13939244
A polynomial time computable metric between point sets
Abstract. Measuring the similarity or distance between sets of points in a metric space is an important problem in machine learning and has also applications in other disciplines e.g. in computational geometry, philosophy of science, methods for updating or changing theories, 
$\ldots$. Recently Eiter and Mannila have proposed a new measure which is computable in polynomial time. However, it is not a distance function in the mathematical sense because it does not satisfy the trian gle inequality. We introduce a new measure which is a metric while being computable in polynomial time. We also present a variant which computes a normalised metric and a variant which can associate different weights with the points in the set.
2884276
Towards Friendly Concept-Learners
We give a general overview of CUNT, a userfriendly interactive concept-learner, which can be used as a module for Learning Apprentice Systems. CLINT combines several interesting features: it uses domain-knowledge, generates examples, copes with indirect relevance, shifts its bias, recovers from errors and identifies concepts in the limit.
44771927
On Interactive Concept-Learning and Assimilation
11842903
Iterative Versionspaces
1487291
Acquiring object-knowledge
Abstract 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.
9701379
Constructive Induction by Analogy
ABSTRACT Concept-learners can be viewed as problem-solvers : they receive as input a set of examples and produce as output a consistent concept-description. In this paradigm, we derive from each solved concept-learning problem a second-order schema, and apply it in analoguous concept-learning situations in order to learn and/or invent new concepts. In this way, a change of representation is achieved and the learning process itself is learned.
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).