* doc/org/tut51.org: Typos.
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@ -8,20 +8,20 @@
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Kripke structures, can be defined as ω-automata in which labels are on
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states, and where all runs are accepting (i.e., the acceptance
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condition is =t=). They are typically used by model checkers to
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represent the state-space of the model to verify.
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represent the state space of the model to verify.
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* Implementing a toy Kripke structure
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In this example, our goal is to implement a Kripke structure that
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constructs its state-space on the fly. The states of our toy model
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constructs its state space on the fly. The states of our toy model
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will consist of a pair of modulo-3 integers $(x,y)$; and at any state
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the possible actions will be to increment any one of the two integer
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(nondeterministicaly). That increment is obviously done modulo 3.
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For instance state $(1,2)$ has two possible successors:
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- $(2,2)$ if =x= was incremented, or
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- $(1,0)$ if =y= was incremented.
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Initially both variables will be 0. The complete state-space is
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Initially both variables will be 0. The complete state space is
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expected to have 9 states. But even if it is small because it is a
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toy example, we do not want to precompute it. It should be computed
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as needed, using [[file:tut50.org::#on-the-fly-interface][the one-the-fly interface]] previously discussed.
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@ -365,9 +365,9 @@ is an implementation that does this.
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Note that the =demo_succ_iterator::recycle= method was introduced for
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this reason.
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* Displaying the state-space
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* Displaying the state space
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Here is a short =main= displaying the state-space of our toy Kripke structure.
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Here is a short =main= displaying the state space of our toy Kripke structure.
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#+NAME: demo-1-aux
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#+BEGIN_SRC C++ :exports none :noweb strip-export
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@ -559,7 +559,7 @@ example of class following this convention is =twa_graph=, were states
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returned by the on-the-fly interface are just pointers into the actual
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state vector (which is already known).
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Even if the state-space is not already known, it is possible to
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Even if the state space is not already known, it is possible to
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implement the on-the-fly interface in such a way that all =state*=
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pointers returned for a state are unique. This requires a state
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unicity table into the automaton, and then =state::clone()= and
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