COMP 2049 (AE2LAC) Languages and Computation Coursework: Floating-Point Literals and Simple Arithmetic Expressions

Total Mark : 100 Weight : 15% of the module mark How to submit : Via Moodle 1 Floating-Point Literals Design a right-linear grammar G1that 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 +1.01or−1.01 •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 +110.011, the value field is 110.011 –1and.01and−.001are acceptable, but 1.is not acceptable. •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+11or−1.11e101 are acceptable, but 1.01e and1.01e-1.1are not accept- able. Furthermore, there must be at least one digit between the decimal point ‘.’ and the letter ‘e’. Hence, strings such as 11.e01are not acceptable. Task 1. Implement the grammar G 1in 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 G1in JFLAP is provided in Figure 1 on the following page. 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 Figure 1 Some sample input values for the right-linear grammar G1. 2 Arithmetic Expressions For the second task, you are required to design a context-free grammar (CFG) G2that 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 )/001must be accepted, whereas (( 11−01) must be rejected because the parentheses do not match. Task 2. Implement the grammar G 2in JFLAP and test it on some input expressions of your choice. Check all the production rules of the grammar G2to see if there are any λ-productions or unit-productions. If there are any such productions, you may 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 λ-productions and unit-productions of the grammar G 2to obtain the grammar G′

- 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 λ-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 G′ 2in JFLAP is provided in Figure 2 on the next page. 3 Submission You must submit three files, named according to the following templates: (1) A JFLAP file for grammar G1of Task 1 named: ID-Surname FirstName-01-Right Linear.jff (2) A JFLAP file for grammar G2of Task 2 named: 2 Figure 2 Some sample input values for the CFG G′
- Note that -00*11 is rejected because -00may only be interpreted as a signed literal, while in G2andG′ 2only unsigned literals are allowed. ID-Surname FirstName-02-CFG.jff (3) A JFLAP file for grammar G′ 2of Task 3 named: ID-Surname FirstName-03-CFG nounit.jff Remark 3.1. In case the grammar G 2of Task 2 that you have designed already has no λ-productions and no unit-productions, then you may submit the same grammar as G′
- Nonetheless, even in this case, you must submit three files with the naming conventions as specified above. 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%) (a) While the grammar G′ 2of Task 3 is generated by JFLAP, the grammars for Tasks 1 and 2 must be written by you. For grammars G1andG2, all productions with the same left-hand-side variable must appear in one block one after another. (15%) (b) The three 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 stan- dard University scale per day, until the mark reaches zero. For example, an original mark of 67% would be successively reduced to 62%, 57%, 52%, 47%, etc.