Commit 965d0ed6 by Alexandre Duret-Lutz

### * doc/org/tut04.org: Show are_equivalent().

parent 6a808492
 ... ... @@ -36,23 +36,21 @@ familiar to =grep= users.) * Python In Python, we can test this via a =language_containment_checker= object: In Python, we can implement this in a number of ways. The easiest is to use the =spot.are_equivalent()= function. #+BEGIN_SRC python :results output :exports both import spot f = spot.formula("(a U b) U a") g = spot.formula("b U a") c = spot.language_containment_checker() print("Equivalent" if c.equal(f, g) else "Not equivalent") are_eq = spot.are_equivalent("(a U b) U a", "b U a") print("Equivalent" if are_eq else "Not equivalent") #+END_SRC #+RESULTS: : Equivalent The equivalence check is done by converting the formulas $f$ and $g$ and their negation into four automata $A_f$, $A_{\lnot f}$, $A_g$, and $A_{\lnot g}$, and then making sure that $A_f\otimes A_{\lnot g}$ and $A_g\otimes A_{\lnot f}$ are empty. The equivalence check is done by converting the input formulas $f$ and $g$ and their negation into four automata $A_f$, $A_{\lnot f}$, $A_g$, and $A_{\lnot g}$, and then making sure that $A_f\otimes A_{\lnot g}$ and $A_g\otimes A_{\lnot f}$ are empty. We could also write this check by doing [[file:tut10.org][the translation]] and emptiness check ourselves. For instance: ... ... @@ -62,7 +60,7 @@ import spot def implies(f, g): a_f = f.translate() a_ng = spot.formula_Not(g).translate() a_ng = spot.formula.Not(g).translate() return spot.product(a_f, a_ng).is_empty() def equiv(f, g): ... ... @@ -75,6 +73,19 @@ print("Equivalent" if equiv(f, g) else "Not equivalent") #+RESULTS: : Equivalent This can also be done via a =language_containment_checker= object: #+BEGIN_SRC python :results output :exports both import spot f = spot.formula("(a U b) U a") g = spot.formula("b U a") c = spot.language_containment_checker() print("Equivalent" if c.equal(f, g) else "Not equivalent") #+END_SRC #+RESULTS: : Equivalent The =language_containment_checker= object essentially performs the same work, but it also implements a cache to avoid translating the same formulas multiple times when it is used to test multiple ... ... @@ -82,7 +93,25 @@ equivalences. * C++ Here is a C++ translation of the first Python example. Here are possible C++ implementations using either =are_equivalent()= or the =language_containment_checker=. Note that the =are_equivalent()= function also work with automata. #+BEGIN_SRC C++ :results verbatim :exports both #include #include #include int main() { spot::formula f = spot::parse_formula("(a U b) U a"); spot::formula g = spot::parse_formula("b U a"); std::cout << (spot::are_equivalent(f, g) ? "Equivalent\n" : "Not equivalent\n"); } #+END_SRC #+RESULTS: : Equivalent #+BEGIN_SRC C++ :results verbatim :exports both #include ... ...
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