Questions tagged [boolean-computation]

Questions on the functionality of Mathematica for Boolean computation.

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106 views

Combinatorics with booleans equations

I have variables $X_i \in \{1,0,-1\}$. Now I add up $m=3$ variables $$S=X_1 + X_2 + X_3$$ and want to find all combinations that give me, $S=1$. I can do this with (see this solution): ...
360 views

Mathematica vs. state-of-the-art SAT solvers

I found some fascinating paper by Marijn Heule and Oliver Kullmann on advances in SAT solvers and automated reasoning. In particular, the authors where able to show (a year earlier) a breakthrough ...
50 views

Can I get mapping as output from SatisfiabilityInstances?

Consider the code: SatisfiabilityInstances[Implies[a, b], {a, b}, All] (* output *) {{True, True}, {False, True}, {False, False}} I would like to obtain the ...
194 views

List of lists elementwise greater/smaller than

I have two lists a = {{3,1,2},{5,1,3},{4,1,1}} b = {{4,0,3},{4,2,2},{5,0,2}} And would like to compare each element within ...
1k views

Create a list of all possible Boolean configurations of three constraints

I have three nonnegativity constraints \begin{equation} A_1>0, A_2>0, A_3>0. \end{equation} I want to create a single List consisting of all possible/inequivalent Boolean configurations of ...
70 views

Solve a constrained four-dimensional integration problem for a “magic simplex” probability

Equation (7) in the 2012 paper, "Complementarity Reveals Bound Entanglement of Two Twisted Photons" of B. C. Hiesmayr and W. Löffler for a state $\rho_d$ in the "magic simplex" of Bell states \begin{...
45 views

Result of BooleanCountingFunction?

Folks, when i use BooleanCountingFunction[{1}, {v1,v2,v3}, "CNF" ] i get a neat output like: ...
63 views

55 views

Reversing evaluation of Boole

I am currently using TransferFunctionPoles[TransferFunctionModel[{{A[w]}}, w]][[1, 1]] to identify the poles of some function $A(w)$. However, $A$ contains one ...
55 views

Extract minterms from DNF

I need to get the list of all minterms (as a list of boolean formulas) for a given DNF formula. For example for formula ...
53 views

How to replace symbolic function call by indexing

I have an expression like this: expr = x \[And] \[Not] x I would like it to behave like a Boolean function of parameter ...
433 views

Simplify a Boolean Algebra expression with don't cares

I want to simplify this expression: BooleanMinimize[(A ∧ ¬ B ∧ C ∧ ¬ D) ∨ (A ∧ B ∧ ¬ C ∧ ¬ D) ∨ (A ∧ B ∧ C ∧ ¬ D)] And I get this: ...
176 views

Plotting RegionIntersection

A new feature added in Mathematica 11.2 gives the ability to easily plot region intersection (see this post, scroll down to 3D Computational Geometry). However, I ...
98 views

Split logic input

I want to make a program that takes the input p&&q->q and then splits the input so I can create truth tables for p, <...
79 views

forward or backward IntegerDigits in pairs must yield different results

I have some pair configurations same as {0,1,1,1,0,1} with {1,0,1,1,0,1} or {1,1,0,1,0,1,1,1}...
32 views

Why does Thread “collapse” my list of truth values when MapThread does not? [duplicate]

If I have v1 = RandomInteger[5, 10]; v2 = RandomInteger[5, 10]; Remove[f] then, not surprisingly ...
34 views

Separating completely independent systems of BooleanCountingFunctions

I have an augmented matrix as a representation of many instances of BooleanCountingFunction[{k},n][vars], and I want to separate it out into many smaller subsystems ...
85 views

Values of sequenced IntegerDigits lists with two fixed elements

How can we access to all values of an IntegerDigits list with a special condition. This restriction is the locality of 0 or <...
220 views

Boolean Expression simplification [closed]

I'm stuck in proving (A+B+C+D)(A′+B′+C′+D′)=AD′+A′B+C′D+B′C using algebraic manipulation. I tried to solve it. I expanded ...
85 views

special boolean operator

I am familiar with some boolean operators. I want to access an operator that does a procedure same as below one. But for simplicity, we can say in the first step we ignore ...
705 views

How can I speed up my code which finds the ratio of two sums that are hard to compute? [closed]

Consider a set $\left\{\left. T(c, d)\right|c, d\in\mathbb{Z}\right\}$, a subset of the rational numbers. I want to compute $D$ D=\lim_{(a,b)\to(-\infty, \infty)}\lim_{(r, t)\to(\infty,\infty)}D'(...
105 views

Boolean operation to obtain volume

Imagine a sphere with $R40$ centered at ${0,0,0}$. Now a cylinder with $R25$ tangent in one of the quadrants of the sphere ending on the surface of the sphere. How do I get the volume of the ...
89 views

Applying the Four-color Theorem to the map of Florida [duplicate]

I'm still wrestling with the following problem; I' m attempting to apply the Four Color Theorem to the map of Florida; USA. The attribute "BorderingCounties" doesn't work for Alachua County (but, it ...
104 views

(FindInstance) Speeding up a slow integer program by converting to a boolean program

Here is an integer program with a bunch of inequality and equality constraints. FindInstance takes 2 seconds to solve it. ...
111 views

FindInstance boolean program is slow, but fast with BooleanConvert

FindInstance can be incredibly slow to solve a boolean program, but it can be significantly improved by using BooleanConvert to ...
276 views

Implementing positivity constraints over a six-dimensional hypercube

This question involves the same subject matter as my previous one (How can one achieve the most accurate estimates of certain six-dimensional integrals under specific constraints?), but with another (...
239 views

boolean casting

In Mathematica one can do something like the following: ...
47 views

Make FindInstance accept only parametrized solutions

I have for example the following conditions: ...