Questions tagged [boolean-computation]
Questions on the functionality of Mathematica for Boolean computation.
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BooleanConvert: Boolean decision tree
The BooleanConvert function includes an available form called "Boolean decision tree": BDT.
What is the formal logical definition of a Boolean decision tree as used here?
What is the ...
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1
answer
104
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Is "and" the exact same as "&&" in Mathematica? [closed]
Does the word "and" compile the exact same way as "&&" or are there differences?
- 111
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35
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Symbolic solutions to systems of Boolean constraints?
Is it possible to solve a system of Boolean constraints symbolically? I'm trying to solve systems like the following, where $X$ is the unknown Boolean expression I'm trying to find, $a, b, c$ are the ...
- 440
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1
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Creating a boolean expression of assumptions between variables
I'm trying to create a boolean expression from a list of lists of variables such that the elements of one list are not equal to the elements of all other lists. I thought this might work:
...
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1
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1
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How to use Mathematica for demonstration of Analysis of Boolean functions?
I am wondering how to use Mathematica to demonstrate some concepts in Analysis of Boolean functions, e.g.:
Influence
Noise stability
Noise operator
$L_q$-norm and $L_\infty$ norm of a boolean ...
- 787
2
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5
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422
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Calculating union of two sets of reals
Given the following two sets of reals:
-(1/4) < x <= 0 || 0 < x <= 1/2 || x > 1/2
x <= -1 || -1 < x < 0
how can I calculate their union? ...
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2
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1
answer
132
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Square Root of a Boolean Matrix
I am trying to find the square roots of transitive Boolean matrices.
Let $B$ be a transitive Boolean matrix, If $A^2= B$, then $A$ is the square root of $B$.
Here is my try
...
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1
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3
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148
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Validity of the number of transitive matrices
I am trying to generate all possible transitive boolean matrices of order nxn which satisfies the following definition of transitivity
Let A=(a_ij)∈M_n(B) be a non-zero matrix. If for any i,j,k in ...
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2
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3
answers
315
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Finding transitive Boolean matrices
I am fairly new here and with Mathematica too.
I have a question regarding Boolean matrices but before this I did a random search and got this
Defining an arbitrary binary relation
But I am unable to ...
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2
votes
1
answer
105
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Is there a function which tests whether a Boolean expression is an inequality?
For something I am doing in Mathematica, it would be very helpful to have a function f[] which, when applied to an atomic Boolean expression, returns True if the Boolean expression is an inequality, ...
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2
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3
answers
158
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Check if a curve is contained in a region
Let's consider a curve described by a function $y = f(x)$ as well as a region $\mathcal{R}$ (consider that this region can be complicated) described by a set of points $\mathcal{X} = (x_{i,1},x_{i,2})$...
- 466
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6
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745
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Similarities between two vectors
Is there simpler and/or faster code for this?
List1={1,2,4,6,7};
List2={1,3,5,6,7};
Rule:
If values at respective positions match, output 1 else output 0.
Result:
...
- 584
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0
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31
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How to count the number of disjoint regions covered by a Boolean expression?
Consider the following Boolean expression as an example:
...
- 9,023
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1
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78
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How to define functions using $Z_2$ coefficients and $Z_N$ variables, e.g, realizing $1+1=0$?
A minimal example is to realize the following:
$x+x = (1+1)x = 0$, and $x^{N+1}y^{N+1}=xy$,
where $N$ is a given positive integer.
- 113
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2
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How to solve logic problem with a joker sometimes tell truth and sometimes lie?
If there are only truth teller and liar, I used to solve with BooleanConvert or SatisfiabilityInstances. However for this one, ...
- 101
2
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1
answer
92
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Evaluation process of And, Or,
Small questions about evaluation process of And, Or.
code 1)
...
- 4,037
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1
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414
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Why False && {False, False} does not preserve list structure?
I am on Mathematica 12.1.1.0 trying to perform a boolean operation over every element of a list, but preserving the list structure.
When I run
...
- 53
2
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2
answers
199
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How can I subtract and calculate the complement of a pair of sets? [closed]
I cannot properly implement these operations. How can I do it?
This is a reduced example:
A={2,3,4}
B={2,4,6}
C={1,2,3,4}
Find
...
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0
answers
51
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Simplifying RegionUnion call after CylindricalDecomposition
I want to simplify unions of output from CylindricalDecomposition calls.
Consider:
...
- 121
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1
answer
64
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Joining a table of statements with And [closed]
How could I algorithmically generate a statement such as
Subscript[a, 1] ∈ Reals && Subscript[a, 2] ∈ Reals && Subscript[a, 3] ∈ Reals
joining a ...
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1
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Can this previously solved three-dimensional constrained integration also be solved with certain added products in the integrand?
In Solved3DConstrainedIntegration
the constrained three-dimensional (Hilbert-Schmidt-metric-based HSmetric) integration problem for the absolute separability probability of the two-qubit (quantum bit)...
- 2,315
1
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1
answer
73
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Mathematica, from a⟺b∨c to (a≤b+c)⋀(a≥b)⋀(a≥c)
I want to enter a⟺b∨c to Mathematica and to have an answer
(a≤b+c)⋀(a≥b)⋀(a≥c)
I tried some BooleanConvert and such functions but cannot find the right one. How to do it?
This example is taken from ...
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4
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Are there any alternatives for NIntegrate to calculate the area for which $f(x,y)<0$?
I have this two-variable function
$$f(x,y)= (8 \cos (x+y)+7)\cos \left(\frac{x}{2}\right)+\cos \frac{x-2 y}{2}+2 \cos \left(\frac{3 x}{2}\right) $$
where $0<x,y<\pi$. I want to calculate ...
user80186
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Symbolic add of 32Bit Registers
I would like to perform multiple 32bit word register additions (mod 32 add. with variables of Boolean type shuffled with symbolic type).
For this task I implemented a ripple adder function:
...
8
votes
2
answers
197
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Efficient uniform sampling of certain Boolean matrices
I want to uniformly sample $(0,1)$-matrices with certain constraints. In particular, I want sum of each row to be rowsum and the sums of columns to equal ...
- 18.6k
5
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4
answers
738
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How to map a function with boolean operators over an array?
I am a beginner in Mathematica. I have this in Mathematica v12:
A = {1, 1, 1, 1}
B = {2, 2, 2, 2}
A+B
(* 3,3,3,3 *)
I'd like to experiment with evaluating ...
- 463
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0
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85
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TautologyQ like feature that also works for inequalities
If a=b and b=c, then a=c.
So in mathematica,
TautologyQ[(a == b) && (b == c) \[Implies] a == c, {a, b, c}]
yields 'True'.
If a<b and b<c, then a<c....
- 4,037
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1
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96
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Minimize Number of Boolean Formulas that Evaluate to True
I'm interested in a MinSat variant: given a list of boolean formulas like
...
- 151
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1
answer
204
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How can I change the Mathematica programming for creating a Venn Diagram?
I am working on using Venn diagram to explain logic and logical connections between sets. After coming upon these answers: Create a Venn Diagram,
How to plot Venn diagrams with Mathematica?,
which I ...
- 1,653
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2
answers
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How can I use Mathematica to solve a complex truth-teller/liar logic problem?
I have a logic puzzle I want to convert to Mathematica to solve:
Person A states, "Exactly two people are truth-tellers,"
Person B states, "I and Person C are truth-tellers."
...
- 1,653
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How to use MaxValue with booleans?
I tried to use MaxValue on Booleans domain:
MaxValue[{x + y, Element[x|y, Booleans]},{x,y}]
However, it fails with ...
- 161
2
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1
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Verify a conjectured formula for a modification of a 3D constrained integration successfully solved using Mathematica
I've acquired somewhat indirect--and not fully conclusive--evidence that the solution of a certain three-dimensional constrained integration takes the form
...
- 2,315
3
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4
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367
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Usage of 'Less than' condition in Sum
I have following sum: $$ \sum_{\substack{n,j\\j<n}}^{3} x_nx_j$$. How can I give this $j<n$ condition in Sum?
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Find the probability (relative volume) of a certain 4-ball with respect to Hilbert-Schmidt measure
Let us consider the set of points {x,y,z,1-x-y-z} and impose the strict ordering constraint
...
- 2,315
1
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2
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Confirm and possibly simplify a 2009 result for a 2D constrained integration
This is a direct descendant of two other recent questions,
3D and Equivalence,
both of which have been
answered in skillful, interesting manners. (See also the comment [actually answer] of JimB to
...
- 2,315
1
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1
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287
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Evaluate 3D- and 5D-constrained integrals for absolute separability probabilities
In a recent posting,
TwoQubits
user JimB, employing a change-of-transformations put forth by N. Tessore, was able to confirm a formula for the "two-qubit absolute separability Hilbert-Schmidt ...
- 2,315
2
votes
3
answers
223
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Simplifying expressions containing binary variables
Consider an expression with two binary variables, $a,b\in\left\{ 0,1\right\} $, given by $F=(1-a-b)^{3}(1-b)$, with truth table:
...
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3
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3
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424
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Evaluate a certain three-dimensional constrained integral
The result of the three-dimensional integration
...
- 2,315
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1
answer
81
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How to evaluate a multidimensional NIntegral in a range where certain conditions must be satisfied by the variables
I have a function f which looks similar to this :
f[a_, b_, c_] := NIntegrate[sigma[a, b, c], {a, -valueA, valueA}, {b, -valueB, valueB}, {c, -valueC, valueC}]
and ...
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0
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Boole does not limit boundaries of interpolation function, which rise in problems when using NIntegrate for multidimensional integral
I tried to use the Boole function to limit the boundaries of an interpolation function I created when integrating, and noticed that despite this condition, the function will always call extrapolated ...
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How do you simplify a boolean expression (!A B)+(B !C)+(BC)+(A !B !C)? [closed]
How would you simplify the following boolean expression (!A B)+(B !C)+(BC)+(A !B !C)?
I factorised B and managed to get B(!A+!C+C)+(A !B !C) = B+(A !B !C), but I do not know where I should go next.
...
user72949
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Create a Venn and/or related diagrams given the eight atoms of a three-set (A,B,C) 256-dimensional Boolean algebra
In my recent answer to How can one expand an arbitrary boolean combination into the $2^n$ atoms of the associated boolean algebra of size $2^{2^n}$?, for the eight atoms
{G[0],G[1],G[2],G[3],G[4],G[...
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How can one expand an arbitrary boolean combination into the $2^n$ atoms of the associated boolean algebra of size $2^{2^n}$?
The answer of user250938 to Can one usefully apply the Boolean functions of Mathematica to measurable Boolean sets? and the second comment of
Monroe Eskew to the answer to https://mathoverflow.net/...
- 2,315
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1
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121
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Can one usefully apply the Boolean functions of Mathematica to measurable Boolean sets?
This is something of an attempted succinct/pointed rephrasing of an earlier question Given measures on sets and on certain Boolean combinations of the sets, can one check their consistency and/or ...
- 2,315
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0
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removing brackets from the argument of a function like XOR [closed]
Xor[0,1,0] gives me the Xor of the elements 0,1 and 0 while Xor[{0,1,0}] gives me {0,1,0}. If I have a long list whose elements I want to Xor, how can I remove brackets from the argument? I tried Xor[...
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What is the meaning of this code section?
I like to know the meaning of this:
Total[#4 Boole[Norm[({x, y} - #1).RotationMatrix[#3]/#2]^2 < 1] & @@@
Data]
I need to make a slight modification to a ...
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0
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37
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BooleanComputation and superfunctions / meta-algorithms
Background :
A friend intends to model biological systems using boolean equations. He needed to write a solver to find out all possible solutions for such equations.
I suggested WL as a viable ...
0
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1
answer
155
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Plot Venn Diagram of Boolean Formula with Mathematica [duplicate]
https://www.wolframalpha.com/input/?i=%28a+and+b+and+c%29+or+%28not+a+and+not+b+and+not+c%29+or+%28not+a+and+b+and+not+c%29+or+%28a+and+not+b+and+not+c%29
How do you plot Venn Diagramm shown in the ...
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