counts the number of possible combinations of variable values that yield True when supplied as arguments to the Boolean function bf.
counts the number of possible combinations of the ai that make the Boolean expression expr be true.
- SatisfiabilityCount[expr] is equivalent to SatisfiabilityCount[expr,BooleanVariables[expr]].
Examplesopen allclose all
Basic Examples (3)
Count the number of cases for which yields true:
This corresponds to the number of times True appears in the truth table:
Count the number of truth cases for a pure Boolean function:
Count the truth instances in an expression with 2000 variables:
Properties & Relations (11)
SatisfiabilityCount for a function of variables is always between and :
SatisfiabilityCount efficiently counts the number of True elements in BooleanTable:
In this case, the BooleanTable would have elements:
SatisfiableQ efficiently tests whether SatisfiabilityCount is greater than zero:
TautologyQ efficiently tests whether SatisfiabilityCount is for an n variable function:
The SatisfiabilityCount for primitives of n variables is simple; for And it is always :
For Or it is :
For Nand it is :
For Nor it is :
For Xor it is :
For Xnor it is :
For Equivalent it is :
For Majority it is for odd and for even :
The size of the truth set for BooleanCountingFunction is the length of Subsets:
The size of the truth set for BooleanCountingFunction can be given by a combinatorial sum:
SatisfiabilityCount for an indexed BooleanFunction is given by DigitCount:
For n variables the number is given by DigitCount of Mod[k,2^2^n]:
SatisfiabilityCount for BooleanMinterms is given by the length of the index list:
For BooleanMaxterms it is given by 2n minus the length of the index list:
Use SatisfiabilityInstances to find explicit instances:
Use CountRoots to count the number of polynomial roots in a real interval:
Wolfram Research (2008), SatisfiabilityCount, Wolfram Language function, https://reference.wolfram.com/language/ref/SatisfiabilityCount.html.
Wolfram Language. 2008. "SatisfiabilityCount." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SatisfiabilityCount.html.
Wolfram Language. (2008). SatisfiabilityCount. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SatisfiabilityCount.html