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Questions tagged [boolean-algebra]

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Simplifying the Boolean expression $A + \bar{A}\bar{B}$?

So I'm trying to simplify the Boolean expression (1) $A + \bar{A}\bar{B}$. I noticed that by Karnaugh maps this is equivalent to $A+\bar{B}$, and I also noticed that if I take the complement of (1), ...
30 views

Does the naive conversion of a Boolean Formula to CNF have a polynomial or exponential complexity?

I am reading the naive conversion to CNF, this procedure is explaining in this book book, but I have not found a conplexity analysis of this algorithm: elimination of equivalence Elimination of ...
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Can numbers (not sets of numbers) in Linear Integer Arithmetic form a Boolean algebra?

As far as I understood, Boolean algebra is just one of the many first-order theories (1). It has the signature $\{\sqcap, \sqcup, \neg, \bot, \top\}$ and the axioms: associativity, commutativity, ...
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Expressing unsigned comparison through signed comparison of 2's complement

Let n > 0 be a natural number and for any two reminders a, b modulo 2^n we have that <...
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3-CNF to “independent form”

Is it possible to convert all logical formulae into a form such that each variable ends up in exactly 1 "factor" of the and operation? ($\wedge$). Any combination of operations is allowed, though the ...
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how do I simplify this particular boolean expression?

so I have spent nearly 5 hours trying to simplify this particular expression but I keep going round and round in circles. I have my hard copy notes to show you where I scribbled for hours and hours to ...
84 views

A universal operator necessarily generates $\neg x$ for input $x,…,x$

I originally posted this on math.stackexchange, but then deleted it and moved it here since I think it would fit this site more. I saw a claim in a slideshow from a basic computer architecture course ...
58 views

how many boolean functions exist that satisfy the condition

How many boolean functions exist that satisfy the following condition? $$\neg f(x_1,x_2,x_3,....,x_n) = f(\neg x_1, \neg x_2,...,\neg x_n)$$
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Logic gate which checks if the input is a negative number and changes its output based on that

I need to create a HDL which will use logic gates to demonstrate if something is a negative number in two's complement. The input is 8 bits, while the output is 1 bit, and if the input is a negative ...
19 views

what does it mean to extend an assignment?

For a constraint satisfaction problem, what does it mean for an assignment x to extend an assignment a? Sorry if this is super trivial, I did not find an answer e.g here: No Small Linear ...
45 views

Principle of Duality

I would like to know how to alter/add NOTs when applying Duality principle. Suppose I have P = XY(X+Y) + NOT(Y), how to find its dual? My book says that while applying Duality Principle to a ...
59 views

Intuition for maxterms

I understand that in terms of minterms, F (Boolean Function) = Sum of Products and thus will yield true when either of the products is true. But I am unable to develop any intuition for maxterms, ...
115 views

Is $A\odot B\odot C = A\oplus B\oplus C$?

(The notations used: $\oplus$ is XOR operator $\odot$ is XNOR operator) I was solving a problem, where they asked which of the given options give equation for the difference of full subtractor. ...
122 views

Is any sudoku solver an SAT solver?

I have recently created a sudoku solver using C#, which outputs the solution to a sudoku after a reasonable amount of time in many cases. I have used the basic sudoku SAT-reduction (i.e. x111 meaning ...
125 views

When is a 1-in-3 SAT clause satisfied?

How does exactly 1 in 3 sat work given the variables Xi, Xy, Xz if one of the variables in the formula are negative. We know that the results are if they are all positive given that: R(Xi, Xy, Xz) = ...
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Emulating equal operator using multiplication

I have two values $A$ and $B$, I want to know if I can implement the equals $=$ operation as the product of the two values. I can apply any function to $A$ and any function to $B$, but I need to use ...
43 views

Boolean expression to a truth table

How do I fill a truth table from the following expression? I can't decide whether it is SOP or POS. Y=(A+B)C+AB+(A+C)C+(`AB)
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If it's Possible to Create the If-Statement from Simpler Primitives

This question is about how to create an if statement (one of the control-flow statements) from scratch. An if-statement is typically a built-in construct in ...
63 views

Are there any techniques for checking whether a clause is subsumed by another clause when adding it to a cnf formula?

When doing variable elimination on a formula in cnf form, there is created a lot of new clauses. Is there any efficient way to check if these are subsumed by other, already existing clauses?