Developing a System for Converting a Numeral Text into a Digit Number: Abacus Application

1 Introduction

As a natural language, Arabic is considered to be one of the most difficult languages to deal with in a localized context. This is because Arabic is rich in syntax, semantics, and morphology. In addition, written letters in Arabic have different shapes according to their position in the word, and accents also play a very important role in the meaning. Therefore, the Arabic language faces many challenges in the field of technology.

Arabic natural language processing has increasing importance, and many systems have been developed for a wide range of applications, including machine translation, information retrieval and extraction, speech synthesis and recognition, localization and multilingual information retrieval systems, text to speech, and tutoring systems. These applications had to deal with several complex problems pertinent to the nature and structure of the Arabic language [7].

In this research, we will focus on the Arabic numerals and how to deal with numbers. Numbers are noted in one or more symbolic formats: as written words (e.g. “one”), or as Arabic digits (e.g. “1”). Writing the numbers as words is a difficult task for a large class of people that have a high probability of errors. They sometimes use one number word in place of another and may write the number with spelling errors. So, we will focus on how to transform written Arabic numeral word format into a string of digits.

In previous works, many approaches and software applications in various languages (such as Swedish, English, French, and German) have been proposed to convert numbers [20].

Regarding the Arabic language, there are few works. For instance, Al-Taani et al. [1] proposed an Arabic Numerals Checker based on finite state transducers (FSTs) to represent numerals and the transformation process. More precisely, the system concentrates only on how to transform a particular number from a string of digits into a multiword format in Arabic language, taking into consideration the gender of the counted object. However, to our knowledge, there is no work for transforming Arabic numerals into digits, which we consider a complex and important point.

Therefore, in this work, we will discuss the difficulties associated with the transformation of Arabic numerals into digits and provide an approach that can deal with them. In fact, there are many problems when writing the numbers as words, especially involving spelling errors; the errors can occur due to deleted, inserted, substituted, and transposed characters, such as “.” Also, numbers may be written in more than one format representing the same number. For instance, the following two formats “” represent the number (223).

After that, we will use the proposed approach for building an Android application as an educational Abacus program for children. This application will help children to develop skills about Abacus, numbers, counting, and to have practice in translating abacus configurations into Arabic numerals and vice versa.

There are many fields in which numbers are written as textual numbers. For instance, in the land department, land space and borders on both sides are written as words and as digits. Hence, the proposed work could be used for automatic validation and for checking the mismatch of the entered number as a word and the digit number. The same thing could be applied for financial transactions (such as in the trading business and in banking), when dealing with checks. Other applications can benefit from this work in searching operations by extracting the numbers in a document that are written as a string of words and converting them to digits.

The rest of this paper is organized as follows. Section 2 is dedicated to related works. Section 3 discusses the difficulties in the transformation process and presents the proposed approach. The dataset as well as the experimental results are presented in Section 4. Section 5 introduces the implementation of the Abacus system. We conclude in Section 6.

2 Related Works

Many authors have proposed works for spatial representation and transcoding of numbers. Most of them have focused on out-of-context number conversion; in other words, converting text numbers into digits and vice versa. Some works provide representations and analyses for numerals in various languages (Swedish, English, French, and German), and they suggest “deep structure” rules for converting numerals into digit representation and vice versa. For instance, the following are some of these rules used for English [20]:

1. Fusion rules: in this step, count the number of digits and divide them into a three-group string from right to left; then, identify the position word as in a hundred that is inserted after position 3.

2. Lexical rules: identify numerals and substitute the suitable texts for them (e.g. 2→twen/+ty|two).

Other approaches [6, 13, 14, 16, 17, 19] have focused on a model that converts from text format into digit format and vice versa. For example, “six thousand four hundred thirty-five”→6000 400 30 5” or 116→“one hundred plus sixteen.” McCloskey et al. [13, 14] proposed a “numerical transcoding” method based on an “abstract internal representation” of numbers, and it is accomplished by two stages: perception and production. The perception process converts the input form into an internal semantic representation, while the production process converts the semantic representation into numeral form. Both perception and production contain components for lexical and syntactic numerical elements. For example, for the numeral text “nine thousand three hundred ten,” the lexical and semantic numerical element forms are as follows:

nine; thousand; three; hundred; ten

The internal semantic representation is

{9}10EXP3; {3}10EXP2; {10}10EXP1

Then, take the individual numbers:

{9}; {3}; {10}

Finally, produce the result as 9310.

McCloskey et al. [14] proposed a structure for the number-production lexicon called the McCloskey model; this model can be placed within the context of a procedurally explicit model of the number-reading process. When a number is read, a number-production syntax device generates a syntactic frame based on number and digits. For example, for the number 4765, the syntactic frame would take the form

The T and H represent instructions for retrieving the phonological forms and the syntactic value /thousand/ and /hundred/; thereafter, producing a number involves successive retrieval of the phonological forms specified by the filled syntactic frame:

/four/ /thousand/ /seven/ /hundred/ /sixty/ /five/

Deloche and Xavier [6] proposed an alternative model instead of using the McCloskey theory; they provided the asemantic procedure in order to perform the transcoding process. The proposed approach drives a verbal numeral from an Arabic numeral, or vice versa, directly without using an abstract internal representation of the number. This is achieved by tracing the following steps to produce a number in a text format. In the first step, divide the digit number into triples from right to left. In the second step, group the result using punctuation marks, transform the leftmost groups into a three-digit frames, and fill empty positions with zero if the group is filled by one or two digits. In the third step, apply a set of rules to produce the first words of verbal numeral. For instance, the number 11,245 is transformed as follows. First, divide it into two groups, 11 and 245. Second, group them by parenthesis as (011) (245). Then, apply a set of rules that produce the words: (011)→eleven thousand and (245)→two hundred and forty-five. Finally, the produced result is eleven thousand and two hundred and forty-five. This approach did not gain accepted results as it fails to be extended to large numbers.

In Ref. [17], the authors have suggested a set of rules for realizing action expressions in a syntactic form <P> <N> (see Figure 1). Figure 2 shows the use of the proposed rules for the derivation of English numeral number 90,999.

Figure 1:

The English Numeral System for Numbers up to 999,999.

Figure 2:

Derivation of English Numeral for Number 90,999.

A semantic transcoding procedure has been proposed in Ref. [16] based on the analysis of numerals in Ref. [17] for translating Arabic numbers. This idea was based on subdividing the digit string and separating each part by a suitable multiplicand word. The procedure passes several iterations before arriving to the correct solution. This process takes some time because the most natural fragmentation strategy may yield a wrong subdivision of the digit string.

Seron and Deloche [19] presented a new way of simulating the cognitive processes of numeral transcoding by mapping verbal morphemes to Arabic digits in three layers and different networks. Verbal numbers used as input (number as a word) are represented in seven fields, and the output is represented in four fields, each of them represents a digit (0–9), or “null.”

More recent works [3, 8, 12, 15, 19] provided models of transcoding from digit to sequence words. The work in Ref. [19] depends on general structure parameters based on item length to transcode numbers from the digit form into the text form. The work in Ref. [15] has applied a semantic model, and Cohen et al. [3] applied a multiroute model (semantic and asemantic); in both, the transcoding process occurs in two routes: a “surface” route mapping any digit string into a word sequence according to the language-specific rules and a “deep” semantic route. Macoir et al. [12] suggested semantic and asemantic models of a number processing and transcoding system. The system includes different code-dependent pathways for transcoding spoken verbal numerals and text verbal numerals. The semantic conversion for Arabic digits is too slow to influence naming. The Stroop task [8] has been used in the number processing.

In Refs. [2, 5], the authors have proposed a model that implements a direct conversion from Arabic input to phonological output. Cipolotti and Butterworth [2] added semantic pathways to the semantic processing that is done by the McCloskey model, and they proposed a triple-code model in Ref. [5].

3 Proposed Methodology

There are several difficulties in transforming written Arabic numeral word format into a string of digits. These difficulties are divided into two levels: word level and sentence level. At the word level, a number written as a word in Arabic is affected mainly by Arabic accents () and added letters (infix and postfix). For instance, the word “” without accent is the same as the word “” with accent. On the other hand, the same word may be written with added letters such as in “” or may be in different words such as “”. Each of these words represents different results, as in “” must be returned as “1,000,000” and “” must be returned as “2,000,000”. In addition, as we mentioned earlier, orthographic errors (errors in spelling) can occur due to inserted characters in the beginning, end, or middle (e.g. “”); deleted character from the beginning, end, or middle (e.g. “”); or a substituted character (e.g. “”).

At the sentence level, more than one word connected together as a sentence may represent a number. This sentence may contain a composite number such as “.” Also, it may be included with different orders, such as “” or “”. When the sentence includes such different orders, the same number (1,021,000) should be returned.

In general, the flow of the proposed approach includes the following five main phases:

• Preprocessing to eliminate the accents from the word (Section 3.1);

• Using stemmer to find the roots for the numbers (Section 3.2);

• Using the similarity to find the nearest number when the word has been written with spelling errors (Section 3.3);

• Rebuilding the sentence to find the correct order if the sentence is unordered (Section 3.4);

• Finally, generating the number according proposed Arabic numeral rules (Section 3.5).

3.2 Stemming

There are many Arabic stemmers proposed for extracting the root from words [9–11, 18]. However, the Arabic stemmers found in the literature could not be used to directly deal with numbers. This is because several word numbers may have the same stem (such as “” and “”). Also, there are some numbers that can be written as a composite number (such as “”). In addition, various words may refer to the same number (such as “”). Therefore, we build a table (Table 1) consisting of a set of stems for the main numbers.

Table 1

Stems for Arabic Numbers.

4 Experiments and Evaluation

In this section, we provide the results of our approach and assess its quality by introducing a set of numeral sentences and converting them to digit numbers. Then, we manually validate the output.

4.1 Dataset

The evaluation has been conducted for two levels: word level and sentence level. For the word level, we have generated “one hundred” numeral words in Arabic that are written correctly without spelling errors (see Table 2). This set represents all the possibilities of single-word digits.

Table 2

The Results for Level of Word.

Regarding the sentence level, we have written “one hundred and six” sentences that are written properly without spelling errors (see Table 3). Some of them are in correct order, while the rest are not in the correct order (about 16 sentences).

Table 3

The Results for Level of Sentence.

5 Implementation

5.3 Interface

There are three ways to enter a number in the virtual abacus (as shown in Figure 3):

1. Enter the digit number in the first field. Press the “” button when done. The abacus will update the number as a numeral word in the second field and represent this number in the abacus panel.

2. Enter the number as a word in the second field. Press the “” button when done. The abacus will update the number as a digit in the first field and representing this number in the abacus panel.

3. Change the beads directly by pressing the button increment “+” and the button decrement “–”. Then, the number will be updated automatically as a digit number as well as a numeral word.

Figure 3:

The Abacus Application with a Given Example.

6 Conclusion

The Arabic language is rich in syntax, semantics, and morphology. Among the many languages, there are sets of rules that should be considered during the processing of the Arabic language. Arabic numeral presentation is one of the special concerns. In this research, we have presented an efficient approach that transforms written Arabic numeral texts into a string of digits according to the Arabic numeral rules and vice versa. We developed an automatic application with a set of rules to convert text numbers into a string. The application is useful to many fields especially for banks, post office services, commercial transactions, financial transactions, and land and education departments. Other applications can benefit from this work in searching operations by extracting the numbers in a document written as a string and converting it into digits.

In our proposed approach, we solved all problems associated with the conversion from an Arabic numeral word into digits, and we proposed a set of stems for numbers, to solve the many problems related to the level of words, such as different writings that refer to the same number like in “”; additional characters; and accents like in “.” In our work, we distinguished between converged words like in “” and composite numbers like in “.” We presented a technique to solve sentences that are entered in unordered format such as “” and “.” Our system is able to deal with these problems and return the same number “7,002,000.”

Tests have been executed using a dataset of numeral texts, where we took a set of Arabic words and sentences that are written properly without spelling errors, and we took all the possibilities of words for the same number and sentences in different order. We entered these words and sentences into our system and obtained the result as digital numbers; we matched them with the supposed results that we obtained manually. The experimental results have demonstrated that the proposed approach is promising in the sense that it provides an efficient and error-free transformation.

The idea of this research was implemented as an educational abacus program for children on Android application in Java programming language and Eclipse environment. This system consists of an abacus panel, two text boxes, and two buttons. This system could be used to convert numbers from abacus to numeral text and digits, and vice versa.