# How can a Boolean representation be displayed as symbolic algebra?

GROUPS:
 Steve M 1 Vote Can Mathematica 9 convert a Boolean representation of an RBD to its symbolic algebraic form?If I have a simple series configuration made up of 2 componentsbexpr1=And[c1,c2]and the corresponding symbolic representation for the system would be RS1 = R1*R2The system I am interested in is more complex and contains 7 components in a 4 path architecture: path1=And[c1,c2,c5,c7]  path2=And[c1,c3,c5,c7]  path3=And[c1,c3,c6,c7]  path4=And[c1,c4,c6,c7]  bexpr2=Or[path1,path2,path3,path4]Of course, other systems can have higher complexity. How can the algebraic form of the reliability function be obtained for bexpr2?Thank you.
5 years ago
5 Replies
 Sean Clarke 1 Vote Are you just looking to use the engineering (+,*) notation for boolean logic?One quick solution is to replace And with Times and Or with Plus:bexpr2 /. {And -> Times, Or -> Plus}c1 c2 c5 c7 + c1 c3 c5 c7 + c1 c3 c6 c7 + c1 c4 c6 c7There are better ways of doing this using the Notation package that will allow Mathematica to still interpret this as a boolean logic statement.
5 years ago
 Sean,Thank you for the reply. I think I should have been more descriptive in my question.The solution I’m trying to confirm can be seen in Eqn. (3) on page 5 in the PDF file at the following link.http://www.reliasoft.com/newsletter/2Q2000/index.htm
 Malte Lenz 1 Vote There is also a more direct way to do this using a Library function, which will probably scale better for large problems:ReliabilityLibraryStructureFunction[bexpr2]