Questions tagged [boolean-algebra]

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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. ...
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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 provide logic ...
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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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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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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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A Combinational circuit Problem

A circuit outputs a digit in the form of 4 bits. 0 is represented by 0000, 1 by 0001, …, 9 by 1001. A Combinational circuit is to be designed which takes these 4 bits as input and ...
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Simplyfing a particular boolean expression

I'm having a lot of trouble with two problems the first is: ...
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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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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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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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Boolean Logic Equation

How can I prove this. what is the way? im up to the second last line. and i dont actually know how can x * (1 + y) then the y just disappears into x * 1. ...
225 views

Is generating MIN-3-UNSAT $\mathsf{NP}$-hard?

Input: amount of variables (with minimum of $10$ since otherwise problem is unsolvable). Output: unsatisfiable formula. Restrictions: Every clause contains exactly 3 variables. Every clause differs ...