### Abstract

A hierarchy of propositional Horn formulas is introduced. The levels σ^{H}_{k} and ∏^{H}_{k} of the hierarchy are defined by way of the number of alternations between players in a certain game related to the satisfiability of Horn formulas. The satisfiability problems for formulas from a given level of the hierarchy are shown to be complete in NSPACE(log n). A certain relationship between the hierarchy and the bounded-depth circuits is exhibited. Using it we show that for some σ^{H}_{k} and ∏^{H}_{k} formulas the equivalent formulas in the lower levels of the hierarchy must be exponentially longer.

Original language | English (US) |
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Pages (from-to) | 113-119 |

Number of pages | 7 |

Journal | Theoretical Computer Science |

Volume | 68 |

Issue number | 1 |

DOIs | |

State | Published - Oct 16 1989 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)