12 papers
A SAT Attack on Tarski's High School Algebra Problem
Bernardo Subercaseaux, Benjamin Przybocki
Tarski's high school algebra problem asks whether every true identity concerning addition, multiplication, and exponentiation of positive integers follows from a list of 11 element…
Toward Satisfiability Modulo Realizability
Andrew Krapivin, Benjamin Przybocki, Marijn J. H. Heule
Problems complete for the existential theory of the reals () arise throughout discrete geometry. We introduce satisfiability modulo realizability, a SAT-based a…
Bringing closure to theory combination properties
Guilherme V. Toledo, Benjamin Przybocki, Yoni Zohar
We consider the closure of three classical combination properties, namely, stable infiniteness, gentleness and shininess (or, equivalently for decidable theories, strong politeness…
Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery
Benjamin Przybocki, John Mackey, Marijn J. H. Heule +1
Ramsey-good graphs are graphs that contain neither a clique of size nor an independent set of size . We study doubly saturated Ramsey-good graphs, defined as Ramsey-good gra…
Automated Reencoding Meets Graph Theory
Benjamin Przybocki, Bernardo Subercaseaux, Marijn J. H. Heule
Bounded Variable Addition (BVA) is a central preprocessing method in modern state-of-the-art SAT solvers. We provide a graph-theoretic characterization of which 2-CNF encodings can…
Near-Optimal Encodings of Cardinality Constraints
Andrew Krapivin, Benjamin Przybocki, Bernardo Subercaseaux
We present several novel encodings for cardinality constraints, which use fewer clauses than previous encodings and, more importantly, introduce new generally applicable techniques…