logic equation suggestions #16194

shubhamabhang77 · 2019-03-07T18:13:37Z

References to other Issues or PRs

#16137

Brief description of what is fixed or changed

expr._rewrite_as_And, expr._rewrite_as_Or, expr._rewrite_as_Nor, expr._rewrite_as_Nand
added to logic equations.

Other comments

Release Notes

logic
- And can be rewritten as Nor, Or as Nand, and Xor as either Oror And.

sympy-bot · 2019-03-07T18:13:39Z

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logic
- And can be rewritten as Nor, Or as Nand, and Xor as either Oror And. (#16194 by @oscargus and @shubhamabhang77)

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#16137 

#### Brief description of what is fixed or changed
```expr._rewrite_as_And, expr._rewrite_as_Or, expr._rewrite_as_Nor, expr._rewrite_as_Nand```
added to logic equations.

#### Other comments


#### Release Notes

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<!-- BEGIN RELEASE NOTES -->

* logic
    * `And` can be rewritten as `Nor`, `Or` as `Nand`, and `Xor` as either `Or`or `And`.

<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

sympy/logic/boolalg.py

oscargus · 2019-03-09T11:18:55Z

sympy/logic/boolalg.py

+            return Or(And(Not(arguments[0]), arguments[1]), And(Not(arguments[1]), arguments[0]))
+        else:
+            for i in range(len(arguments)-1):
+                eq = Or(And(Not(arguments[i]), arguments[i+1]), And(Not(arguments[i+1]), arguments[i])).simplify()


Is Xor defined for more than two variables? In that case, how? (I would assume parity, although it can be argued if there actually is an XOR-function for more than two variables.

I searched regarding XOR of more than 2 inputs then it was showing that it exists. So I did this. Without simplify() output was not in simplified form. We can do one thing rather using simplify multiple times we can use it while returning.

I checked the documentation and Xor seems to be parity/add-modulo-2 so OK with multiple inputs (although the doubt was more from a formal perspective, it makes senses from a practical perspective).

OK. I guess that one can figure out a way to write it by looking at e.g. SOPform and the line
Or(*[_convert_to_varsSOP(x, variables) for x in essential]) where essential would be a list of all combinations of len(args) variables with an odd number of ones (can be generated by ibin, see sympy.utilities.iterables, and some filtering) and variables are args.

Not sure if it is required though. But feel free to give it a try. For a three-input Xor, the list essential should look like [[1, 0, 0], [0, 1, 0], [0, 0, 1], [1, 1, 1]] and so on.

Can we reuse one of the other methods here, like to_cnf or to_dnf?

It does not give the same result if the arguments are boolean functions in themselves.

to_cnf(Xor(And(x, z), y, z))

Xor(And(x, z), y, z).rewrite(And)

(With reservations for that I have messed up my installation running two different sources...)

They both simplify to the same expression though. It think the rewrite approach is slightly more suitable here as one most likely would except the expression on a certain form (not cnf, but as a rewrite based on the original expression). (I'm also a bit surprised that the z and ~z is simplified in the last cnf-expression.)

Of course one can argue which is the "best" form... One way is of course to just recreate a minimal cnf/nnf (SOP/POS) expression, but since there are other methods for that, I think this makes sense.

oscargus · 2019-03-09T11:21:14Z

Ideally it should be possible to call expr.rewrite(And) etc and it should probably be figured out if it is is possible and, if not (which seems to be the case), if it is possible to get it working.

For the code there are some comments how to write it more efficiently.

simplify is a bit risky to use since ideally it should simplify it back to xors...

shubhamabhang77 · 2019-03-11T09:52:25Z

Ideally it should be possible to call expr.rewrite(And) etc and it should probably be figured out if it is is possible and, if not (which seems to be the case), if it is possible to get it working.

For the code there are some comments how to write it more efficiently.

simplify is a bit risky to use since ideally it should simplify it back to xors...

    def rewrite(self, e):
        if str(e) == "Nor":
            return Nor(*[Not(arg) for arg in self.args])

This can be done.
What you say?

oscargus · 2019-03-11T09:55:42Z

As I wrote in the issue thread, simply renaming the methods to _eval_rewrite_as_Nand etc should allow that. I simply suggested the wrong name initially...

asmeurer · 2019-03-11T18:14:19Z

sympy/logic/tests/test_boolalg.py

+
+def test_rewrite_as_Nand():
+    expr = (y & z) | (z & ~w)
+    assert str(expr._rewrite_as_Nand()) == '~(~(y & z) & ~(z & ~w))'


Test this directly, not using the str form.

asmeurer · 2019-03-11T18:16:49Z

Please be more descriptive in the release notes.

shubhamabhang77 · 2019-03-12T06:14:06Z

When I use _eval_rewrite_as_Nand this in code and when I call rewrite(Nand) some problems in occuring regarding no. of arguments.

shubhamabhang77 · 2019-03-12T06:14:35Z

Please be more descriptive in the release notes.

Okay

oscargus · 2019-03-12T08:44:49Z

I've read up a bit more. You need arguments as follows:
def _eval_rewrite_as_Nand(self, arg, **kwargs):

where arg is the arguments to use (I assume it may be the same as self.args, but not sure).

Also, Or(*[_convert_to_varsSOP(x, arg) for x in list(filter(lambda x: sum(x)%2, ibin(len(arg), 'all')))]) should do the trick to convert the an Xor to And/Or.

shubhamabhang77 · 2019-03-12T12:32:36Z

I've read up a bit more. You need arguments as follows:
def _eval_rewrite_as_Nand(self, arg, **kwargs):

where arg is the arguments to use (I assume it may be the same as self.args, but not sure).

Also, Or(*[_convert_to_varsSOP(x, arg) for x in list(filter(lambda x: sum(x)%2, ibin(len(arg), 'all')))]) should do the trick to convert the an Xor to And/Or.

What should be the given arguments when we are going to call .rewrite(Nand)? Where did you read about it?

oscargus · 2019-03-13T08:27:52Z

I just looked at other _eval_rewrite_as_XX methods in the source and tried to figure out how they did it.

shubhamabhang77 · 2019-03-14T11:55:56Z

I just looked at other _eval_rewrite_as_XX methods in the source and tried to figure out how they did it.

What did you find?

oscargus · 2019-03-14T16:22:25Z

What those arguments are. There are plenty of these functions around so look at one.

oscargus · 2019-06-24T18:49:13Z

I've updated this now. Hopefully the tests will pass. (I did it on the original branch and as I'm not very fluent with that I wasn't able to run the tests locally...)

oscargus · 2019-06-25T07:38:06Z

As there is a risk that this is not seen in a while by potential mergers, being a rather old PR: ping @oscarbenjamin @smichr @asmeurer

oscarbenjamin · 2019-06-25T11:06:12Z

sympy/logic/boolalg.py

+    def _eval_rewrite_as_And(self, *args, **kwargs):
+        a = self.args
+        return And(*[_convert_to_varsPOS(x, self.args)
+                     for x in _get_even_parity_terms(len(a))])


Are these two functions converting to CNF/DNF (SOP/POS)? If so is that not already implemented?

See this comment: #16194 (comment)

Basically, it has to do with the expected form. Rewrite rewrites using a closed form expression, keeping sub-expressions, while to_cnf/to_nnf tried to simplify the expression (to some extent) and keeping everything on an SOP/POS form (but not simplifying it to the minimal SOP/POS form). I think both have their use.

Sounds like you're more qualified than me to merge this :)

My only comment would be that it would be good to add tests that demonstrate the similarity/difference between this and the related methods.

I can do that in another PR where I can more easily run the tests locally.

I have the following in my .git/config:

[remote "upstream"] url = https://github.com/sympy/sympy.git fetch = +refs/heads/*:refs/remotes/upstream/* fetch = +refs/pull/*/head:refs/remotes/upstream/pr/*

The means that git fetch upstream gives me a local copy of every PR. I can then check this out with

$ git fetch upstream $ git checkout upstream/pr/16194

The first time you run git fetch with this is slow.

I'm still not quite sure what is the best way to push to a PR using this setup...

Thanks for the hint! Indeed a good way to try out PRs I believe.

I'll merge this for now then and submit a new PR with more tests.

logic equation suggestions

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Rewrote the rewrite-functions

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oscargus merged commit 5f13feb into sympy:master Jun 25, 2019

oscargus mentioned this pull request Jun 26, 2019

[GSoC][Discussion] Improving New Assumptions #17066

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logic equation suggestions #16194

logic equation suggestions #16194

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shubhamabhang77 commented Mar 7, 2019 • edited by oscargus Loading

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Brief description of what is fixed or changed

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Release Notes

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shubhamabhang77 commented Mar 7, 2019 •

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