algorithmgraphsathorn# Horn SAT algorithm using graphs

For some restricted classes of logical formulae, the satisfiability problem can be solved efficiently in polynomial time or even linear. One such class is that of Horn formulae, which consist only of Horn clauses with at most one positive literal. I've heard that it is possible to solve Horn SAT in linear time using graphs, but couldn't find any implementation of such solution. Now I'm really interested whether it is possible and if it is, how would algorithm look like?

Solution

If you're familiar with Davis–Putnam–Logemann–Loveland, Horn clauses are a class of formulae that can be solved using one round of unit propagation, with no backtracking.

In graph terms, we do the obvious thing and set up a bipartite graph with variables on one side, clauses on the other, and edges to represent a variable appearing as a negative literal in a clause. We also have a work queue of clauses consisting of a single positive literal. While the work queue is not empty, pop any element, identify the node corresponding to the variable, and delete it and its neighbors. For each clause vertex that now has degree zero, one of two things happens. If that clause has a positive literal, then we add it to the work queue. Otherwise, we've proved that the formula is unsatisfiable. If we reach the end of the work queue without finding such a clause, then the formula is satisfiable, and one satisfying assignment is to set all variables that entered the work queue to true, and all others to false.

- Difference between back tracking and dynamic programming
- How can we optimize this algorithm from O(N ** 2) to better complexity in order to pass performance test?
- How do I predict the required size of a Base32 Decode output?
- Reversing AND Bitwise
- Why does my binary search need an extra comparison? log2(N)+1
- How to build a trie for finding exact phonetic matches, sorted globally by weight, and paginated? (Building off this example)
- What is the Time Complexity and Space Complexity of extending a string according to a rule?
- Skyscraper puzzle algorithm
- Check if all elements in a list are equal
- Bitwise Interval Arithmetic
- fast algorithm for drawing filled circles?
- How to find distance from the latitude and longitude of two locations?
- Determine if two rectangles overlap each other?
- Randomly Splitting a Graph according to Conditions
- Maximize distance while pushing crates
- Free a binary tree without recursion
- How can I estimate number of nodes in given tree structure?
- Explanation of class Definition for Binary Trees in leetcode
- Procedural Generation of 2D Rooms
- Is there an algorithm to find the closest element to X in an unsorted array in Ω(logN)?
- Advanced Java idiom for 2+ classes implementing a generic interface
- Is there any algorithm in c# to singularize - pluralize a word?
- Number of Common sub sequences of two strings
- Trying to solve problem 19 on Euler Project
- is a "non-decreasing" sequence "increasing"?
- Is it possible to get the original value of a number, after several multiplications **with overflow**?
- Algorithm to determine the highest and lowest possible finishing position of a team in a league
- Algorithm to calculate the number of divisors of a given number
- Rolling or sliding window iterator?
- best way to pick a random subset from a collection?