# Questions tagged [boolean-algebra]

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### Why do Karnaugh maps work?

The question is quite straightforward: Why do Karnaugh maps work? What was the reasoning that led Maurice Karnaugh to come up with these maps? At first glance, it doesn't seem a natural approach, ...
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### Can minimal CNF contain clause longer than initial CNF?

Let $\Phi$ be a k-CNF and $\Phi_{min}$ be a minimal CNF (one that contains smallest amount of literal occurences) that is equal to $\Phi$. Can $\Phi_{min}$ contain a clause of size $m > k$? What ...
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### How do I optimize a set of sub-lists which can combine to recreate higher level lists?

I am writing a function which XORs 32 boolean variables to produce a 32 bit output. To this end I have 32 lists of boolean variables (the lists have between 12 and 17 elements). Every variable in list ...
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### Boolean function minimization

Does there exist a Boolean function for which no sum-of-products expression that minimizes the number of products also simultaneously minimizes the number of literals (counting repetitions)? ...
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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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### How does one calculate the block-sensitivity of a function?

I am looking at this paper : http://arxiv.org/pdf/1411.3419v1.pdf But somehow I am not being able to fish out a method to calculate this quantity called the "block-sensitivity". Can someone kindly ...
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### Real versus Finite field polynomials

Let $f$ be a Boolean function. Let $g$ be the minimum degree real polynomial that represents $f$ with degree $d$. Let $g_{p}$ be the minimum degree $\Bbb F_p$ polynomial that represents $f$ with ...
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### Connection between formula size and time complexity

Supposing we have a problem $P$ with input size $n$ encoded as a boolean formula $f$ in $n$ variabes which is a multilinear polynomial. Let $f$ have the smallest degree. Is there a connection between ...
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### How do I triangularise a netlist?

I have a circuit that is represented as a netlist (specifically, an and-inverter graph). The desired outputs of this circuit are known. We can assume that some combination of the primary inputs will ...
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### What is the current state of research on the representation of boolean functions using wavelets

The harmonic representation of boolean functions such as XOR or AND has been studied in different course note lectures that can be found on Google. http://cs.mcgill.ca/~hatami/comp760-2011/ http://...
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### Simplifying circuits using boolean algebra

I am having a lot of trouble simplifying my circuit using boolean algebra. I am very new to this and any explanation would be greatly appreciated. I have y'+z+w'x+wx' I feel like I could use DeMorgan'...
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### How to combine multiple Boolean Functions in CDNF efficiently for implementation on a CPU?

I am trying to see how fast I can implement a 6-bits to 6-bites lookup table. Generally, I am attempting to do this by using the common method mentioned in CS textbooks of using the Quine-McCluskey ...
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### Prove the boolean function E = F + G contains of the sum of the minterms of F and G

I'm given a boolean function E which is result of the sum of F and G (Where both F and G are boolean functions for sure). By using K-Map I can easily understand why E would have the sum of the ...
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### is duality principle in boolean algebra is true for every expression

Let say A = 1 and B = 1 and then A+B = 1 now by using duality(replacing or gate by and gate and 1 by 0) we can say that, A.B = 0 but this is not 0, because 1.1 = 1, so please anyone clear my ...
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### Karnaugh Map: does maximal overlap always produce simplest boolean expression?

Suppose I have a 4x4 Karnaugh map with a few cells that are don't cares, and there are two ways of producing 3 groups of 4 cells. One of these ways overlaps groupings more that the other. Is one way ...
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### Minimizing the length a Boolean Algebra Expression in disjunctive normal form

I'm looking to minimize the length of an expression in boolean algebra that has been given in disjunctive normal form and is free from redundancy. To remove redundancy from the original expression I ...
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### What does it mean to “show algebraically” in propositional logic?

The biconditional operator $\iff$ of Propositional Logic can be defined by the identity $p \iff q \equiv (\lnot p \lor q) \land (\lnot q \lor p) \quad (1.1)$ Use the identity $(1.1)$ and identities ...
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### How can I parse a boolean expression to group it based on the conjunction?

I have to design an algorithm to parse an array of terms and conjunctions into a grouped boolean expression. I never studied computer science and don't usually need this for web development, but today ...