Q1) Let a three bit binary counter. This has three spaces for digits which can be 0 or 1. Initially all the bits are set to 0 (i.e. the counter reads 000). Incrementing the counter leads to the following sequence of readings 001, 010, 011, 100, 101, 110, 111, returning again then to 000 and so on. Let x, y and z stand for each of the bits where z represents the most significant bit (at the left hand side), y is the bit in the middle and x the least significant (at the right hand side) where x represents 1 in the right hand column and :x represents 0 in the right hand column (and similarly for y and z). For example z = T, y = F and x = F would represent 100 n the counter. Specify the three bit counter using LTL. The following are properties we may wish to try and prove are valid given the specification of the three bit counter.

(a) Eventually the counter reaches 111.

(b) It is not possible to reach a state where the counter reads 010 and in the next moment the counter reads 100.

Prepare these properties in LTL. Create a model which satisfies the specification and both the above properties.

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