Generating logical expressions from positive and negative examples via a branch-and-bound approach

17] E. Morreale. Recursive operators for prime implicant and irredundant normal form determination. A calculus and an algorithm for the multiple-output 2-level minimization problem. A new method for solving large Satissability problems. A new algorithm for generating prime implicants. 7] J.F. Gimpel. A method of producing a boolean function having an arbitrarily prescribed prime implicant table. experience with an interior point algorithm on the Satissability problem. 11] N. Karmarkar. Riemannian geometry underlying interior-point methods for linear programming. interior point algorithm to solve computationally diicult set covering problems. An interior-point approach to the maximum independent set problem in dense random graphs. Inductive inference is an essential ingredient in systems that exhibit truly intelligent behavior. Since intelligent answers to questions are often ranked by their simplicity, optimization plays an important role in eeective inductive inference systems. In this paper, we applied a method of continuous function minimization to implement an inductive inference system. This approach is based on an integer programming formulation for Boolean function synthesis. The introduction of on-line cuts, described in Section 3, enabled our implementation to solve a larger number of problems than our previous implementation, used in 9]. The preliminary computational results presented in this study indicate the feasibility of this approach to inductive inference. In forthcoming papers, we will use similar methods to approach other inference problems. These include: Multiple output Boolean model. This model is similar to the single output Boolean model, except that the hidden function is of the form F : f0; 1g n ! f0; 1g m , i.e. it has m outputs. Boolean model with correlated variables. This model has no input or output variables. Instead, one is given generic Boolean variables and examples of variable values, with the objective of inferring a relationship between the variables. Threshold gate model. Given a black box with a xed network of threshold gates (in place of Boolean gates) and a partial list of input-output examples, the problem is to infer the weights so that the input-output sample is duplicated by the inferred network. Continuous inputs. All of the above models can be formulated with continuous inputs in place of Boolean inputs. Finite state machine model. A nite state machine is deened by an input alphabet , a state set S, a start state s 0 2 S, a transition function f t and a set of accept states A S. Let L be the …