# Assignment

Computing Skills Assignment Help

### COS4014B Mathematics for Computing Assignment Help

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You must follow the Essential Requirements given below.

## Essential Requirements:

You will loose marks if you do not follow these specifications!

The handout week for the present coursework sheet is Teaching Week 5 of Semester 1 (23-27 October 2017).

The handin deadline is 23rd November 2017 (Thursday), by 4.00 pm. This day is in Teaching Week 9 of Semester 1 (20-24 November 2017).

Solutions to be submitted (electronically) as specified by the University Regulations.

You are requested also to submit a hardcopy to the SSO in a box which will be specifically prepared for this purpose. (If, as will be the case for the majority of students, you will scan in your handwritten copy, you may as well submit that very copy after your electronic copy is ready – no paper waste will thereby be produced!)

Submission is not anonymous.

You must write on the first page of your submission your name

Number the pages of your submission in the style of this document.

### Introductory Considerations for Tasks 1 & 2

Let the language L0 be defined as the set of all strings over the alphabet Σ = {a b} where the number of the letter a is even and consecutive copies of the letter a are separated by at least two copies of the letter b. To make it more obvious, let me consider a few examples:

The string babbbabbb is in L0. (Obviously.)

The nullstring Λ is in L0. Why? Because the number of the letter a in the nullstring is zero and zero is an even number and there are no consecutive copies of a (so there is nothing to be separated).

The string abbbabbbbababbb is not in L0 since the third and the fourth a are separated by one b only.

The string bbabbbabbabbbbbabbbbbbabbbbab is in L0. (Obviuosly. Check the condition!)

The last example may serve us as a specific example for examining the structure of the strings in L0. We may group the the letters in the string as indicated below:

bbabbbabbabbbbbabbbbbbabbbbab = bbabbbab babbbbbabb bbbbabbbbab

Each of the three substrings (indicated by framing) has the same structure:

b . . . b bab b . . . b bab b . . . b

i.e. two bab ‘cores’ placed next to each other and some (possibly none) copies of the letter b filling the gaps as indicated by b . . . b. And, all this is preceeded and/or followed by a group of the letter b (which may comprise no letters at all); this is again indicated by b . . . b.

Let the language L1 be defined in plain English by

L1 = set of all strings containing exactly two copies of the letter a AND the letters a are separed by at least two copies of the letter b Define the language L1 by recursion.

The max. achievable number of marks for this task is 20. marking advice

### Guidance

The words in the language L1 have obviously the structure

b . . . b bab b . . . b bab b . . . b

as spelt out in the Introductory Considerations. They will (in the next task) serve as building blocks of the words of the language L0.

You are advised to proceed as follows:

(i) First define by recursion the language L1.a, say, which is defined in plain English as

L1.a = all strings containing exactly one a

(ii) Now define L1 as L1 = L1.abbL1.a (1)

This simple latter step does not involve recursion but multiplication of languages (as seen in the lectures and tutorials). For full marks, please write down (1) using a set theoretic notation.

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