In this paper we study the satisfiability of constant-free quantified
boolean formulas. We consider the following classes of quantified
boolean formulas. Fix a finite set of basic boolean logical functions.
Take conjunctions of these basic functions applied to variables in
arbitrary way. Finally, quantify existentially or universally some of
Schaefer earlier studied the satisfiability of quantified boolean
formulas with constants. He showed that every such problem is either
in P or PSPACE-complete and he gave a complete classification of
the tractable cases. We extend the PSPACE-hardness results
to constant-free quantified boolean formulas obtaining a dichotomy
theorem for the satisfiability of constant-free quantified boolean
formulas. We find that, in fact, constants do not make a
considering the satisfiability of quantified boolean formulas.
We also prove a dichotomy theorem that allows us to improve a previous
result on the learnability of quantified boolean formulas getting rid
of the constants.
CitationDalmau, V. "Some dichotomy theorems on constant-free quantified Boolean formulas". 1997.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder. If you wish to make any use of the work not provided for in the law, please contact: firstname.lastname@example.org