Recognizing more random unsatisfiable 3-SAT instances efficiently

Certifying Unsatisfiability of Random 2k-SAT Formulas Using Approximation Techniques

It is known that random k-SAT formulas with at least (2 · ln 2) ·n random clauses are unsatisfiable with high probability. This result is simply obtained by bounding the expected number of satisfying assignments of a random k-SAT instance by an expression tending to 0 when n, the number of variables tends to infinity. This argument does not give us an efficient algorithm certifying the unsatisf...

Using CSP Look-Back Techniques to Solve Exceptionally Hard SAT Instances

While CNF propositional satisfiability (SAT) is a sub-class of the more general constraint satisfaction problem (CSP), conventional wisdom has it that some well-known CSP look-back techniques -including backjumping and learning -are of little use for SAT. We enhance the Tableau SAT algorithm of Crawford and Auton with look-back techniques and evaluate its performance on problems specifically de...

Efficient Recognition of Random Unsatisfiable k-SAT Instances by Spectral Methods

Minimally Unsatisfiable Boolean Circuits

Automated reasoning tasks in many real-world domains involve analysis of redundancies in unsatisfiable instances of SAT. In CNF-based instances, some of the redundancies can be captured by computing a minimally unsatisfiable subset of clauses (MUS). However, the notion of MUS does not apply directly to non-clausal instances of SAT, particularly those that are represented as Boolean circuits. In...

Consequences of Hardness of Refuting Random CSPs

A constraint satisfaction problem (CSP) is a decision problem for which the instances are sets of constraints, and the answer is ”yes” (the CSP is satisfiable) if there exists an object satisfying all the constraints, and ”no” (the CSP is unsatisfiable) if no such object exists. Examples of CSPs include 3-SAT, graph coloring, and linear programming. A random instance of a CSP is one created by ...