3204350
A New Approach to Formal Language Theory by Kolmogorov Complexity
We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate deterministic context-free languages and nondeterministic context-free languages. The use of the new "incompressibility arguments" is illustrated by many examples. The approach is also successful at the high end of the Chomsky hierarchy since one can quantify nonrecursiveness in terms of Kolmogorov complexity.
9397376
Inferring a DNA Sequence from Erroneous Copies
Abstract We suggest a novel approach for efficiently reconstructing an original DNA sequence from erroneous copies.
871253
Kolmogorov Complexity Arguments in Combinatorics
Abstract The utility of a Kolmogorov complexity method in combinatorial theory is demonstrated by several examples.
43310555
Twist-Rotation Transformations of Binary Trees and Arithmetic Expressions
The paper studies the computational complexity and efficient algorithms for the twist?rotation transformations of binary trees, which is equivalent to the transformation of arithmetic expressions over an associative and commutative binary operation. The main results are (1) a full binary tree with n labeled leaves can be transformed into any other in at most 3nlogn+2n twist and rotation operations, (2) deciding the twist?rotation distance between two binary trees is NP-complete, and (3) the twist?rotation transformation can be approximated with ratio 6logn+4 in polynomial time for full binary trees with n uniquely labeled leaves.
553776
Linear approximation of shortest superstrings
We consider the following problem: given a collection of strings s1, ••• ,sm, find the shortest string s such that each s; appears as a substring (a consecutive block) of s. Although this problem is known to be NP-hard, a simple greedy procedure appears to do quite well and is routinely used in DNA sequencing and data compression practice, namely: repeatedly merge the pair of (distinct) strings with maximum overlap until only one string remains. Let n denote the A. Blum was supported by a National Science Foundation (NSF) Graduate Fellowship. Part of this work was done while A. Blum was visiting AT & T Bell Labs. T. Jiang was supported in part by a grant from SERB, McMaster University and NSERC Operating Grant OGP0046613. M. Li was supported in part by the NSERC Operating Grants OGP0036747 and OGP0046506. J. Tromp was supported in part by NSERC Grant OGP0036747 while the author was visiting at the University of Waterloo. Authors' present addresses: A. Blum, School of Computer Science, Carnegie-Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213. E-mail: avrim@theory.cs.cmu.edu; T. Jiang, Department of Computer Science, McMaster University, Hamilton, Ont., Canada L8S 4Kl. E-mail: jiang<Q•maccs. mcmaster.ca; M. Li, Department of Computer Science, University of Waterloo, Waterloo, Ont., Canada N3L 30 I. E-mail: mli@watmath.waterloo.edu; J. Tromp, CWI, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands. E-mail: tromp@cwi.nl; M. Yannakakis, Room 2C-319, AT&T Bell Labs, 600 Mountain Avenue, Murray Hill, NJ 07974. E-mail: mihalis@research.att.com. Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. © 1994 ACM 0004-5411/94/0700-0630$03.50 Journal of the Association for Computing Machinery, Vol. 41, No. 4, July 1994, pages 630-647. Linear Approximation of Shortest Superstrings 631 length of the optimal superstring. A common conjecture states that the above greedy procedure produces a superstring of length O(n) (in fact, 2n), yet the only previous nontrivial bound known for any polynomial-time algorithm is a recent O(n log n) result. We show that the greedy algorithm does in fact achieve a constant factor approximation, proving an upper bound of 4n. Furthermore, we present a simple modified version of the greedy algorithm that we show produces a superstring of length at most 3n. We also show the superstring problem to be MAX SNP-hard, which implies that a polynomial-time approximation scheme for this problem is unlikely.
14168735
Inductive Reasoning and Kolmogorov Complexity
Abstract Reasoning to obtain the “truth” about reality, from external data, is an important, controversial, and complicated issue in man's effort to understand nature. (Yet, today, we try to make machines do this.) There have been old useful principles, new exciting models, and intricate theories scattered in vastly different areas including philosophy of science, statistics, computer science, and psychology. We focus on inductive reasoning in correspondence with ideas of R. J. Solomonoff. While his proposals result in perfect procedures, they involve the noncomputable notion of Kolmogorov complexity. In this paper we develop the thesis that Solomonoff's method is fundamental in the sense that many other induction principles can be viewed as particular ways to obtain computable approximations to it. We demonstrate this explicitly in the cases of Gold's paradigm for inductive inference, Rissanen's minimum description length (MDL) principle, Fisher's maximum likelihood principle, and Jaynes' maximum entropy principle. We present several new theorems and derivations to this effect. We also delimit what can be learned and what cannot be learned in terms of Kolmogorov complexity, and we describe an experiment in machine learning of handwritten characters. We also give an application of Kolmogorov complexity in Valiant style learning, where we want to learn a concept probably approximately correct in feasible time and examples.
33110840
A Level Set Approach for Shape Recovery of Open Contours
In this paper, a geometric deformable model for shape recovery of open contours in noisy images is presented. We use two level set functions to model the open contour and find the end points of the open contour as the intersection of the two level set functions. The evolutions of both level set functions do not depend on the gradient of the images, as in the classical geometric deformable models, but are decided by a region-based band velocity. The band velocity is different from region information introduced by other deformable models which can only be used to find the closed contours in images, it is designed for evolutions of both closed and open contours and particularly unique for contours which are open and do not enclose any region. Prior shape information is also integrated into the contour evolution process, which prevents two level set functions from intersecting at other places than at the contour end points. With the described method open contours can be recovered from noisy images. Successful experiments on several data sets are presented in this paper.
12322208
Gemini: Probabilistic Routing Algorithm in Structured P2P Overlay
In this paper, we propose a new structured overlay protocol, which is more efficient and scalable than previous ones. We call it Gemini, because its routing table consists of two parts, one containing nodes with common prefix and the other containing nodes with common suffix. Gemini routes messages to their destinations in just 2 hops, with a very high probability of 0.99. When running in a p2p network of 5,000,000 peers, each Gemini node consumes only 6 messages per second for maintenance. This cost, as well as routing table size, varies as a \(O {\sqrt{N}}\) function to the overlay scale, so Gemini can also run well in an even larger environment.
44742126
A New Association Rules Mining Algorithms Based on Directed Itemsets Graph
In this paper, we introduced a new data structure called DISG (Directed itemsets graph) in which the information of frequent itemsets was stored. Based on it, a new algorithm called DBDG (DFS Based -DISG) was developed by using depth first searching strategy. At last we performed a experiment on a real dataset to test the run time of DBDG. The experiment showd that it was efficient for mining dense datasets.
5412677
Middleware for streaming 3D progressive meshes over lossy networks
Streaming 3D graphics have been widely used in multimedia applications such as online gaming and virtual reality. However, a gap exists between the zero-loss-tolerance of the existing compression schemes and the lossy network transmissions. In this article, we propose a generic 3D middleware between the 3D application layer and the transport layer for the transmission of triangle-based progressively compressed 3D models. Significant features of the proposed middleware include. 1) handling 3D compressed data streams from multiple progressive compression techniques. 2) considering end user hardware capabilities for effectively saving the data size for network delivery. 3) a minimum cost dynamic reliable set selector to choose the transport protocol for each sublayer based on the real-time network traffic. Extensive simulations with TCP/UDP and SCTP show that the proposed 3D middleware can achieve the dual objectives of maintaining low transmission delay and small distortion, and thus supporting high quality 3D streaming with high flexibility.
14678918
End-to-end QoS framework for heterogeneous wired-cum-wireless networks
With information access becoming more and more ubiquitous, there is a need for providing QoS support for communication that spans wired and wireless networks. For the wired side, RSVP/SBM has been widely accepted as a flow reservation scheme in IEEE 802 style LANs. Thus, it would be desirable to investigate the integration of RSVP and a flow reservation scheme in wireless LANs, as an end-to-end solution for QoS guarantee in wired-cum-wireless networks. For this purpose, we propose WRESV, a lightweight RSVP-like flow reservation and admission control scheme for IEEE 802.11 wireless LANs. Using WRESV, wired/wireless integration can be easily implemented by cross-layer interaction at the Access Point. Main components of the integration are RSVP-WRESV parameter mapping and the initiation of new reservation messages, depending on where senders/receivers are located. In addition, to support smooth roaming of mobile users among different basic service sets (BSS), we devise an efficient handoff scheme that considers both the flow rate demand and network resource availability for continuous QoS support. Furthermore, various optimizations for supporting multicast session and QoS re-negotiation are proposed for better performance improvement. Extensive simulation results show that the proposed scheme is promising in enriching the QoS support of multimedia applications in heterogeneous wired-cum-wireless networks.