Solver state merging in parallel constraint satisfaction problem (CSP) solvers. Solver state during processing of a computational thread of parallel CSP solvers is represented as a set of support graphs. The support graphs are merged in a pairwise fashion, yielding a new conflict-free graph. The merge process is free of cycles, conflicts are removed, and thread processing is lock-free. The architecture can be applied, generally, in any CSP solver (e.g., a Boolean SAT solver) having certain formal properties. A system is provided that facilitates solver processing, the system comprising a bookkeeping component for representing input solver state of a computational thread as a set of graphs, and a merge component for pairwise merging of at least two input graphs of the set of graphs into a merged graph that represents final state of the computational thread.