic building
blocks. (Ekunday0, 1975)
1=`kan, 2=`j` 3=`ta, 4=`rin, 5=`r´n, 6=`f`, 7=`je, 8=`jo,
o
. e ı, e
. e
. au ea
. e e.
.
9=esan, 10=ewa, 20=og´n, 30=ogbon, 200=igba, 300=odunrun,
u
400=ir´ o, 20,000=oke
ınw´
Special positional words exists for addition (l´), subtraction (d´
e ın)
and multiplication (`n`).
o a
.
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10. What a Yor`b´ Speaker/Hearer knows about Yor`b´
u a u a
numeral
All numbers can be represented within the Yor`b´ numerals.
u a
There are subgroups within the Yor`b´ numerals based on their
u a
syntactic derivational rules.
Linguistic skills (contraction, vowel harmony, elision and euphonic
assimilation) are required for the representations of some numerals.
There exist multiple representations for numerals with low
functional load.
The largest single number that can be represented is 20,000 `k´
o e
. .
Higher numbers are derived from 20,000 `k´
o e
. .
Subtraction has a heavy functional load than addition
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11. Subgroups of Yoruba Numeral
1 - 14: Behaves as decimal
15 - 199: Derived with 20 as the multiplicative base.
200 - 1999: Derived with 200 as the multiplicative base.
2000 - 19999: Derived with 2000 as the multiplicative base.
2000 and above: Derived with 20000 as the multiplicative base.
So from above, the multiplicative base of Yoruba numeral are:
20, 200, 2000, 20000
which can be represented as: 2(10)1 ,2(10)2 ,2(10)3 , 2(10)4
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12. SY Numerals Derivation
Three of the four basic arithmetical operations (addition,
subtraction & multiplication) are employed for the derivation of an
infinite set of SY numerals from the sixteen vocabulary items.
(Ekundayo, 1977)(Zaslavsky, 1999)
A single number can be generatedfrom multiple subtractions.
Number Yor`b´u a Derivation
15 ``d´g´n
ee o u
.. 20-5
65 `´d´rin
aa o
. (4*20)-10-5
565 `´d´rin l´ l`´d´gb`ta
aa o
. e ee e e
.. . . (3*200)-100+(4*20)-
10-5
17,565 `´d´rin l´ l`´d´gb`ta (9*2000)-
aa o . e ee e e
.. . .
l´ l`´d´gb`as´n
e ee e a a
.. . 1,000+(3*200)-
100+(4*20)-10-5
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13. Special Type of Subtraction
A special type of subtraction exist when you subtract 5, 10, 100
and 1000
This brings about the eedin phenomenum
eedin(A)
we will assume an implied subtraction from A of the following
kinds.
1. 5 iff A = 20 or 30
2. 10 iff A = 60,80,100,....,200
3. 100 iff A = 600,800,1000,....,2000
4. 1000 iff A = 4000,6000,8000,....,20000
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14. Methodology
A review of the theory, process and computation underlying the SY
numerals was conducted by consulting appropriate literature.
A computational model was formulated using automata theory
based approach. The proposed model was captured with a set of
Push-Down Automata (PDA) using Java Formal Language and
Automata Package (JFLAP), a simulation tool for experimenting
with Formal Languages and Automata Theory.
The model was implemented using the Python programming
language.
Evaluation of the system was carried out using the Mean Opinion
Score (MOS) which is a Turing test for computational intelligence.
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15. Software Design
Arabic
Start
Number
Is number in basic
numerals? Yes
No
Decomposition of Translation
Number to Basic Number to
Units Yoruba
Yoruba Morphological
Stop
Numeral Analysis
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16. Push Down Automata
A non-deterministic PDA is defined as a sextuple
Q, Σ, Γ, q0 , F , δ, z0 ,
Q is a finite set of states
Σ is a finite set of input alphabet
Γ is a finite set of stack alphabet
z0 Γ is a the initial symbol on top of the stack
q0 Q is the initial state
F ⊆ Q is the set of final states
δ is the set of transitions is a finite subset of
Q × (Σ ∪ ε ∪ #) × (Γ) → Q × (Γ ∪ ε)
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17. Push Down Automata
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18. Processing of 67
Generate Magnitude
60 + 7#
Decompose to Vigesimal
4*20-10-3#
PDA processing of string
eta d´ aad´ og´n erin
. ın ın u .
Apply linguistic skills
eta d´ aad´ ogorin
. ın ın . .
eta d´ `´dota
. ın aa .
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19. Example: Processing of 19669
Ekundayo(1977) presented 7 canonical representations for 19669, but
we were able to produce 3 more forms for 19669. Which are
eedegb``w´ ´ l´ ota-l´-legbeta ´ l´ mes´n
. . . aa a o e . e . . o e . a
eedegb``w´ ´ l´ orin-´-legbeta d´ mokanl`´
. . . aa a o e . e . . ın . aa
eedegb``w´ ´ l´ ´j` e-legbeta ´ l´ mokan-d´ . gbon
. . . aa a o e o ı-l´ . . o e . ın-lo .
eedegb``w´ ´ l´ egbeta ´ l´ mokan-d´
. . . aa a o e . . o e . ın-laadorin
.
eedegb``w´ ´ l´ eedegberin ´ d´ mokan-l´-logbon
.. . aa a o e . . . . o ın . e . .
oke ´ d´ ir´ o ´ l´ mokan-d´
. . o ın ınw´ o e . ın-laadorin
.
oke ´ d´ od´nr´n ´ d´ mokan-l´-logbon
. . o ın . u u o ın . e . .
oke ´ d´ oj` e-lod´nr´n ´ l´ mes´n
. . o ın ı-l´ . u u o e . a
´gb`j` ın-logor´n ´ l´ mokan-d´
e e ı-d´ . . u o e .
. ın-laadorin
.
eed´gbokan-d´ . gor´n ´ d´ mokan-l´-logbon
.. e .
. ın-lo . u o ın . e . .
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20. Deep structures form for 19669
19000 + 660 + 9
19000 + 680 - 11
19000 + 640 + 29
19000 + 600 + 69
19000 + 700 - 31
20000 - 400 + 69
20000 - 300 - 31
20000 - 340 + 9
19600 + 69
19700 - 31
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21. Surface structures form for 19669
1000- 2000* 10 + 200* 3 + 20* 3 + 9
1000- 2000* 10 + 200* 3 + 20* 4 - 1 + 10
1000- 2000* 10 + 200* 3 + 20* 2 + 30 - 1
1000- 2000* 10 + 200* 3 + 20* 3 + 9
1000- 2000* 10 + 200* 4-100 - 30 + 1
20000 - 200* 2 + 20* 4 - 10 - 1
20000 - 300 - 30 + 1
20000 - 40 + 300 + 9
200* 98 + 20* 4 - 10 - 1
200*99 - 100 - 30 + 1
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22. Grammar for Yor`b´ Numeral
u a
This is a slight modification of grammar discussed by Hurford (2006)
to accomodate subtraction
NUMBER → PHRASE (NUMBER) #addition
PHRASE → DIGIT
REDUCE
PHRASE → PHRASE #Subtraction
SUB
PHRASE → M PHRASE #Multiplication
The rule follows that curly braces implies that either of the options
can be used and parentheses indicate that the content of the
parentheses can be left out.
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23. Parse tree for 19669
19669 = 1000- 2000* 10 200* 3 10- 20* 4 - 1
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24. Parse tree for 19669
19669 = 1000- 2000* 10 40 200* 3 1 - 30
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25. Ongoing Work
Evaluation of the software is on-going
Effort is being made to develop the software for handheld devices
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26. References
Ekundayo, S. A. (1977).
Vigesimal numeral derivational morphology: Yor`b´ grammatical
u a
competence epitomized.
Anthropological Linguistics, 19(9):436–453.
Fab`nmi, F. A. (2010).
u
Vigesimal numerals on if` (togo) and if` (nigeria) dialects of yor`b´.
e
. e
. u a
Linguistik online, 43:pages.
Longe, O. (2009).
A Yor`b´ Decimal Number System.
u a
Bookbuilders, Ibadan.
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