A hierarchy of propositional Horn formulas

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A hierarchy of propositional Horn formulas is introduced. The levels σHk and ∏Hk 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 σHk and ∏Hk formulas the equivalent formulas in the lower levels of the hierarchy must be exponentially longer.

Original languageEnglish (US)
Pages (from-to)113-119
Number of pages7
JournalTheoretical Computer Science
Issue number1
StatePublished - Oct 16 1989
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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