Questions on the functionality of Mathematica for Boolean computation.

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40
votes
7answers
6k views

Intersecting graphics

Does the Mathematica graphics system have any concept of intersecting graphics? I've not found much in the documents so far. For example, if I want to show the intersection of two shapes: ...
29
votes
5answers
2k views

Are there “All” and “Any” functions in Mathematica?

In Python, there is a function all which returns true if all of its arguments are true, and any which returns true if at least ...
21
votes
8answers
762 views

Applying And to lists of Booleans

I'd like to take {True,True,False} and {True,False,False} and apply And to get ...
14
votes
1answer
248 views

Why is SatisfiabilityCount faster than SatisfiableQ?

Consider the following (large) Boolean expression, which arose in a SAT problem. (The expression is not satisfiable.) ...
13
votes
3answers
537 views

Binary decision diagrams (BDD)

I would like to use Mathematica to help me simplify a given Binary Decision Diagram (i.e. pick the optimal variable ordering). I don't seem to find anything at all on the topic, although it is ...
13
votes
2answers
848 views

How to solve the liar problem?

In an island live two kinds of people: liar and truth-teller, the former only tells lies and the latter only tells truth, now there're two men A and B from the island, A said: "B is a truth-teller." B ...
13
votes
2answers
909 views

Simplify assumes Boolean 1 and 0 in logical expressions

Per this chat discussion and this previous question where I encountered the strange behaviour: ...
8
votes
2answers
1k views

Implementation of a new Game of Life Rule

I need to implement a new "game of life" in Mathematica: I have three states — black, red and white. Black means go forward, red go back and white take no action. I would like to implement the ...
7
votes
2answers
477 views

Bitwise operators - Hamlet for Mathematica

What is the best way to check this famous equation: 0x2b || ~0x2b == 0xff Mathematica doesn't seem to have a handy bitwise negation operator. The best thing I ...
6
votes
2answers
255 views

How to simplify Boolean expression

I would like to simplify $$((p\oplus q)=True)\wedge(p=True)$$ to $$q=False$$ I was hoping BooleanMinimize[((p ⊻ q) == 1) ∧ (p == True)] would do the trick, but ...
5
votes
1answer
109 views

“And” to continue evaluation after “False”

Below, is it possible to print No and have x be 2. That is, I'm looking for an And-like function that looks at all arguments ...
5
votes
2answers
182 views

How to get the boolean value of an inequality involving an InterpolatingFunction?

Here's the code: yan = FunctionInterpolation[x^2, {x, -1, 1}]; FullSimplify[yan[x] > -1, -1 < x < 1] Needless to say, what I expect to see in the output ...
5
votes
1answer
566 views

Prenex and Skolem normal forms

In MMA version 7 there was a big advance in logic support ("Boolean computations" is the official name). This was not further developed in version 8.0. So now we have a fairly robust support for ...
5
votes
2answers
190 views

Short circuit logical operators [duplicate]

Suppose I want to compute $f(1)\vee f(2) \vee \ldots \vee f(10^{10})$, but I know a priori that $f(n)$ is True for some $n \ll 10^{10}$ with high probability. For ...
5
votes
1answer
374 views

Using Boole to integrate over region

I have a complex and long piecewise function to integrate, so I have written a Mathematica script that cuts the whole range of integration, evaluates the integrand in each region and then integrates ...
5
votes
0answers
127 views

Theorem Proving

It's a hard for me to write english so I'll try to go straight to my problem. There is abstract predicate f, that takes two parameters. There are also two other ...
4
votes
3answers
389 views

Fast method for combining two lists

I have two lists, v1 and v2. Each element of the lists may be positive or negative. I want to create a list ...
4
votes
3answers
253 views

Importing an array from text file and convert it to truth table

I am new to Mathematica, and would like some help in the following operation. I have a truth table stored in a text file. I want to read this in Mathematica, and find its Boolean Rule. Suppose I have ...
4
votes
3answers
143 views

Is there an equivalent of Sum for And?

Is there an equivalent to Sum for And? That is, just like instead of ...
4
votes
0answers
189 views

Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
4
votes
0answers
175 views

Can I define an axiomatic (Boolean algebra) system and prove theorems using Mathematica?

The general question is Can I define an axiomatic system and prove theorems using Mathematica? The more concrete one is about Boolean algebra. I consider this axiomatic Boolean algebra system ...
3
votes
2answers
177 views

Sequence and boolean And

I'm trying to figure out if a calculation result it's a valid result. As it return a matrix, I need to test that every element it's a number, so I thought this could work... ...
3
votes
2answers
281 views

How to rewrite this function to be faster: Find sub-matrixes of boolean board which imply a given boolean pattern

I have Boolean matrix A (called "board") and Boolean matrix B with smaller dimensions (called "pattern"). I am trying to find sub-matrixes C of A such that C has same dimensions as B, and ...
3
votes
2answers
270 views

How to evaluate Boolean expression and get an answer in bitwise form?

I am trying to evaluate the following expression: 11000 AND ( 01011 OR 11011 ) I am able to get the answer on paper. The answer is: ...
3
votes
1answer
768 views

Converting truth tables to boolean expressions

I have a truth table for a Boolean expression represented like this ...
3
votes
1answer
76 views

Using TrueQ with conditions

Say I want to ask Mathematica whether $|x| = x$ for all $x > 0$. Obviously, if I try TrueQ[Abs[x] == x], I get False, ...
3
votes
4answers
251 views

Simplify binary expressions

Is it possible for Mathematica to do simplifications for expressions where the variables are binary, such as: a + b = 1 + 2*c => a + b = 1 Here c must be 0 because if it is 1, the RHS is 3 but ...
3
votes
1answer
262 views

Convert boolean test function to pattern?

What is a "reverse" to MatchQ? MatchQ converts pattern into boolean function. So how to convert back? Suppose I want to use ...
3
votes
1answer
137 views

Defining an Implies operation that works for Boolean matrices

I have two Boolean matrices, that both have dimensions m x n. I want to create a function TableImplies, which would return True ...
3
votes
1answer
93 views

Defining an arbitrary binary relation

I am trying to define some binary operators. A binary operator operates on a set of variables V and is defined by a subset S of pairs of those variables {Vi,Vj}. For example, "=",">",">=" are all ...
2
votes
2answers
114 views

How to negate a boolean vector?

The !True returns False but how can I negate a boolean vector such as {True, False, True}? ...
2
votes
3answers
78 views

Applying boolean logic to a 2D array

How can I make a function that creates a particular size 2D matrix that determines "True" or "False" if a random value between 0 and 1 is at or below a certain number? Below is what I have written but ...
2
votes
2answers
98 views

Boolean algebra does not simplify

I am doing some simple Boolean algebra and wanted to perform some calculations in Mathematica but found it doesn't work. Let us consider the expression: ...
2
votes
2answers
330 views

Given a system of inequalities, how to make Solve find out that two variables should be equal?

Given two boolean variables x1 and x2 (in the sense that they are in the range [0,1]), if I try to solve the following equation system with Solve: ...
2
votes
0answers
165 views

What are the steps using boolean algebra for transforming one equation into another?

I have a special case where I have two equations, which I have solved in a better and quicker way, but I need to solve with Boolean algebra. Using the laws of Boolean algebra, I have to prove that ...
1
vote
3answers
535 views

Creating a Specific Boolean Function

How can I implement a Boolean function F(A,B) that has outputs that are not specific and, therefore, the truth table output of this two-input function will be (a, b, c, d) -- here the first term ...
1
vote
2answers
100 views

Infinite sums with Boole and EvenQ

Suppose I am interested in a sum across a set of even numbers, such as: Sum[x, {x, 2, 20, 2}] 110 or ...
1
vote
2answers
477 views

3D Contour Plot parts of sphere with gradient less than 0, equal to 0 and more than 0

I want to plot only parts of the sphere of radius 1 where the gradient $\frac{\partial z}{\partial x}$ is < 0, = 0 and > 0. The full sphere is given by: ...
1
vote
3answers
449 views

Matlab-style Find in Mathematica? Value list and Boolean List, how to select values according to the boolean list?

I want to select elements with the true value (Indices list) in the corresponding point to the value list (MCS). Is there anything like Matlab-style Find to get the indices of true values in the ...
1
vote
1answer
149 views

Conditionals slower than operators?

I want to make my application faster. I tried to replace an If condition with operators. The If condition is ...
1
vote
1answer
72 views

How can I draw truth tables using Mathematica [duplicate]

For instance, the given expression p ⊕ (p v q) In the problem I'm trying to solve. There's a Mathematica answer to this: ...
1
vote
2answers
77 views

Discrete Measure between Binary Vectors

I would like a discrete distance measure between two binary vectors (or strings). Like HammingDistance but I want the vectors to be considered closer if they have ...
1
vote
1answer
179 views

3D Contour Plot - parts with gradients less and more than zero

I'm trying to plot sections of the 3D Contours, with gradient less than zero, and more than zero and equal to zero. It manages to solve for the derivative, but when I apply the conditions ...
1
vote
3answers
324 views

Conditional Check on Matrix

Suppose I have the following matrix (i,j): ...
1
vote
1answer
511 views

How to generate the truth table to prove logical equivalence?

How to generate the truth table to show that $p \implies (q \vee r)$ is equivalent to $(p \wedge \neg q ) \implies r$ ? Can I use BooleanTable?
1
vote
2answers
96 views

Numbering of cases implied by a subset of Boolean vectors

In the course of a programming problem I stumbled upon the following sub-problem. Given an arbitrary, but fixed, number of Boolean variables, I would like to be able to pick a subset of the ...
1
vote
1answer
229 views

boolean return value in mathematica

why does the following instruction ok in mathematica, and it returns a boolean value In[398]:= catenary[x, 1, 0, 0] == catenary[-x, 1, 0, 0] Out[398]:= True and ...
1
vote
0answers
51 views

Algorithm for converting truth tables to Boolean functions

The function BooleanFunction is able to convert a truth table into a Boolean function. Does anyone know what is the mathematical background and/or algorithm that ...
0
votes
2answers
82 views

How to combine all possible N boolean values?

Is there any simpler formula than Tuples[{False, True}, 3] to generate tuples of all combinations of boolean values?
0
votes
2answers
152 views

How to add variables to boolean expression and get conjunctive normal form?

I have the boolean expression (a && !b). I want to add variables c, d into the ...