Perm | Perm is a library that makes it simple to check and request | Android library

First, it's good to note the difference between equivalence and equisatisfiability. In general, converting an arbitrary boolean formula (say, something in DNF) to CNF can result in a exponential blow-up in size.

This blow-up is the issue with your from_dnf approach: whenever you handle another product term, each of the literals in that product demands a new copy of the current cnf clause set (to which it will add itself in every clause). If you have n product terms of size k, the growth is O(k^n).

In your case n is actually a function of k!. What's kept as a product term is filtered to those satisfying the view constraint, but overall the runtime of your program is roughly in the region of O(k^f(k!)). Even if f grows logarithmically, this is still O(k^(k lg k)) and not quite ideal!

Because you're asking "is this satisfiable?", you don't need an equivalent formula but merely an equisatisfiable one. This is some new formula that is satisfiable if and only if the original is, but which might not be satisfied by the same assignments.

For example, (a ∨ b) and (a ∨ c) ∧ (¬b) are each obviously satisfiable, so they are equisatisfiable. But setting b true satisfies the first and falsifies the second, so they are not equivalent. Furthermore the first doesn't even have c as a variable, again making it not equivalent to the second.

This relaxation is enough to replace this exponential blow-up with a linear-sized translation instead.

The critical idea is the use of extension variables. These are fresh variables (i.e., not already present in the formula) that allow us to abbreviate expressions, so we don't end up making multiple copies of them in the translation. Since the new variable is not present in the original, we'll no longer have an equivalent formula; but because the variable will be true if and only if the expression is, it will be equisatisfiable.

If we wanted to use x as an abbreviation of y, we'd state x ≡ y. This is the same as x → y and y → x, which is the same as (¬x ∨ y) ∧ (¬y ∨ x), which is already in CNF.

Consider the abbreviation for a product term: x ≡ (a ∧ b). This is x → (a ∧ b) and (a ∧ b) → x, which works out to be three clauses: (¬x ∨ a) ∧ (¬x ∨ b) ∧ (¬a ∨ ¬b ∨ x). In general, abbreviating a product term of k literals with x will produce k binary clauses expressing that x implies each of them, and one (k+1)-clause expressing that all together they imply x. This is linear in k.

To really see why this helps, try converting (a ∧ b ∧ c) ∨ (d ∧ e ∧ f) ∨ (g ∧ h ∧ i) to an equivalent CNF with and without an extension variable for the first product term. Of course, we won't just stop with one term: if we abbreviate each term then the result is precisely a single CNF clause: (x ∨ y ∨ z) where these each abbreviate a single product term. This is a lot smaller!

This approach can be used to turn any circuit into an equisatisfiable formula, linear in size and in CNF. This is called a Tseitin transformation. Your DNF formula is simply a circuit composed of a bunch of arbitrary fan-in AND gates, all feeding into a single arbitrary fan-in OR gate.

Best of all, although this formula is not equivalent due to additional variables, we can recover an assignment for the original formula by simply dropping the extension variables. It is sort of a 'best case' equisatisfiable formula, being a strict superset of the original.

To patch this into your code, I added:

itertools.product is indeed what you want.

You could map new entries from the object and take the mapped new structure.

Android is an event driven OS that runs on a single main thread. Drawing is an event. That means in order to draw the main thread needs to return to the event loop. Your code does not return to the event loop until after you do all your processing. Thus it won't draw until after the processing is done.

The way to solve this is to use either a Thread or a Kotlin coroutine to do the processing, and allow the main thread to return to the event loop. BTW, if you have long lasting processing you should not be doing it on the main thread anyway- it freezes your UI and makes your app appear non responsive, for the same reason. The main thread should do short quick calculations and respond to OS events only.

Make sure the number of channels are the same as the last dimension of your input data. Also adding a comma here: f = self.query(x), creates a tuple, which you probably do not want: Here is a working example:

As described in the docs, a discord.Permissions object defines the __iter__-method by returning a list of tuples (permission_name, permission_value), where permission_value will be True if the member has the permission and False otherwise. You simply need to add a check if the value is true before appending the name to your list like so:

The procedure receives a name as its argument and returns a server-side cursor with that name. On the client side, after calling the procedure you must declare a named cursor with the same name and use it to access the query results. You must do this before committing the connection, otherwise the server-side cursor will be destroyed.

"TypeError: Cannot read properties of undefined (reading 'has')" means that mention.permissions is undefined. It's because your mention variable is a User and only GuildMembers have permissions.

Another error is that you try to check if the role.id is equal to a number/integer but snowflakes (like 589850931785498624) should always be strings as these are greater than the MAX_SAFE_INTEGER.

To implement Heap's algorithm in R, here is a solution that outputs the result in a matrix for further processing: