1020303
Experiences with Enumeration of Integer Projections of Parametric Polytopes
Many compiler optimization techniques depend on the ability to calculate the number of integer values that satisfy a given set of linear constraints. This count (the enumerator of a parametric polytope) is a function of the symbolic parameters that may appear in the constraints. In an extended problem (the “integer projection” of a parametric polytope), some of the variables that appear in the constraints may be existentially quantified and then the enumerated set corresponds to the projection of the integer points in a parametric polytope. 
 
This paper shows how to reduce the enumeration of the integer projection of parametric polytopes to the enumeration of parametric polytopes. Two approaches are described and experimentally compared. Both can solve problems that were considered very difficult to solve analytically.
7279598
Analytical computation of Ehrhart polynomials: enabling more compiler analyses and optimizations
Many optimization techniques, including several targeted specifically at embedded systems, depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes. It is well known that this parametric count can be represented by a set of Ehrhart polynomials. Previously, interpolation was used to obtain these polynomials, but this technique has several disadvantages. Its worst-case computation time for a single Ehrhart polynomial is exponential in the input size, even for fixed dimensions. The worst-case size of such an Ehrhart polynomial (measured in bits needed to represent the polynomial) is also exponential in the input size. Under certain conditions this technique even fails to produce a solution.Our main contribution is a novel method for calculating Ehrhart polynomials analytically. It extends an existing method, based on Barvinok's decomposition, for counting the number of integer points in a non-parametric polytope. Our technique always produces a solution and computes polynomially-sized Ehrhart polynomials in polynomial time (for fixed dimensions).
12907113
Declarative bias for specific-to-general ILP systems
A comparative study is presented of language biases employed in specific-to-general learning systems within the Inductive Logic Programming (ILP) paradigm. More specifically, we focus on the biases employed in three well known systems: CLINT, GOLEM and ITOU, and evaluate both conceptually and empirically their strengths and weaknesses. The evaluation is carried out within the generic framework of the NINA system, in which bias is a parameter. Two different types of biases are considered: syntactic bias, which defines the set of well-formed clauses, and semantic bias, which imposes restrictions on the behaviour of hypotheses or clauses. NINA is also able to shift its bias (within a predefined series of biases), whenever its current bias is insufficient for finding complete and consistent concept definitions. Furthermore, a new formalism for specifying the syntactic bias of inductive logic programming systems is introduced.
18510804
Acquiring Object-Knowledge for Learning Systems
A novel approach to interactively acquire knowledge about new objects in a logic environment is presented. When the user supplies an unknown fact containing unknown objects (constants), the system will ask interesting membership and existential queries about the objects. The answers to these questions allow the system to update its knowledge base. Two basic strategies are implemented: one that examines existing Horn-Clauses for the predicate and another one that uses types. Furthermore, a powerful heuristic, based on analogy, to pose the most interesting questions first is presented.