Chapter 1: Exercises (1)

DFA Exercise 1

Given the following DAF, use Cyclone to find all strings that have a length of 5.

DFA Exercise 2

Given the following DFA, use Cyclone to find all strings that have a length of 6 and do not end with a b.

DFA Exercise 3

Find all strings such that every string has a length of 6 and does not end with a substring abb. You can assume Σ here is: {a,b}. Hint: you need to draw a DFA first,then use Cyclone to find all strings.

De-icing Taxiways

During the winter seasons, many major international airports need a service of de-icing their taxiways connecting multiple terminals. Each taxiway has its own direction sign. No airplanes can take off or land during the de-icing process. Typically, de-icing takes sometime to complete and can be very expensive. Hence, many international airports always seek an optimal way of faster de-icing and keeping their cost low at same time.

To find an optimal solution, an airport must compute a route for its deicer (a de-icing vehicle) to deice every taxiway. It is quite obvious that the best solution is to deice every taxiway exactly once (based on its direction sign).

For example, the following graph shows a basic layout of a major international airport. Terminal A,B,C,D are passenger terminals. E and F are cargo terminals. The main taxiways are marked as edges in the graph. Each taxiway has its own direction sign. For example, an airplane can move from Terminal D to B through taxiway t1 (but cannot move from B to D). This also applies to a deicer.

Now use Cyclone to help this airport to compute a route for its deicer such that every taxiway gets deiced exactly once.

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