27866706
A New Method of Circumscribing Beliefs: The Propositional Case
We propose here a new notion of a minimal model for forming circumscription in belief-logic by incorporating the notion of minimal models in the prepositional logic. This results in a new circumscription operation for belief-formulas than the one considered in [4-6]. An important feature of the new circumscription operation is its close relationship with the circumscription of prepositional formulas. For instance, we have CIRC[Bp] = B(CIRC[p]), where p is a prepositional formula. We give several examples to show that the new notion of circumscription fits quite well with intuition.
27409853
The Strong Semantics for Logic Programs
Recently, the well-founded semantics of a logic program P has been strengthened to the well-founded semantics-by-case (WF C ) and then again to the extended well-founded semantics (WF E ). An important concept used in both WF C and WF E is that of derived rules. We extend the notion of derived rules by adding a new type of derivation and define the strong semantics of P, which has the following important property, known as the GCWA-property: if an atom p = false in all minimal models of P, then p = false in the strong semantics of P. In general, the WF C -semantics and the WF E -semantics do not have the GCWA-property. If we first apply the WF E -semantics to P and then apply the strong semantics to a suitably simplified form of P based on its WF E -semantics, then the resulting semantics is stronger than the WF E -semantics and has the GCWA-property.
14208339
Using Nondeterminism to Design Efficient Deterministic Algorithms
Abstract
In this paper we illustrate how nondeterminism can be used
conveniently and effectively in designing efficient deterministic
algorithms. In particular, our method gives a parameterized
algorithm of running time O((5.7 k)k n) for the 3-D matching
problem, which significantly improves the previous algorithm by
Downey et al. The algorithm can be generalized to
yield an improved algorithm for the r-D matching problem for any
positive integer r. The method can also be employed in designing
deterministic algorithms for other optimization problems as well.


42163647
Nearly optimal one-to-many parallel routing in star networks
Star networks were proposed recently as an attractive alternative to the well-known hypercube models for interconnection networks. Extensive research has been performed that shows that star networks are as versatile as hypercubes. This paper is an effort in the same direction. Based on the well-known paradigms, we study the one-to-many parallel routing problem on star networks and develop an improved routing algorithm that finds n-1 node-disjoint paths between one node and a set of other n-1 nodes in the n-star network. These parallel paths are proven of minimum length within a small additive constant, and our algorithm has an optimal time complexity. This result significantly improves the previous known algorithms for the problem. Moreover, the algorithm well illustrates an application of the orthogonal partition of star networks, which was observed by the original inventors of the star networks but seems generally overlooked in the subsequent study. We should also point out that similar problems are already studied for hypercubes and have proven useful in designing efficient and fault tolerant routing algorithms on hypercube networks.
33317527
Learning Large-Alphabet and Analog Circuits with Value Injection Queries
We consider the problem of learning an acyclic discrete circuit with n wires, fan-in bounded by k and alphabet size s using value injection queries. For the class of transitively reduced circuits, we develop the Distinguishing Paths Algorithm, that learns such a circuit using (ns)O(k) value injection queries and time polynomial in the number of queries. We describe a generalization of the algorithm to the class of circuits with shortcut width bounded by b that uses (ns)O(k+b) value injection queries. Both algorithms use value injection queries that fix only O(kd) wires, where d is the depth of the target circuit. We give a reduction showing that without such restrictions on the topology of the circuit, the learning problem may be computationally intractable when s = nΘ(1), even for circuits of depth O(log n). We then apply our large-alphabet learning algorithms to the problem of approximate learning of analog circuits whose gate functions satisfy a Lipschitz condition. Finally, we consider models in which behavioral equivalence queries are also available, and extend and improve the learning algorithms of [5] to handle general classes of gates functions that are polynomial time learnable from counterexamples.
33085304
An Intuitive and Effective New Representation for Interconnection Network Structures
Based on the classical voltage graph theory, we develop a new representation scheme for interconnection network structures. We show that all popular interconnection networks have very simple and intuitive representations under the new scheme. The new representation scheme offers powerful tools for the study of network routing and network emulation. As examples, we present simple constructions for optimal network emulations from cube-connected cycles networks to butterfly networks, and from butterfly networks to hypercube networks.
1250825
Enhancing Training Set for Face Detection
We present a novel method to enhance training set for face detection with nonlinearly generated examples from the original data. The motivation is from support vector machines (SVM) that, for classification problems, examples lying close to class boundary usually have more influence and thus are more informative than those far from the boundary. We utilize a nonlinear technique - reduced set (RS) method and a new image distance metric to generate new examples, and then add them to the original collected database to enhance it. Extensive experiments show that the proposed approach has an encouraging performance