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DFA algorithms in a Python library (Re: Confusing "decidable problem" and "complete algorithm")

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Hi,

DFS algorithms can nevertheless gain some completness
power on rational trees when paired with loop checking.
Like @kuniaki.mukai was using in compare_with_stack/3.
They might be not as good as HK though.

You find a DFA subset and equality relation here,
implemented via DFS algorithms using a visitor set:

def find_equiv_counterexample(dfa_a, dfa_b):
     # Symmetric difference: strings accepted by exactly one DFA
     return find_word(dfa_a ^ dfa_b)

def find_subset_counterexample(smaller, bigger):
     # Intersection of "smaller" with the complement of "bigger"
     return find_word(~bigger & smaller)

https://pypi.org/project/dfa/

The later results in ordering DFAs by a partial order
and not by a total order. The project has also a DFA
minimization algorithm. But I didn’t get my head around
yet implementing it,

and I don’t know whether @kuniaki.mukai implemented
the DFA minimization algorithm that has supposedly
O(N log(N)) complexity.

Bye

Mild Shock schrieb:
> Hi,
> 
> This is a nice confusion of the highest order.
> 
>  > observations on the decidability
> 
> Well in summary the existence of a pretest (==)/2
> makes Mercio's decidable. Equality on rational trees
> is decidable, even if it comes in disguise as Mercio’s
> mathematical definition, which gives a total order
> 
> which is unfortunately not a natural order:
> 
> A=B :⟺ A' =lex B'
> 
> A<B :⟺ A' <lex B'
> 
> Natural order of rational trees?
> https://math.stackexchange.com/a/210730
> 
> Why is Mercio’s mathematical definition of equality
> decidable? Because it is semantically equivalent to
> bisimulation as implemented in (==)/2 , and decidable
> is a semantic notion:
> 
> Decidability (logic)
> In logic, a true/false decision problem is decidableif there
> exists an effective method for deriving the correct answer.
> Decidability (logic) - Wikipedia
> 
> So if you talk about semi-decidable, decidable etc..
> its always about the existence of an algorithm in
> the large space of effective method according to
> the Church hypothesis.
> 
> If you want to talk about a particular algorithm
> you would use the terminology “incomplete”. Like for
> example DFS algorithms are “incomplete” compared to
> BFS algorithms on certain problems.
> 
> Bye

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