Journal of Automated Reasoning

, Volume 44, Issue 4, pp 401-424

First online:

Deciding Effectively Propositional Logic Using DPLL and Substitution Sets

  • Ruzica PiskacAffiliated withMicrosoft Research
  • , Leonardo de MouraAffiliated withMicrosoft Research
  • , Nikolaj BjørnerAffiliated withMicrosoft Research Email author 

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We introduce a DPLL calculus that is a decision procedure for the Bernays-Schönfinkel class, also known as EPR. Our calculus allows combining techniques for efficient propositional search with data-structures, such as Binary Decision Diagrams, that can efficiently and succinctly encode finite sets of substitutions and operations on these. In the calculus, clauses comprise of a sequence of literals together with a finite set of substitutions; truth assignments are also represented using substitution sets. The calculus works directly at the level of sets, and admits performing simultaneous constraint propagation and decisions, resulting in potentially exponential speedups over existing approaches.


DPLL SAT BDDs Effectively propositional logic