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Guys can you please explain me what the difference is between the State-transition diagram and a Use case? Because it seems to me that those things are very similar and I can't find any proper definition which will show the differences. I'll be very grateful if someone at least give me a hint where I can read about this!

Andrejs
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Use case:

  • High profile overview
  • Shows actors (people) interacting with system(s)

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State diagram:

  • Shows the evolution of an object's state

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One of the best Intro articles on UML I found is by Donald Bell is this one

Andrejs
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Both describe system behaviour. But they are very different in approach.

The state diagram captures how a system has a state and how it behaves in that state, going to another state. This is not 'going anywhere'. They tend to the abstract and originated in 1949. A nice example could be network communication.

Use cases focus on how a system reacts to an outside actor, which often but not always is a user. It consists of a series of steps towards a goal. This is a compact way to capture requirements and is usually quite readable for the stakeholders of a project. They were introduction in 1992. A nice example could be 'Buyer creates account'.

Both methods are widely adopted and have acquired different 'tastes'. They only really come to life when applied, reading about them can only take you so far.
Some of the differences can be seen here.

References:
https://en.wikipedia.org/wiki/State_diagram
https://en.wikipedia.org/wiki/Use_case
http://tynerblain.com/blog/2007/03/21/use-case-vs-statechart/

Bookeater
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The difference between them is Use case testing :technique that help us identify test cases that exercise the whole system on trunscation by trunscation basis from start to finish State transitional testing : technique which change in input condition causes state change in (AUT)