Threshold Behavior in a Boolean Network Model for SAT
نویسندگان
چکیده
Boolean satisfiability (SAT) is the canonical NP-complete problem that plays an important role in AI and has many practical applications in Computer Science in general. Boolean networks (BN) are dynamical systems that have recently been proposed as an algorithm for solving SAT problems [7]. We have carried out a detailed investigation of the dynamical properties of BN corresponding to random SAT problems of different size. We varied the problem size by changing the number of variables and the number of clauses in the Boolean formula. We show that dynamics of BN corresponding to 3-SAT problems display a threshold-like behavior, although this transition occurs far below the well known phase transition in the computational complexity of random 3-SAT. This threshold behavior does not appear to be connected to the transition between frozen and chaotic dynamics regimes of random BN.
منابع مشابه
Sat-based Model Checking for Region Automata
For successful software verification, model checkers must be capable of handling a large number of program variables. Traditional, BDD-based model checking is deficient in this regard, but SAT-based model checking, i.e. bounded model checking (BMC), shows some promise. However, unlike traditional model checking, for which time systems have been thoroughly researched, BMC is less capable of mode...
متن کاملOn Sharp Thresholds in Random Geometric Graphs
We give a characterization of vertex-monotone properties with sharp thresholds in a Poisson random geometric graph or hypergraph. As an application we show that a geometric model of random k-SAT exhibits a sharp threshold for satisfiability.
متن کاملTight Thresholds for The Pure Literal Rule
We consider the threshold for the solvability of random k-SAT formulas (for k ≥ 3) using the pure literal rule. We demonstrate how this threshold can be found by using differential equations to determine the appropriate limiting behavior of the pure literal rule.
متن کاملSatisfiability Threshold of the Skewed Random k-SAT
We consider the satisfiability phase transition in skewed random k-SAT distributions. It is known that the random k-SAT model, in which the instance is a set of m k-clauses selected uniformly from the set of all k-clauses over n variables, has a satisfiability phase transition at a certain clause density. The essential feature of the random k-SAT is that positive and negative literals occur wit...
متن کاملGenerating functions and the satisfiability threshold
The 3-SAT problem consists in determining if a boolean formula with 3 literals per clause is satisfiable. When the ratio between the number of clauses and the number of variables increases, a threshold phenomenon is observed: the probability of satisfiability appears in simulations to decrease sharply from 1 to 0 in the neighbourghood of a threshold value, conjectured to be close to 4.25. Altho...
متن کامل