Complexity of the Decidability of One Class of Formulas in Quantifier-Free Set Theory with a Set-Union Operator

M. Tetruashvili

doi:10.1515/GMJ.1996.97

Published by De Gruyter February 23, 2010

Complexity of the Decidability of One Class of Formulas in Quantifier-Free Set Theory with a Set-Union Operator

M. Tetruashvili

From the journal Georgian Mathematical Journal

https://doi.org/10.1515/GMJ.1996.97

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Abstract

We consider the quantifier-free set theory MLSUn containing the symbols U, \, =, ∈, Un. Un(p) is interpreted as the union of all members of the set p. It is proved that there exists an algorithm which for any formula Q of the MLSUn theory containing at most one occurrence of the symbol Un decides whether Q is true or not using the space cn³ log₂n (n is the length of Q).

Key words and phrases.: Complexity of decidability; set theory; set-union operator

Received: 1993-12-23

Published Online: 2010-02-23

Published in Print: 1996-February

Complexity of the Decidability of One Class of Formulas in Quantifier-Free Set Theory with a Set-Union Operator

Abstract

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