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Questions tagged [boolean-algebra]

The tag has no usage guidance.

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computer science question 2 java [on hold]

Write a method createMines that creates and returns a 10x10 array of boolean. Set 10 random entries in the table to true. The rest of the entries should be false.
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Computer Science Question 1 java [on hold]

Write a void method, showMap, that takes a 2-dimensional array of boolean as a parameter and prints the array in the following tabular format: if the corresponding entry is true, then an 'X' is ...
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1answer
23 views

Simplifying SOP: implementing OR with NAND

I am learning how to implement basic logic gates using NAND. I have learnt that you can use De Morgan's theorem as such: $a+b = \bar{\bar a} + \bar{\bar b} = \overline{(\bar a *\bar b)}$ In other ...
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0answers
21 views

How to create a jump code for the following boolean expression?

I want to create a jump code statement for the following boolean expression how can I do that? Can someone give me an example which helps me to solve further problems related to the same? ...
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0answers
20 views

Difference Between Boolean Operators

In laymen's terms, what are the major differences between the AND, OR, XOR, TEST and NOT statements as they relate to writing programs in languages like Assembly and C.
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1answer
34 views

How to “logically” solve boolean logic

I came across of one excellent book Elements of Computing Systems and in chapter 1 we need to implement the "primitive" logic gates (for example: Not, And, Or, Xor, Mux, etc) based on a Nand gate. ...
4
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1answer
60 views

Why are there two not operators in lambda calculus?

From Wikipedia: $\mathrm{true} = \lambda a. \lambda b. a$ $\mathrm{false} = \lambda a. \lambda b. b$ Because true and false choose the first or second parameter they may be combined to ...
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1answer
19 views

Number of literals in the given boolean expression

Count the number of literals in the following expression : F = AB' + BC' + CD' + DE' According to me, the answer should be 8. But my solution suggests that the answer should be 6. Can anyone help me ...
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2answers
43 views

Boolean Functions

Say you have N input Boolean function, let's use a parity tree for the example. The function outputs a one or a zero depending on the values of the N inputs. Are the N inputs considered the preimage ...
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1answer
20 views

Representing chained XOR operations as linear inequalities

I'm trying to solve an integer linear program (ILP) in which a constraint of the following kind must be met: $x_1 \oplus x_2 \oplus \cdots \oplus x_n = 1$ where $\oplus$ is the binary xor operator. ...
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OR functions and SQ-Learning

Anyone can describe or give a reference which has a clear description and detailed proof of the SQ-Learning algorithm for the OR class of Boolean functions?
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1answer
33 views

Minimal representation of an AND with two-input NOR

Let $x_1,x_2,x_3,x_4$ be boolean variables (i.e $x_i \in \{0,1\}$) Consider $f(x_1,x_2,x_3,x_4) = x_1 \wedge x_2 \wedge x_3 \wedge x_4 $ I want to write $f$ in terms of two-input NOR gates. I.e, $\...
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1answer
63 views

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 ...
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1answer
58 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 ...
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0answers
26 views

how many boolean functions exist that satisfy the condition

how many boolean functions exist that satisfy the condition : $Not[f(x_1,x_2,x_3,....,x_n)]$ = $f(Not(x_1), Not(x_2),...,Not(x_n))$
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1answer
29 views

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 ...
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1answer
14 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 ...
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2answers
28 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 ...
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1answer
25 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, ...
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3answers
99 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. ...
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1answer
58 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 ...
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1answer
55 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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1answer
21 views

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 ...
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1answer
41 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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2answers
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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 ...
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0answers
20 views

How to Represent an If Statement with Boolean Algebra Primitives

I saw this: Generic method for implementing if-else statement in hardware (using gates,mux-demux,flip flops ) etc. However it's a bit over my head atm. I am wondering, instead of an ...
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Application-scope, run-time disable-able conditional statements

Background Mainstream programming languages support conditional statements, such as: if( condition ) { operation; } Once coded, changing the condition often ...
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1answer
49 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?
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1answer
30 views

When using resolution variable elimination to simplify a cnf, does that change the truth values of the other variables?

When you use resolution variable elimination to preprocess/simplify a formula in cnf form the resulting formula is equisatisfiable. What I wonder about is if I can use this technique to remove ...
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0answers
301 views

Boolean Algebra : Using identities, prove x(x + y) = x

Example: Prove the ABSORPTION LAW: $$ x(x + y) = x $$ $ Solution: \\ x(x + y) \\ = (x + 0)(x + y) \;\;\;\;\; Identity \;Law \\ = x + (0 · y) \;\;\;\;\;\;\;\;\;\;\; Distributive \;Law \\ = x + y · 0 ...
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0answers
70 views

Simple example of exponential gap between monotone and non-monotone circuits

Is there a simple example of a Boolean function $f:\{0,1\}^m \to \{0,1\}$ that we know can be computed by a polynomial-size circuit, but cannot be computed by any polynomial-size monotone circuit? ...
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0answers
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About sign-rank of Boolean functions

Do we know of any necessary condition for a Boolean function or say a depth $2$ LTF circuit to have a low (~poly(dim)) sign-rank?
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1answer
83 views

Does XNOR of three variable equals XOR of same three variables

I came across following excerpt: $(x'y'+xy)'z'+(x'y'+xy)z=x\oplus y\oplus z$ What I see is left hand side is XNOR of $x,y$ and on right, $z$ and I get XOR of of $x,y$ and $z$ !!! In other word, ...
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1answer
808 views

Proof of Demorgan's law [duplicate]

how can i prove Demorgan's law (X+Y)'=X'. Y'?I already tried studying book but doesn't understand the first step so plz answer in detail.(beginner here)
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1answer
39 views

What's difference between SUM and OR?

While studying ALU I came across this example, now what's difference between operations of OR Gate and SUM(Adder), in binary language
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1answer
164 views

How can i design this function using only NAND and XOR gates?

I have this initial function \begin{split}(\overline{A}+\overline{B})(\overline{D}+\overline{C})+AB\overline{(\overline{C}+\overline{D})}\end{split} Which i reduced to \begin{split}{\overline{AB}*\...
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3answers
187 views

How many 3-SAT expressions with up to N variables are satisfiable?

TL;DR There are exactly 255 possible 3-sat expressions with exactly 3 variables (more meticulously defined below). Of those, exactly 254 are satisfiable. There are exactly 4,294,967,295 possible 3-...
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1answer
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Programmatically checking equivalence of statements

So as part of a theorem-prover/checker, I'm using Prolog to try to determine the equivalence of statements that have been parsed into tree form, e.g. $x=2$ is represented as ...
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1answer
54 views

Common parse tree for several formulas

I have a large (~1k) number of boolean formulas like: f1(x) = p1 AND p2 f2(x) = (p1 AND p2) OR p3 f3(x) = p4 OR !p5 The argument x is a set, and the predicates (...
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1answer
25 views

Does the 3SAT problems have to have consistent operators?

What are the rules pertaining to 3SAT as to the actual boolean equation? The main thing I do not understand is in a given boolean expression within a single clause can you have both AND + OR ...
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1answer
54 views

LTF circuits and $AC^0$

Do we know if all of $AC^0$ can be captured by polynomial sized depth $2$ LTF circuits? (with or without polynomially bounded weights). For any vector $w \in \mathbb{R}^n$ and any number $c \in \...
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1answer
28 views

Taking mod $2$ with LTF gates

Consider the function : $\mathbb{Z}^{\geq 0} \rightarrow \{0,1\}$ given as $n \mapsto n \bmod 2$. Does this have an easy implementation using Linear Threshold Function gates? I do not mean that the ...
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0answers
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Are there quantum algorithm that solve the boolean satisfiability problem in subexponential time?

Are there quantum algorithms that solve the boolean satisfiability problem in subexponential time? Do they just give a determination as to whether an expression can ever evaluate to true, or can they ...
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3answers
57 views

Simplyfing a particular boolean expression

I'm having a lot of trouble with two problems the first is: ...
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1answer
137 views

Infinite Boolean circuits as a model of computation

Boolean circuits are non-uniform models of computation in that they require a different circuit for each length of input. The typical way of uniformizing a family of Boolean circuits is to define a ...
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1answer
37 views

Determine whether a variable has positive influence in Boolean function

Given a Boolean function $f$ over the set of variables $X =\{ x_1,...,x_n \}$, the influence of $x_i$ is defined as the probability that changing only $x_i$ on random input changes $f$. Given a ...
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Is such variant of SAT always satisfiable?

Let we have a SAT instance where every clause has length $\ge3$ (when length $2$ is allowed, it can be unsatisfiable) and each pair of literals appear only once. Non-example: $(x\lor y\lor z)\land(x\...
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1answer
26 views

2CNF with 3 variable occurences

If we do not allow unit clauses, can 2CNF containing 3 occurences per variable be unsatisfiable? Every time I try to connect opposing variables to a cycle, I need to draw 4 edges for at least one ...
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0answers
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Determining when equal 2CNF has pure literal

Let us assume that we have a 2CNF $\varphi(X,y)$. Then we want to see if there is equal formula where $y$ (or $\overline y$) is pure literal. Can this be done in polynomial time? Are there some ...
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0answers
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Maximal combinations in a Boolean algebra

Consider a finite set $X$ and the boolean algebra $\mathcal{P}(X)$ of the subsets of $X$. While I focus on $\mathcal{P}(X)$ in this question, the problem could be expressed more generally in any ...