# Writing a sat solver online

### Sat solver algorithm

We do not care which assignment we get. Notice that we are now using the lp. For brevity, this post will only contain relevant excerpts, but you can find the entire resulting code on GitHub . The fifth last clause is true because x2. Benchmarks As far as I could tell from a cursory search, there are no standard test suites for benchmarking Sudoku solvers. If a positive literal has a corresponding structural variable with value 1, then we assign its logical variable to true. This forces each clause to be true. Recall our CNF formula. The first thing we need to solve is addressing variables, specifically converting a row, column, value triple into a specific value that represents it in the SAT solver. Each of these lines is a space-separated list of variables; a positive value means that corresponding variable so 4 means x4 , and a negative value means the negation of that variable so -5 means -x5. If not we return None. In the iterative case, we will store the state using d which is the current depth of the backtrack tree we are currently in, and also the variable we are to assign to currently, and the state list which keeps track of which assignments for each variable have been tried so far. Parameters: budget int — the upper bound on the number of conflicts. We access this last added row, and assign to its matrix attribute.

The first thing we need to solve is addressing variables, specifically converting a row, column, value triple into a specific value that represents it in the SAT solver. It would have been equivalent to assign 1. The argument expects a list of clauses, each clause being a list of literals, i. Then we get the last row, which is the one we just added note the use of the -1 index to address the last rowand assign to its matrix attribute.

Note that literal x1 corresponds to column 0, x2 to column 2, x3 to column 4, and so forth. You can view this as a single expression. Let's consider an example first, and then look at Stephen Cook's result that established SAT as the first NP-complete problem, to get a sense of both practical applications of SAT, and its theoretical importance.

Each line must end in a space and the number 0.

## Sat solver github

The short answer is that many other problems, often "difficult" problems, can be reduced to SAT. An assignment of None indicates unboundedness in this direction. A model is provided if a previous SAT call returned True. A SAT solver can determine if it is possible to find assignments to boolean variables that would make a given expression true, if the expression is written with only AND, OR, NOT, parentheses, and boolean variables. To convert them into CNF, we have to use some of the identities in the previous section on converting formulas to CNF. Note that none of the other solvers supports native AtMostK constraints. Otherwise, None is reported. If the budget is set to 0 or -1, the upper bound on the number of conflicts is disabled. Initially we have no columns at all. In the iterative case, we will store the state using d which is the current depth of the backtrack tree we are currently in, and also the variable we are to assign to currently, and the state list which keeps track of which assignments for each variable have been tried so far. If a limited SAT call was interrupted using the interrupt method, this method must be called before calling the SAT solver again. As input, we will take the number of regions n n , and assume the regions are labelled using numbers 1. We now go about turning this into a mixed-integer program. Because we want literal consistency, we specify that the sum of all literal pair structural variables must be 1. He seems to dislike recursion, see for example this story on Quora.

In this case, we are specifying that the row's constraint coefficients should be 1. Return type: list str or None.

## Writing a sat solver online

That is all for part 1, but I have much more I want to say about SAT solvers, so you can expect more posts about both using them, and about their internals and the theory behind why are they so fast. For brevity, this post will only contain relevant excerpts, but you can find the entire resulting code on GitHub . For each clause, we define a constraint specifying that the sum of all its literal structural variables must be at least 1. Return type: list str or None. However, what if we wanted as many of our logical variables to be true as possible? Thomas Finley, , We must tell the solver that we want to have a certain number of queens set to true. This is because we operate with an unstated assumption, that each position can contain only one number. In simplest terms, it states that the regions in any map can be coloured using at most four colours such that no two neighbouring regions are coloured the same. See Solver for the parameters description. You can view this as a single expression. Then we get the last row, which is the one we just added note the use of the -1 index to address the last row , and assign to its matrix attribute. What a horrible abuse of types! LPX Construct an empty linear program. First we run the simplex solver imlying a relaxed problem where the structural variables can range from 0 to 1.

If it is SAT, the second line will be set of assignments to the boolean variables that satisfies the expression. Each of these lines is a space-separated list of variables; a positive value means that corresponding variable so 4 means x4and a negative value means the negation of that variable so -5 means -x5. What is interesting, is that the number of outliers above the box, and the relative lengths of the whiskers, suggest that the underlying distribution of solver's running time over all of the inputs is heavy-tailed.