WhatвЂ™s nice about CNF is that there are many different tools to convert your problem language into CNF. (parts of) computer programs, logical circuits (e.g. These types of equations, also known as CNF, can express quite complicate things, e.g. something like: вЂњ(a OR b) AND (b OR c OR d) AND (-f OR -g)вЂќ. True/False), and equations being nothing but an вЂњAND of ORsвЂќ, i.e. One type of equations that is quite popular is to have all variables boolean (i.e. If you want to check that your system is in most cases doing the right thing, you can ask for uniform solutions at random and check the states for inconsistencies or unexpected behaviors.

Now, uniform solutions to these equations will be examples of the state space of your program. Say, your equations describe how a program can run. if you want to make sure to cover a good chunk of the potential states in a system. Uniformity is useful not only in gambling, but also e.g. Now, if you give me nothing but 1вЂ™s IвЂ™d be slightly confused, and eventually would think you may be trying to cheat. In this case, if the system is not cheating, it should give me solutions exactly like a random dice would give: 1.6, each with the same probability of 1/6. Say, I have a set of equations that only has the solutions x=1вЂ¦6, and I ask you to give me solutions uniformly at random. Uniform sampling is pretty simple: there are a set of solutions to a set of equations, and I want you to give me N solutions uniformly at random.

Sat problem