39256502
Bifinite Chu Spaces
This paper studies colimits of sequences of finite Chu spaces and their ramifications. We consider three base categories of Chu spaces: the generic Chu spaces (C), the extensional Chu spaces (E), and the biextensional Chu spaces (B). The main results are: (1) a characterization of monics in each of the three categories; (2) existence (or the lack thereof) of colimits and a characterization of finite objects in each of the corresponding categories using monomorphisms/injections (denoted as iC, iE, and iB, respectively); (3) a formulation of bifinite Chu spaces with respect to iC; (4) the existence of universal, homogeneous Chu spaces in this category. Unanticipated results driving this development include the fact that: (a) in C, a morphism (f, g) is monic iff f is injective and g is surjective while for E and B, (f, g) is monic iff f is injective (but g is not necessarily surjective); (b) while colimits always exist in iE, it is not the case for iC and iB; (c) not all finite Chu spaces (considered set-theoretically) are finite objects in their categories. This study opens up opportunities for further investigations into recursively defined Chu spaces, as well as constructive models of linear logic.
12232435
Rational Transformations of Formal Power Series
Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve rationality, generalizing the recent results of Zhang [15] to the formal power series setting. We show, for example, that the "square-root" operation, while preserving regularity for formal languages, preserves rationality for formal power series when the underlying semiring is commutative or locally finite, but not in general.
10438151
Complexity of power default reasoning
This paper derives a new and surprisingly low complexity result for inference in a new form of Reiter's propositional default logic (1980). The problem studied here is the default inference problem whose fundamental importance was pointed out by Kraus, Lehmann, and Magidor (1980). We prove that "normal" default inference, in propositional logic, is a problem complete for co-NP(3), the third level of the Boolean hierarchy. Our result (by changing the underlying semantics) contrasts favorably with a similar result of Gottlob (1992), who proves that standard default inference is II/sub 2//sup P/-complete. Our inference relation also obeys all of the laws for preferential consequence relations set forth by Kraus, Lehmann, and Magidor (1990). In particular we get the property of being able to reason by cases and the law of cautious monotony. Both of these laws fail for standard propositional default logic. The key technique for our results is the use of Scott's domain theory to integrate defaults into partial model theory of the logic, instead of keeping defaults as quasiproof rules in the syntax. In particular, reasoning disjunctively entails using the Smyth powerdomain.
14387948
Axiomatic Aspects of Default Inference
This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called a default structure. We study axioms for the nonmonotonic consequence relation derived from extensions as in Reiter's default logic, using skeptical reasoning, but extensions are now used for the construction of possible worlds in a default information structure. 
In previous work we showed that skeptical reasoning arising from default-extensions obeys a well-behaved set of axioms including the axiom of cautious cut. We show here that, remarkably, the converse is also true: any consequence relation obeying this set of axioms can be represented as one constructed from skeptical reasoning. We provide representation theorems to relate axioms for nonmonotonic consequence relation and properties about extensions, and provide one-to-one correspondence between nonmonotonic systems which satisfies the law of cautious monotony and default structures with unique extensions. Our results give a theoretical justification for a set of basic rules governing the update of nonmonotonic knowledge bases, demonstrating the derivation of them from the more concrete and primitive construction of extensions. It is also striking to note that proofs of the representation theorems show that only shallow extensions are necessary, in the sense that the number of iterations needed to achieve an extension is at most three. All of these developments are made possible by taking a more liberal view of consistency: consistency is a user defined predicate, satisfying some basic properties.
14595938
Clausal Logic and Logic Programming in Algebraic Domains
We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixed-point semantics for disjunctive logic programs, and prove their equivalence; finally, we apply our results to give both a syntax and semantics for default logic in any coherent algebraic dcpo. 2001 Elsevier Science
717123
Experimenting with Power Default Reasoning
In this paper we explore the computational aspects of Propositional Power Default Reasoning (PDR), a form of non-monotonic reasoning in which the underlying logic is Kleene's 3-valued propositional logic. PDR leads to a concise meaning of the problem of skeptical entailment which has better complexity characteristics than the usual formalisms (co-NP(3)-Complete instead of ?2P-Complete). We take advantage of this in an implementation called powdef to encode and solve hard graph problems and explore randomly generated instances of skeptical entailment.
7914535
Stereoscopic Video Synthesis from a Monocular Video
This paper presents an automatic and robust approach to synthesize stereoscopic videos from ordinary monocular videos acquired by commodity video cameras. Instead of recovering the depth map, the proposed method synthesizes the binocular parallax in stereoscopic video directly from the motion parallax in monocular video, The synthesis is formulated as an optimization problem via introducing a cost function of the stereoscopic effects, the similarity, and the smoothness constraints. The optimization selects the most suitable frames in the input video for generating the stereoscopic video frames. With the optimized selection, convincing and smooth stereoscopic video can be synthesized even by simple constant-depth warping. No user interaction is required. We demonstrate the visually plausible results obtained given the input clips acquired by ordinary handheld video camera.
38503566
Pseudo-one-factorizations of regular graphs of odd order - II. products of graphs
Abstract We study the pseudo-one-factorization of regular graphs of odd order. It is shown that some classes of products (including composition and cartesian product) of graphs are pseudo-one- factorizable. In particular, we prove that a complete regular t -partite graph of odd order has this property.
2928763
GeoGrid: A Scalable Location Service Network
This paper presents GeoGrid, a geographical location service overlay network system, for providing scalable location-based services to a large and growing number of mobile users. GeoGrid is designed as a decentralized and geographical location aware overlay network and provides system-level facilities and optimizations for balancing load in the presence of node heterogeneity, dynamically moving hot-spots (location queries), and unpredictable rate of node join, departure and failure. GeoGrid uses geographical mapping of nodes to regions and geographical proximity based routing to take advantage of the similarity between physical and network proximity. Furthermore, GeoGrid exploits multiple opportunities for dynamic workload adaptation in the presence of static hotspot queries and moving hotspot queries. Its dynamic load balancing algorithms can efficiently utilize the heterogeneous capacities of end systems and balance both the location query workload and the routing workload. Our initial prototype development and experimental study demonstrate that GeoGrid can effectively reduce the workload imbalance by an order of magnitude.
30701744
Single change covering designs
A single-change covering designSC (v, k, b) on av-setV is a sequence ofb k-sets (blocks) onV which together cover every pair of elements ofV at least once, such that two successive blocks havek−1 elements in common. It is desirable to minimizeb. Some constructions and lower bounds forb are given.
36095353
Extremal Regular Graphs with Prescribed Odd Girth
The odd girth of a graph G gives the length of a shortest odd cycle in G. Let ?(k, g) denote the smallest n such that there exists a k-regular graph of order n and odd girth g. It is known that ?(k, g) ? kg/2 and that ?(k, g) = kg/2 if k is even. The exact values of ?(k, g) are also known if k = 3 or g = 5. Let ?x?e denote the smallest even integer no less than x, ?(g) = (?1)g ? 1/2, and s(k) = min {p + q | k = pq, where p and q are both positive integers}. It is proved that if k ? 5 and g ? 7 are both odd, then formula] with the exception that ?(5, 7) = 20.