COMP2049 Floating-Point Numbers and Simple Arithmetic

【重点解析：】

Task1: 注意 right-linear grammar 右线性语法的定义，可以有前置 0，小数点左右的要求需要体现在语法里，+- 号可在数字里出现两次

Task2: 注意式子整体必须包含至少一个运算符，也就是整体不能只是一个数。难点是括号的循环嵌套与运算符分级

Task3: Task2 的升级版，考察运用 JFLAP 的 remove unit production 功能，最终的效果是保证如同 Task2 正确性的前提下，速度大大提升。比如对例子 “1+1-(1/1*1)”，G2 与 G3 最终都可以 accept，但 G3 的速度要快得多

vvvv: csprojhelp

Floating-Point Numbers

Design a right-linear grammar G 1 that generates the language of binary floating-point literals according to the following rules:

• Each number may be signed or unsigned.

– unsigned as in 1.01, signed as in +1.01 or -1.10

• The numerical part (also called the value field) must be non-empty and may optionally include a decimal point ’.’, in which case it must be followed by some other digits. For instance:

– In the number +110.11, the value filed is 110.11.

– 1 and .01, -.001, 001 are all acceptable, but 1., +, - and ! are not.

• There may be an optional exponent field, in which case, it must contain the letter ’e’, followed by a signed or unsigned integer.

– For instance, 101e+1 or -1.1e10 are acceptable, but 1.01e, 1.01e-1.1 and e11 are not.

Furthermore, there must be at least one digit between the decimal point ’.’ and the letter ’e’. Hence, strings such as 11.e01 are not acceptable.

Task 1.

Implement the grammar G 1 in JFLAP, and test it on some input strings of your choice.

A screenshot of the result of parsing of some sample input strings for grammar G 1 in JFLAP is provided in Figure 1.

Figure 1: Some sample input and the corresponding results

Remark 1.1 In all of the tasks of this coursework, the default parsing method should be the “brute force parsing”. Hence, to test your grammars in JFLAP on several input strings, choose the tab “Input” and then the item “Multiple Brute Force Parse”.

1 2

Arithmetic Expressions

For the second task, you are required to design a context-free grammar (CFG) G 2 that generates the language of arithmetic expressions over natural numbers in binary format. Each arithmetic expression is constructed from the following:

• Binary unsigned integer literals, with leading zeros accepted;

• Arithmetic operators +, -, *, and /;

• Properly nested parentheses.

For instance, an expression such as (11+0101)/001 must be accepted, whereas ((11-01) must be rejected because the parentheses do not match.

Task 2.

Implement the grammar G 2 in JFLAP and test it on some input expressions of your choice.

Check all the production rules of the grammar G to see if there are any !-productions or unitproductions. If there are any such productions, you may2 notice that for more complicated input strings, it takes a long time for JFLAP to parse the string. In fact, at times it may enter into a non-terminating loop.

Task 3. Use JFLAP to remove the !-productions and unit-productions of the grammar G 2 to obtain the grammar G 3 . Then, try to parse the same strings as before and notice that it takes a shorter time to parse them, and the parser does not enter into non-terminating loops.

In JFLAP, to remove !-productions and unit-productions, you may first choose the tab “Convert”, and then the item “Transform Grammar”. A screenshot of the result of parsing of some sample input strings for grammar G3 in JFLAP is provided in Figure 2. To compare the e!ciency of G 2 and G 3 , you may use the sample input “1+1-(1/1*1)”.

Figure 2: Some sample input and the corresponding results

3

Submission

You must submit one zip file which contains three JFLAP files, named according to the following templates:

1. A JFLAP file for grammar G 1 of Task 1 named:

ID_Surname_FirstName_01.jff

2. A JFLAP file for grammar G 2 of Task 2 named:

ID_Surname_FirstName_02.jff

3. A JFLAP file for grammar G 3 of Task 3 named:

ID_Surname_FirstName_03.jff

4. The zip file named:

ID_Surname_FirstName.zip

2 Remark 3.1 In case the grammar G 2 of Task 2 that you have designed already has no !-productions and no unit-productions, then you may submit the same grammar as G 3 . Nonetheless, even in this case, you must submit three files with the naming conventions as specified above.

• Release date: Tuesday, April 2 nd , 2024

• Deadline: Friday, April 19 th , 2024, 17:00

• Weight: 15% of the module mark

• How to submit: Via Moodle

4

Marking Scheme

Correctness: (80%) Correct answers for the three tasks contribute to 80% of the total mark, as follows:

• Task 1: 40%

• Task 2: 20%

• Task 3: 20%

Format: (20%)

1. While the grammar G 3 of Task 3 is generated by JFLAP, the grammars for Tasks 1 and 2 must be written by you. For grammars G 1 and G 2 , all productions with the same left-hand-side variable must appear in one block one after another. (15%)
2. The zip file and three JFLAP files must be named according to the templates given above. (5%).

Late Submissions: The standard University penalty for late submission is applied, i.e., 5% absolute standard University scale per day, until the mark reaches zero.

Use of Other Technologies: If you use technologies other than those specified in the assignment brief, e.g., chatGPT, 50% absolute deduction.