Computer Science Syntax Definitions Worksheet

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CSc 600 – Homework #1.1 - Syntax Dr. Jozo Dujmović

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1. Write the syntax definitions of the following objects:

(a) Natural number (1, 2, 3, …)

(b) Unsigned integer (0, 1, 2, 3, …)

(c) Integer (…, -2, -1, 0, 1, 2, …)

(d) Odd number (…, -3, -1, 1, 3, …)

(e) Even number (…, -4, -2, 0, 2, 4, …)

(f) Integer divisible by 5 (…, -10, -5, 0, 5, 10, …)

Solve each problem from (a) to (f) using BNF, EBNF, syntax diagrams, and the

parenthetic notation. At the end compare all solutions and write what is in your opinion the

most suitable metalanguage for solving this type of problems.

2. Following is an example of assignment statement in C++ :

alpha5[i][j] = 12.34*a[5]/rate + 3.14*(x[2*i-1][3 + j] -1);

Based on this example, write a BNF definition of the syntax of arbitrary assignment

statements in C++. Do not expand your definition beyond components shown in the above

example. So, variables can be scalar or can have any number if indexes that can be

expressions. Use only basic arithmetic operations (+, - , * , /) . Do not use functions or

multiple assignments. The goal is to create a basic definition of arbitrary expressions based on

the combinations of variables and basic arithmetic operations.

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Note #1: Your solution should be submitted as a single pdf file. This file must be prepared

using a text editor (like Notepad) or a word processor (like MS Word) and then converted to pdf.

Graphical components (circles, rectangles, arrows) can be inserted in any readable way including

by hand. You can also use approximations and simplifications such as this example:

.-------.

------>| digit |---.----->

^ ‘-------’ |

| |

‘---------------’

Note #2: Individual solving of homework problems is the best preparation for exam.