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What is the interpretation of the following quoted sentences from UML Reference Manual?
When an orthogonal state is entered, the number of control threads
increases as a direct substate in each orthogonal region becomes
active.
When the orthogonal state is exited, the number of control
threads decreases.
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September 2022) In optics, polarization states are said to be orthogonal when they propagate independently of each other, as in vertical and horizontal linear polarization or right- and left-handed circular polarization.
Definition. We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product of the two vectors is zero.
In order to check if two qubits are orthogonal, you should check that the inner product between them equals zero. This can be written like ⟨u1|u2⟩=0. Knowing that ⟨0|0⟩=1, ⟨0|1⟩=0, ⟨1|0⟩=0 and ⟨1|1⟩=1 it should be easy to solve the problem by yourself.
In the social sciences, variables that affect a particular result are said to be orthogonal if they are independent. That is to say that by varying each separately, one can predict the combined effect of varying them jointly. If synergistic effects are present, the factors are not orthogonal.
This is a complex part of the UML spec. In the simplest case, when you enter a state containing orthogonal regions, the initial psuedo state in each orthogonal region essentially starts a separate thread of control. There are lots of complicated rules about how events are consumed by these threads and how the threads join back together.
But, according to a methodologist I highly recommend (H. S. Lahman), you really shouldn't use more than plain old Moore state machines. For more information on why one should use Moore state machines (which you can model perfectly well in UML) instead of Mealy or Harel state machines, please see this excerpt from Lahman's book. For more information on the difference between a Moore and a Mealy state machine, please see this StackExchange question.
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