Questions tagged [boolean-algebra]

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Boolean formula that agrees with most truth assignments

Let $X_1,\dots,X_n$ be $n$ boolean variables. I have an unknown predicate $P(X_1,\dots,X_n)$ on these boolean variables. Of course, I can view the predicate as a function $f_P : \{0,1\}^n \to \{0,1\}...
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123 views

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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46 views

Iterating over a union of sets denoted by bitmasks

Consider the set $\mathbb{B}^n$ of all $n$-digit binary numbers. Let us define a bitmask as a tuple $M=(m_0,\ldots,m_{n-1})$, where $m_i\in \{0,1,*\}$. Such bitmask denotes a set $S \subset \mathbb{B}^...
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127 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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44 views

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 ...
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51 views

substituting expressions

I have a set of expressions $E_1 .. E_n$ over boolean variables and I'm looking for an assignment to the variables so that all expressions are satisfied. Normally this would be NP-complete, but I ...
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99 views

Methods for optimizing short-circuit evaluation for conditions of varying evaluation-cost

I have a bunch of boolean conditions, let's call them A, B, C, D, .... In my code, I need to use these conditions to distinguish between several different possible ...
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42 views

Petrick's Méthod With Maxterms

I recently learnt about Quine-McCluskey and Petrick's methods and they are all okay by me using minterms the procedure is as follows : 1- Reduce the prime implicant chart by eliminating the essential ...
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166 views

How do I get the NAND gate configuration for full adder from the logic table?

I'm self-studying, but I've gotten stuck already. If I'm given the logic table for a full-adder or any two-output table, how do I figure out the NAND-gate configuration, preferably methodically? ...
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85 views

Can I use the Quine-McCluskey to simplify a CNF which is not a product of maxterms?

As I understand it the Quine-McCluskey method allows you to start with a set of maxterms (or minterms), and combine them pairwise in a systematic way into a smaller set of clauses with a smaller set ...
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39 views

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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201 views

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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77 views

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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58 views

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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49 views

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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24 views

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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103 views

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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58 views

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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52 views

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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119 views

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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15 views

Simulating Boolean Circuit with RAM

Statement: Every $T(n)$ size bounded Boolean circuit family, could be simulated with $(T(n))^2$ time bounded Random Access Turing Machine (RAM). Could you please supply me with a reference to an ...
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K Maps: Getting simplified boolean form

I have been trying to work out the simplest Boolean form for the following K-map: I get the following expression: (x2 AND X3) OR (x1 AND x2) OR (x0 AND x2) However, via Boolean algebra, I get (x3 OR ...
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20 views

Which gates are “pre computation” universal?

In the following, by “functions” I will mean 2 input 1 output Boolean logic functions (for conciseness). A function is called “universal” if by using it (sometimes multiple times, chained together), ...
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30 views

Why does this finite state machine state transition diagram solution has more states than my solution?

I can't figure out what is wrong with my solution and why does it differ from book's solution. I think the only thing that matters is the previous state of A so that there should be two states, one ...
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33 views

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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158 views

how to evaluate a boolen expression

what is an easy but efficient way to evaluate Boolean Expression. I have been searching a lot in google but not really finding a good book or site which has working algorithm. Input string (A=100) ...
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44 views

Truth table and logic circuit problem

Does anyone know how to make this into a truth table and a logic circuit? (x•y)+x If so please send me the answer.
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1answer
932 views

How to convert a graph into a Boolean formula that represents all paths from a source node to a sink node?

I have a DAG. I want to construct a boolean formula $\varphi$ that represents all paths from a source node to a sink node. In particular, I have a variable for each vertex. A path $v_1 \to v_2 \to \...