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We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and then apply state of the art techniques to prove termination of the string rewrite system. We present three such transformations, and prove for all of them that they are sound and complete. In this way not only termination of string rewriting of the transformed system implies termination of the original cycle rewrite system, a similar conclusion can be drawn for non-termination. Apart from this transformational approach, we present a uniform framework of matrix interpretations, covering most of the earlier approaches to automatically proving termination of cycle rewriting. All our techniques serve both for proving termination and relative termination. We present several experiments showing the power of our techniques.
Since Mobile Virtual Assistants are rising in popularity and come with most new smartphones out of the box and theoretical work in the field is hard to come by, a test is in order to establish the status quo of development. We did a manual test on six different Mobile Virtual Assistants in the categories Voice Recognition, Online Search, Phone Control and Natural Conversation and the results show that Siri is currently the best Mobile Virtual Assistant on the market with a success rate of 65.8% on average over all four categories.
Paging is one of the prominent problems in the field of on-line algorithms. While in the deterministic setting there exist simple and efficient strongly competitive algorithms, in the randomized setting a tradeoff between competitiveness and memory is still not settled. Bein et al. [4] conjectured that there exist strongly competitive randomized paging algorithms, using o(k) bookmarks, i.e. pages not in cache that the algorithm keeps track of. Also in [4] the first algorithm using O(k) bookmarks (2k more precisely), Equitable2, was introduced, proving in the affirmative a conjecture in [7].
We prove tighter bounds for Equitable2, showing that it requires less than k bookmarks, more precisely ≈ 0.62k. We then give a lower bound for Equitable2 showing that it cannot both be strongly competitive and use o(k) bookmarks. Nonetheless, we show that it can trade competitiveness for space. More precisely, if its competitive ratio is allowed to be (Hk + t), then it requires k/(1 + t) bookmarks.
Our main result proves the conjecture that there exist strongly competitive paging algorithms using o(k) bookmarks. We propose an algorithm, denoted Partition2, which is a variant of the Partition algorithm byMcGeoch and Sleator [13]. While classical Partition is unbounded in its space requirements, Partition2 uses θ(k/ log k) bookmarks. Furthermore, we show that this result is asymptotically tight when the forgiveness steps are deterministic.
For the efficient management of large image databases, the automated characterization of images and the usage of that characterization for searching and ordering tasks is highly desirable. The purpose of the project SEMACODE is to combine the still unsolved problem of content-oriented characterization of images with scale-invariant object recognition and modelbased compression methods. To achieve this goal, existing techniques as well as new concepts related to pattern matching, image encoding, and image compression are examined. The resulting methods are integrated in a common framework with the aid of a content-oriented conception. For the application, an image database at the library of the university of Frankfurt/Main (StUB; about 60000 images), the required operations are developed. The search and query interfaces are defined in close cooperation with the StUB project “Digitized Colonial Picture Library”. This report describes the fundamentals and first results of the image encoding and object recognition algorithms developed within the scope of the project.
The prevention of credit card fraud is an important application for prediction techniques. One major obstacle for using neural network training techniques is the high necessary diagnostic quality: Since only one financial transaction of a thousand is invalid no prediction success less than 99.9% is acceptable. Due to these credit card transaction proportions complete new concepts had to be developed and tested on real credit card data. This paper shows how advanced data mining techniques and neural network algorithm can be combined successfully to obtain a high fraud coverage combined with a low false alarm rate.
We study the approximability of the following NP-complete (in their feasibility recognition forms) number theoretic optimization problems: 1. Given n numbers a1 ; : : : ; an 2 Z, find a minimum gcd set for a1 ; : : : ; an , i.e., a subset S fa1 ; : : : ; ang with minimum cardinality satisfying gcd(S) = gcd(a1 ; : : : ; an ). 2. Given n numbers a1 ; : : : ; an 2 Z, find a 1-minimum gcd multiplier for a1 ; : : : ; an , i.e., a vector x 2 Z n with minimum max 1in jx i j satisfying P n...
In the last years, much effort went into the design of robust anaphor resolution algorithms. Many algorithms are based on antecedent filtering and preference strategies that are manually designed. Along a different line of research, corpus-based approaches have been investigated that employ machine-learning techniques for deriving strategies automatically. Since the knowledge-engineering effort for designing and optimizing the strategies is reduced, the latter approaches are considered particularly attractive. Since, however, the hand-coding of robust antecedent filtering strategies such as syntactic disjoint reference and agreement in person, number, and gender constitutes a once-for-all effort, the question arises whether at all they should be derived automatically. In this paper, it is investigated what might be gained by combining the best of two worlds: designing the universally valid antecedent filtering strategies manually, in a once-for-all fashion, and deriving the (potentially genre-specific) antecedent selection strategies automatically by applying machine-learning techniques. An anaphor resolution system ROSANA-ML, which follows this paradigm, is designed and implemented. Through a series of formal evaluations, it is shown that, while exhibiting additional advantages, ROSANAML reaches a performance level that compares with the performance of its manually designed ancestor ROSANA.
We address to the problem to factor a large composite number by lattice reduction algorithms. Schnorr has shown that under a reasonable number theoretic assumptions this problem can be reduced to a simultaneous diophantine approximation problem. The latter in turn can be solved by finding sufficiently many l_1--short vectors in a suitably defined lattice. Using lattice basis reduction algorithms Schnorr and Euchner applied Schnorrs reduction technique to 40--bit long integers. Their implementation needed several hours to compute a 5% fraction of the solution, i.e., 6 out of 125 congruences which are necessary to factorize the composite. In this report we describe a more efficient implementation using stronger lattice basis reduction techniques incorporating ideas of Schnorr, Hoerner and Ritter. For 60--bit long integers our algorithm yields a complete factorization in less than 3 hours.
Given a real vector alpha =(alpha1 ; : : : ; alpha d ) and a real number E > 0 a good Diophantine approximation to alpha is a number Q such that IIQ alpha mod Zk1 ", where k \Delta k1 denotes the 1-norm kxk1 := max 1id jx i j for x = (x1 ; : : : ; xd ). Lagarias [12] proved the NP-completeness of the corresponding decision problem, i.e., given a vector ff 2 Q d , a rational number " ? 0 and a number N 2 N+ , decide whether there exists a number Q with 1 Q N and kQff mod Zk1 ". We prove that, unless ...
We generalize the concept of block reduction for lattice bases from l2-norm to arbitrary norms. This extends the results of Schnorr. We give algorithms for block reduction and apply the resulting enumeration concept to solve subset sum problems. The deterministic algorithm solves all subset sum problems. For up to 66 weights it needs in average less then two hours on a HP 715/50 under HP-UX 9.05.