• Corpus ID: 1977836

Hard and Easy Distributions of SAT Problems

@inproceedings{Mitchell1992HardAE,
  title={Hard and Easy Distributions of SAT Problems},
  author={David G. Mitchell and Bart Selman and Hector J. Levesque},
  booktitle={AAAI},
  year={1992}
}
We report results from large-scale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult. Our results provide a benchmark for the evaluation of satisfiability-testing procedures. 

Topics from this paper

Generating Hard Satisfiability Problems
TLDR
It is shown that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult.
Generating Hard Satis ability Problems ?
We report results from large-scale experiments in satissability testing. As has been observed by others, testing the satissability of random formulas often appears surprisingly easy. Here we show
Generation of Hard Non-Clausal Random Satisfiability Problems
TLDR
This proposal is a generalisation of the random k-SAT model that introduces non-clausal formulas and exhibits interesting features such as experimentally observed sharp phase transition and the easy-hard-easy pattern.
Finding hard instances of the satisfiability problem: A survey
TLDR
The performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions are considered.
Resolution Complexity of Random Constraints
TLDR
An analysis that shows why deciding satisfiability of instances from some distributions is challenging for current complete methods is presented, and shows that when constraints are not too tight almost all unsatisfiable instances have a structural property which guarantees that unsatisfiability proofs in a certain resolution-like system must be of exponential size.
Easy Problems are Sometimes Hard
TLDR
It is demonstrated that problem classes and regions of the phase transition previously thought to be easy can sometimes be orders of magnitude more difficult than the worst problems in problem classesand regions ofThe phase transition considered hard.
The exact satisfiability threshold for a potentially intractable random constraint satisfaction problem
TLDR
The exact threshold of satisfiability for random instances of a particular NP-hard constraint satisfaction problem is determined, and the analogue of the (2+p)-SAT conjecture is proved for a class of problems that includes this problem and XOR-SAT.
Redundancy in Random SAT Formulas
TLDR
It is shown that small size formulas have at least a characteristic that makes them relatively easier than the larger ones (beyond the increase in the size of the formulas), which is the redundancy.
An Algorithm for SAT Above the Threshold
TLDR
Positive algorithmic results are obtained, showing that highly constrained formulas restricted to satisfiable instances can be solved in low exponential time.
A Model for Generating Random Quantified Boolean Formulas
TLDR
This work defines and study a general model for generating random QBF instances, and exhibits experimental results showing that the model bears certain desirable similarities to the random SAT model, as well as a number of theoretical results concerning the model.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 33 REFERENCES
Probabilistic analysis of the Davis Putnam procedure for solving the satisfiability problem
TLDR
A ‘reasonable’ family of instance distributions F is presented and it is shown that for each distribution in F a variant of the Davis Putnam Procedure without the pure literal rule requires exponential time with probability 1.
A New Method for Solving Hard Satisfiability Problems
TLDR
A greedy local search procedure called GSAT is introduced for solving propositional satisfiability problems and its good performance suggests that it may be advantageous to reformulate reasoning tasks that have traditionally been viewed as theorem-proving problems as model-finding tasks.
Algorithms for Testing the Satisfiability of Propositional Formulae
TLDR
This work shows by means of a set of experiments that the efficiency of DG is not only theoretical but practical as well, and proposes two relaxation schemes which map instances of SAT into instances of HORN-SAT, which are used to derive two new enumerative algorithms for SAT : HORN 1 and HORN 2.
Where the Really Hard Problems Are
TLDR
It is shown that NP-complete problems can be summarized by at least one "order parameter", and that the hard problems occur at a critical value of such a parameter.
Probabilistic performance of a heuristic for the satisfiability problem
TLDR
The combined algorithm is effective in some limited sense in verifying unsatisfiability on instances of SAT that have solutions and the algorithm dynamically assigns values to literals appearing in a given instance until a satisfying assignment is found.
A Rearrangement Search Strategy for Determining Propositional Satisfiability
TLDR
Experimental data shows that for one easily computed upper bound the reduction in the size of the search space more than compensates for the overhead involved in selecting the next variable.
Resolution vs. cutting plane solution of inference problems: Some computational experience
Resolvents in the propositional calculus correspond to certain cutting planes in integer programming models of inference problems. We compare the performance of a rudimentary cutting plane algorithm
The Intractability of Resolution
  • Armin Haken
  • Computer Science, Mathematics
    Theor. Comput. Sci.
  • 1985
Abstract We prove that, for infinitely many disjunctive normal form propositional calculus tautologies ξ, the length of the shortest resolution proof of ξ cannot be bounded by any polynomial of the
Probabilistic analysis of a generalization of the unit-clause literal selection heuristics for the k satisfiability problem
TLDR
Two algorithms for the k-satisfiability problem are presented and a probabilistic analysis is performed and it is shown that the first algorithm finds a solution with probability approaching one for a wide range of parameter values.
Probabilistic Analysis of Algorithms for NP-Complete Problems.
Abstract : The goal of this research is to develop and analyze algorithms which can, in some practical sense, solve certain NP-complete problems efficiently. By solve we mean determine whether a
...
1
2
3
4
...