Principles of Programming languages

Assignment 1


  1. [5 marks each]. For each of the following languages, create a regular expression that matches strings in the language. Note: You can use. (a dot/period) to denote “any” character in the alphabet. Additionally, you may only use Regular Expression Tools shown in class (i.e., you cannot use lookbacks).


  1. The language, over the lower case English alphabet, of words with at least 2 vowels, where a vowel is a, e, i, o, or u.




  1. The language, from the alphabet Σ = { 0, 1 }, where the length of the string in the language is a multiple of 4.




  1. The language, from the alphabet Σ = { 0, 1, 2, … , 9 }, of integers divisible by 5.




  1. The language of strings over the alphabet Σ = { x, y, z } that do not contain the substring zx. (e.g., xyzyxxz).




  1. [10 marks each]. For each of the following languages, present a DFA that recognises the language.


  1. The language, over the alphabet Σ = { 0, 1, 2 } of strings that end with the same digit twice; e.g., strings that end in 00, 11, 22.




  1. The language, over the alphabet Σ = { 0, 1 } of strings with even parity (i.e., they have an even number of 1’s).




  1. The language, over the alphabet Σ = { a, b, c }, of words that do not contain the same letters side by side. That is, strings that do not contain aa, bb, or cc.


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