X def b.c.0+ b.d.0Y def X+ b.(c.0 + d.o)defZW def a.Ya.Y + a.X(a) Draw a...

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Algebra

X def b.c.0+ b.d.0Y def X+ b.(c.0 + d.o)defZW def a.Ya.Y + a.X(a) Draw a labelled transition system which includes the above states X, Y, Z and W.[5 marks](b) Explain why Z2 W but Z 3 W. That is, argue that the second player has the winning strategy inthe copy-cat (bisimulation) game which lasts for two rounds, but that the first player has the winningstrategy in the game which lasts for three rounds.[3 marks](c) Give a formula P of the modal logic M which is satisfied by Z but not by W.[2 marks]

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X def b.c.0+ b.d.0Y def X+ b.(c.0 + d.o)defZW def a.Ya.Y + a.X(a) Draw a labelled transition system which includes the above states X, Y, Z and W.[5 marks](b) Explain why Z2 W but Z 3 W. That is, argue that the second player has the winning strategy inthe copy-cat (bisimulation) game which lasts for two rounds, but that the first player has the winningstrategy in the game which lasts for three rounds.[3 marks](c) Give a formula P of the modal logic M which is satisfied by Z but not by W.[2 marks]