9598402
Time-space tradeoffs in the counting hierarchy
Extends the lower-bound techniques of L. Fortnow (2000) to the unbounded-error probabilistic model. A key step in the argument is a generalization of V.A. Nepomnjas/spl caron/c/spl caron/ii/spl breve/'s (1970) theorem from the Boolean setting to the arithmetic setting. This generalization is made possible due to the recent discovery of logspace-uniform TC/sup 0/ circuits for iterated multiplication (A. Chiu et al., 2000). As an example of the sort of lower bounds that we obtain, we show that MAJ-MAJSAT is not contained in PrTiSp(n/sup 1+o(1)/, n/sup /spl epsiv//) for any /spl epsiv/<1. We also extend one of Fortnow's lower bounds, from showing that S~A~T~ does not have uniform NC/sup 1/ circuits of size n/sup 1+o(1)/, to a similar result for SAC/sup 1/ circuits.
14665111
Oblivious Symmetric Alternation
We introduce a new class $\rm {O}^p_2$ as a subclass of the symmetric alternation class $\rm {S}^p_2$. An $\rm {O}^p_2$ proof system has the flavor of an $\rm {S}^p_2$ proof system, but it is more restrictive in nature. In an $\rm {S}^p_2$ proof system, we have two competing provers and a verifier such that for any input, the honest prover has an irrefutable certificate. In an $\rm {O}^p_2$ proof system, we require that the irrefutable certificates depend only on the length of the input, not on the input itself. In other words, the irrefutable proofs are oblivious of the input. For this reason, we call the new class oblivious symmetric alternation. While this might seem slightly contrived, it turns out that this class helps us improve some existing results. For instance, we show that if NP⊂P/poly then $\rm PH = {O}^p_2$, whereas the best known collapse under the same hypothesis was $\rm PH = {S}^p_2$. 
 
We also define classes $\rm Y{O}^p_2$ and $\rm N{O}^p_2$, bearing relations to $\rm {O}^p_2$ as NP and coNP are to P, and show that these along with $\rm {O}^p_2$ form a hierarchy, similar to the polynomial hierarchy. We investigate other inclusions involving these classes and strengthen some known results. For example, we show that $\rm MA \subseteq N{O}^p_2$ which sharpens the known result $\rm MA \subseteq {S}^p_2$ [16]. Another example is our result that $\rm AM \subseteq O_2 \cdot NP \subseteq {\prod}^p_2$, which is an improved upper bound on AM. Finally, we also prove better collapses for the 2-queries problem as discussed by [12,1,7]. We prove that $\rm P^{NP[1]} = P^{NP[2]} \Longrightarrow PH = {NO}^p_2 \cap Y{O}^p_2$.
2670464
Grid graph reachability problems
We study the complexity of reachability problems on various classes of grid graphs. Reachability on certain classes of grid graphs gives natural examples of problems that are hard for NC1 under AC0 reductions but are not known to be hard far L; they thus give insight into the structure of L. In addition to explicating the structure of L, another of our goals is to expand the class of digraphs for which connectivity can be solved in logspace, by building on the work of Jakoby et al. (2001), who showed that reachability in series-parallel digraphs is solvable in L. We show that reachability for single-source multiple sink planar dags is solvable in L
7441506
Derandomization and distinguishing complexity
We continue an investigation of resource-bounded Kolmogorov complexity and derandomization techniques begun in [E. Allender (2001), E. Allender et al., (2002)]. We introduce nondeterministic time-bounded Kolmogorov complexity measures (KNt and KNT) and examine the properties of these measures using constructions of hitting set generators for nondeterministic circuits [P. B. Miltersen et al., (1999), R. Shaltiel et al., (2001)]. We observe that KNt bears many similarities to the nondeterministic distinguishing complexity CND of [H. Buhrman et al., (2002)]. This motivates the definition of a new notion of time-bounded distinguishing complexity KDt, as an intermediate notion with connections to the class FewEXP. The set of KDt-random strings is complete for EXP under P/poly reductions. Most of the notions of resource-bounded Kolmogorov complexity discussed here and in [E. Allender (2001), E. Allender et al., (2002)] have close connections to circuit size (on different types of circuits). We extend this framework to define notions of Kolmogorov complexity KB and KF that are related to branching program size and formula size, respectively. The sets of KB- and KF-random strings lie in coNP; we show that oracle access to these sets enables one to factor Blum integers. We obtain related intractability results for approximating minimum formula size, branching program size, and circuit size. The NEXP/spl sube/NC and NEXP/spl sube/L/poly questions are shown to be equivalent to conditions about the KF and KB complexity of sets in P.
411400
Parity Problems in Planar Graphs
We consider the problem of counting the number of spanning trees in planar graphs. We prove tight bounds on the complexity of the problem, both in general and especially in the modular setting. We exhibit the problem to be complete for Logspace when the modulus is 2k, for constant k. On the other hand, we show that for any other modulus and in the non-modular case, our problem is as hard in the planar case as for the case of arbitrary graphs. This completely settles the question regarding the complexity of modular computation of the number of spanning trees in planar graphs. The techniques used rely heavily on algebraic-topology. In the spirit of counting problems modulo 2k, we also exhibit a highly parallel oplusL algorithm for finding the value of a Permanent modulo 2k. Previously, the best known result in this direction was Valiant's result that this problem lies in P.
14932066
On line predictive appearance-based tracking
We present a novel predictive statistical framework to improve the performance of an eigentracker. In addition, we use fast and efficient eigenspace updates to learn new views of the object being tracked on the fly. We also incorporate a new importance sampling mechanism which increases the robustness of the eigentracker and enables it to track nonconvex objects better. Our eigentracker is flexible-it is possible to use it symbolically with other trackers. We show its successful application in hand gesture analysis; and face and person tracking.
6539802
Robot localization using uncalibrated camera invariants
We describe a set of image measurements which are invariant to the camera internals but are location variant. We show that using these measurements it is possible to calculate the self-localization of a robot using known landmarks and uncalibrated cameras. We also show that it is possible to compute, using uncalibrated cameras, the Euclidean structure of 3-D world points using multiple views from known positions. We are free to alter the internal parameters of the camera during these operations. Our initial experiments demonstrate the applicability of the method.
8456161
Negation as Failure as Resolution
Providing a clean procedural semantics of the “Negation As Failure rule” in Logic Programming has been an open problem for some time now. This rule has been treated as a technique in nonmonotonic reasoning, not as a rule in classical logic. This paper contains a demonstration of the negation as failure rule as a resolution procedure in first-order logic. We present a sound and complete resolution scheme for negation as failure rule for the larger class of constraint logic programs. The approach is to consider a canonical partition of the completion of a definite (constraint) program into the IF and the FI programs. We show that a negated goal, provable from the completed definite program is provable from just the FI part. The clauses in this program have a structure dual to that of definite Horn clauses. We describe a sound and complete linear resolution rule for this fragment, and show that a resolution proof of the negated goal from the FI part corresponds to a finite failure tree resulting from classical linear resolution applied to the goal on the If part of the original definite program. Our work shows that negation as failure rule can be computationally efficient in the sense that the SLD-resolution on the If part of a definite program along with the negation as failure rule is more efficient than a direct resolution procedure on the completion of that program.
18611387
Robust Fingerprint Classification Using An Eigen Block Directional Approach
This paper describes a method of fingerprint classification using Eigen Block Directional Fingerprints. The method we propose dispenses off with the preprocessing stages such as segmentation, binarisation, thinning etc. We determine the block directional representation of a fingerprint and the location of the core points in a set of template fingerprints which belong to the same class. In the next step, we determine the most prominent eigen vectors of each template, which we term as the Eigen Block Directional Fingerprints. To determine the classification of a fingerprint, we extract the Block Directional Fingerprint of the query image and determine the alignment parameters between the template and the query images using eigen tracker which minimises the robust error. We declare the class of the query image as the class of the Eigen Block Directional Fingerprint which result in the least robust error norm.
27759262
Automatic categorization of web sites based on source types
An important issue with the Web is verification of the accuracy, currency and authenticity of the information associated with Web sites. One way to address this problem is to identify the "source" or "sponsor" of the Web site. However, source identification is non-trivial because the source of a Web site cannot always be determined by the URL or content of the site. In this paper, we propose a method for source identification that uses various types of inbound, outbound and internal interactions that arise due to hyperlinks between and within Web sites.