@phdthesis{Ghasemzadeh2005,
  author    = {Ghasemzadeh, Mohammad},
  title     = {A new algorithm for the quantified satisfiability problem, based on zero-suppressed binary decision diagrams and memoization},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-6378},
  school      = {Universit{\"a}t Potsdam},
  year      = {2005},
  abstract  = {Quantified Boolean formulas (QBFs) play an important role in theoretical computer science. QBF extends propositional logic in such a way that many advanced forms of reasoning can be easily formulated and evaluated. In this dissertation we present our ZQSAT, which is an algorithm for evaluating quantified Boolean formulas. ZQSAT is based on ZBDD: Zero-Suppressed Binary Decision Diagram , which is a variant of BDD, and an adopted version of the DPLL algorithm. It has been implemented in C using the CUDD: Colorado University Decision Diagram package. The capability of ZBDDs in storing sets of subsets efficiently enabled us to store the clauses of a QBF very compactly and let us to embed the notion of memoization to the DPLL algorithm. These points led us to implement the search algorithm in such a way that we could store and reuse the results of all previously solved subformulas with a little overheads. ZQSAT can solve some sets of standard QBF benchmark problems (known to be hard for DPLL based algorithms) faster than the best existing solvers. In addition to prenex-CNF, ZQSAT accepts prenex-NNF formulas. We show and prove how this capability can be exponentially beneficial.},
  subject      = {Bin{\"a}res Entscheidungsdiagramm},
  language  = {en}
}
@article{DoerrNeumannSutton2016,
  author    = {Doerr, Benjamin and Neumann, Frank and Sutton, Andrew M.},
  title     = {Time Complexity Analysis of Evolutionary Algorithms on Random Satisfiable k-CNF Formulas},
  series = {Algorithmica : an international journal in computer science},
  volume    = {78},
  journal   = {Algorithmica : an international journal in computer science},
  publisher = {Springer},
  address   = {New York},
  issn      = {0178-4617},
  doi       = {10.1007/s00453-016-0190-3},
  pages     = {561 -- 586},
  year      = {2016},
  abstract  = {We contribute to the theoretical understanding of randomized search heuristics by investigating their optimization behavior on satisfiable random k-satisfiability instances both in the planted solution model and the uniform model conditional on satisfiability. Denoting the number of variables by n, our main technical result is that the simple () evolutionary algorithm with high probability finds a satisfying assignment in time when the clause-variable density is at least logarithmic. For low density instances, evolutionary algorithms seem to be less effective, and all we can show is a subexponential upper bound on the runtime for densities below . We complement these mathematical results with numerical experiments on a broader density spectrum. They indicate that, indeed, the () EA is less efficient on lower densities. Our experiments also suggest that the implicit constants hidden in our main runtime guarantee are low. Our main result extends and considerably improves the result obtained by Sutton and Neumann (Lect Notes Comput Sci 8672:942-951, 2014) in terms of runtime, minimum density, and clause length. These improvements are made possible by establishing a close fitness-distance correlation in certain parts of the search space. This approach might be of independent interest and could be useful for other average-case analyses of randomized search heuristics. While the notion of a fitness-distance correlation has been around for a long time, to the best of our knowledge, this is the first time that fitness-distance correlation is explicitly used to rigorously prove a performance statement for an evolutionary algorithm.},
  language  = {en}
}