### Citations

2873 |
The Design and Analysis of Computer Algori thms
- Hopcroft
- 1966
(Show Context)
Citation Context ...perties, including planarity for graphs of bounded valence, are in the symmetric logspace hierarchy. It follows that they are also in BPL. Reif also showed that BPL is contained in O[log n] timeandn O=-=[1]-=- processors on a probabilistic hardware modi cation machine (HMM). 3sa c A Figure 1: An alternating graph with two universal nodes: a� c. Theorem 1.5 (Re84) . Sym-L BPL Prob-HMM-TIME[log n],PROC[n O[1... |

744 | A Mathematical Introduction to Logic - Enderton - 1972 |

578 | The complexity of relational query languages - Vardi - 1982 |

317 | The polynomial-time hierarchy - Stockmeyer - 1976 |

315 | Relational queries computable in polynomial time - Immerman - 1986 |

313 | Generalized first-order spectra and polynomialtime recognizable sets - Fagin - 1974 |

263 | Structure and complexity of relational queries - Chandra, Harel - 1982 |

226 | Universality of data retrieval languages, in - Aho, Ullman - 1979 |

131 | Alternation - Chandra, Kozen, et al. - 1981 |

74 | Borel sets and circuit complexity - Sipser - 1983 |

65 | The Monotone and Planar Circuit Value Problems are Log Space Complete for P - Goldschlager - 1977 |

57 | A complexity theory based on Boolean algebra - Skyum, Valiant - 1981 |

56 | Languages which capture complexity classes
- Immerman
- 1987
(Show Context)
Citation Context ...ence using the xed point operator which cannot be expressed with a single application of transitive closure. SIAM J. of Computing 16:4 (1987), 760-778. A preliminary version of this paper appeared as =-=[17]-=-. y Research supported by an NSF postdoctoral fellowship. Current address: Computer Science Dept., UMass, Amherst, MA 01003. 1sIn previous work [Im81], [Im82b], we showed that the complexity of a prop... |

41 | Upper and lower bounds for first order expressibility - Immerman - 1982 |

38 | Complexity classes and theories of finite models - Lynch - 1982 |

30 | Symmetric complementation - Reif - 1982 |

23 | Maze recognizing automata and nondeterministic tape complexity - Savitch - 1973 |

14 | and Uzi Vishkin. Simulation of parallel random access machines by circuits - Stockmeyer - 1984 |

11 | P 1 1 -formulae on finite structures", Annals of Pure and Applied logic 24 - Ajtai - 1983 |

11 | The spectra of first-order sentences and computational complexity - Grandjean - 1984 |

10 | of Quanti ers is Better than Number of Tape Cells - Immerman, \Number - 1981 |

9 | Uzi Vishkin. Constant depth reducibility - Chandra, Stockmeyer - 1984 |

8 | Reducibility by algebraic projections," L'Enseignement math'ematique 28 - Valiant - 1982 |

6 | S.: One-Way Log Tape Reductions - Hartmanis, Immerman, et al. - 1978 |

2 | Symmetric Space Bounded Computation," Theoret - Lewis, Papadimitriou - 1982 |

2 | Some Remarks on Generalized Spectra," Zeitchr. f. math, Logik und Grundlagen d - Lov'asz, G'acs - 1977 |

1 | On the De nability of Properties of Finite Graphs - Turan |

1 | Yao,\Separating the Polynomial-Time Hierarchy byOracles - Chi-Chih - 1985 |