The following techniques for word-level networks are presented: constraints solving, case-based learning and bit-slice solving. Generation of a word-level network to model a constraints problem is presented. The networks utilized have assigned, to each node, a range of permissible values.Constraints are solved using an implication process that explores the deductive consequences of the assigned range values.The implication process may include the following techniques: forward or backward implication and case-based learning. Case-based learning includes recursive or global learning.As part of a constraint-solving process, a random variable is limited to a single value. The limitation may be performed by iterative relaxation. An implication process is then performed. If a conflict results, the value causing the conflict is removed from the random variable by range splitting, and backtracking is performed by assigning another value to the random variable.A procedure is provided for efficiently solving bit-slice operators.