OpenRaiser/Intern-Atlas huggingface dataset:
Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification
Venue: arXiv cs.CG 2007
Year: 2007

We present an efficient method for classifying the morphology of the intersection curve of two quadrics (QSIC) in PR3, 3D real projective space; here, the term morphology is used in a broad sense to mean the shape, topological, and algebraic properties of a QSIC, including singularity, reducibility, the number of connected components, and the degree of each irreducible component, etc. There are in total 35 different QSIC morphologies with non-degenerate quadric pencils. For each of these 35 QSIC morphologies, through a detailed study of the eigenvalue curve and the index function jump we establish a characterizing algebraic condition expressed in terms of the Segre characteristics and the signature sequence of a quadric pencil. We show how to compute a signature sequence with rational arithmetic so as to determine the morphology of the intersection curve of any two given quadrics. Two immediate applications of our results are the robust topological classification of QSIC in computing B-rep surface representation in solid modeling and the derivation of algebraic conditions for collision detection of quadric primitives.
Group Secret Key Generation Algorithms
Venue: arXiv cs.IT 2007
Year: 2007

We consider a pair-wise independent network where every pair of terminals in the network observes a common pair-wise source that is independent of all the sources accessible to the other pairs. We propose a method for secret key agreement in such a network that is based on well-established point-to-point techniques and repeated application of the one-time pad. Three specific problems are investigated. 1) Each terminal's observations are correlated only with the observations of a central terminal. All these terminals wish to generate a common secret key. 2) In a pair-wise independent network, two designated terminals wish to generate a secret key with the help of other terminals. 3) All the terminals in a pair-wise independent network wish to generate a common secret key. A separate protocol for each of these problems is proposed. Furthermore, we show that the protocols for the first two problems are optimal and the protocol for the third problem is efficient, in terms of the resulting secret key rates.
Universal Algorithmic Intelligence: A mathematical top->down approach
Venue: arXiv cs.AI 2007
Year: 2007

Sequential decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. Solomonoff's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameter-free theory of universal Artificial Intelligence. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline how the AIXI model can formally solve a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXItl that is still effectively more intelligent than any other time t and length l bounded agent. The computation time of AIXItl is of the order t x 2^l. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other AI approaches.
A novel set of rotationally and translationally invariant features for images based on the non-commutative bispectrum
Venue: arXiv cs.CV 2007
Year: 2007

We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pixel intensities and provide a richer representation of the original image than most existing systems of invariants. Our construction is based on the generalization of the concept of bispectrum to the three-dimensional rotation group SO(3), and a projection of the image onto the sphere.
Time and the Prisoner's Dilemma
Venue: arXiv cs.GT 2007
Year: 2007

This paper examines the integration of computational complexity into game theoretic models. The example focused on is the Prisoner's Dilemma, repeated for a finite length of time. We show that a minimal bound on the players' computational ability is sufficient to enable cooperative behavior. In addition, a variant of the repeated Prisoner's Dilemma game is suggested, in which players have the choice of opting out. This modification enriches the game and suggests dominance of cooperative strategies. Competitive analysis is suggested as a tool for investigating sub-optimal (but computationally tractable) strategies and game theoretic models in general. Using competitive analysis, it is shown that for bounded players, a sub-optimal strategy might be the optimal choice, given resource limitations.
Trusted Ticket Systems and Applications
Venue: arXiv cs.CR 2007
Year: 2007

Trusted Computing is a security base technology that will perhaps be ubiquitous in a few years in personal computers and mobile devices alike. Despite its neutrality with respect to applications, it has raised some privacy concerns. We show that trusted computing can be applied for service access control in a manner protecting users' privacy. We construct a ticket system -- a concept which is at the heart of Identity Management -- relying solely on the capabilities of the trusted platform module and the standards specified by the Trusted Computing Group. Two examples show how it can be used for pseudonymous and protected service access.
Supplement to: Code Spectrum and Reliability Function: Binary Symmetric Channel
Venue: arXiv cs.IT 2007
Year: 2007

A much simpler proof of Theorem 1 from M.Burnashev "Code spectrum and reliability function: Binary symmetric channel" is presented.
Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in<br> SAT-Based Planning
Venue: arXiv cs.AI 2007
Year: 2007

In Verification and in (optimal) AI Planning, a successful method is to formulate the application as boolean satisfiability (SAT), and solve it with state-of-the-art DPLL-based procedures. There is a lack of understanding of why this works so well. Focussing on the Planning context, we identify a form of problem structure concerned with the symmetrical or asymmetrical nature of the cost of achieving the individual planning goals. We quantify this sort of structure with a simple numeric parameter called AsymRatio, ranging between 0 and 1. We run experiments in 10 benchmark domains from the International Planning Competitions since 2000; we show that AsymRatio is a good indicator of SAT solver performance in 8 of these domains. We then examine carefully crafted synthetic planning domains that allow control of the amount of structure, and that are clean enough for a rigorous analysis of the combinatorial search space. The domains are parameterized by size, and by the amount of structure. The CNFs we examine are unsatisfiable, encoding one planning step less than the length of the optimal plan. We prove upper and lower bounds on the size of the best possible DPLL refutations, under different settings of the amount of structure, as a function of size. We also identify the best possible sets of branching variables (backdoors). With minimum AsymRatio, we prove exponential lower bounds, and identify minimal backdoors of size linear in the number of variables. With maximum AsymRatio, we identify logarithmic DPLL refutations (and backdoors), showing a doubly exponential gap between the two structural extreme cases. The reasons for this behavior -- the proof arguments -- illuminate the prototypical patterns of structure causing the empirical behavior observed in the competition benchmarks.
A Peer-to-Peer Browsable File Index using a Popularity Based Global Namespace
Venue: arXiv cs.DC 2007
Year: 2007

The distribution of files using decentralized, peer-to-peer (P2P) systems, has significant advantages over centralized approaches. It is however more difficult to settle on the best approach for file sharing. Most file sharing systems are based on query string searches, leading to a relatively simple but inefficient broadcast or to an efficient but relatively complicated index in a structured environment. In this paper we use a browsable peer-to-peer file index consisting of files which serve as directory nodes, interconnecting to form a directory network. We implemented the system based on BitTorrent and Kademlia. The directory network inherits all of the advantages of decentralization and provides browsable, efficient searching. To avoid conflict between users in the P2P system while also imposing no additional restrictions, we allow multiple versions of each directory node to simultaneously exist -- using popularity as the basis for default browsing behavior. Users can freely add files and directory nodes to the network. We show, using a simulation of user behavior and file quality, that the popularity based system consistently leads users to a high quality directory network; above the average quality of user updates. Q
A Static Analyzer for Large Safety-Critical Software
Venue: arXiv cs.PL 2007
Year: 2007

We show that abstract interpretation-based static program analysis can be made efficient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to particular programs of the family by the end-user through parametrization. This is applied to the proof of soundness of data manipulation operations at the machine level for periodic synchronous safety critical embedded software. The main novelties are the design principle of static analyzers by refinement and adaptation through parametrization, the symbolic manipulation of expressions to improve the precision of abstract transfer functions, the octagon, ellipsoid, and decision tree abstract domains, all with sound handling of rounding errors in floating point computations, widening strategies (with thresholds, delayed) and the automatic determination of the parameters (parametrized packing).
Power Optimal Scheduling for Guaranteed Throughput in Multi-access Fading Channels
Venue: arXiv cs.IT 2007
Year: 2007

A power optimal scheduling algorithm that guarantees desired throughput and bounded delay to each user is developed for fading multi-access multi-band systems. The optimization is over the joint space of all rate allocation and coding strategies. The proposed scheduling assigns rates on each band based only on the current system state, and subsequently uses optimal multi-user signaling to achieve these rates. The scheduling is computationally simple, and hence scalable. Due to uplink-downlink duality, all the results extend in straightforward fashion to the broadcast channels.
Comment on Improved Analysis of List Decoding and Its Application to Convolutional Codes and Turbo Codes
Venue: arXiv cs.IT 2007
Year: 2007

In a recent paper [1] an improved analysis concerning the analysis of List Decoding was presented. The event that the correct codeword is excluded from the list is central. For the additive white Gaussian noise (AWGN) channel an important quantity is the in [1] called effective Euclidean distance. This was earlier considered in [2] under the name Vector Euclidean Distance, where also a simple mathematical expression for this quantity was easily derived for any list size. In [1], a geometrical analysis gives this when the list size is 1, 2 or 3.
Searching for low weight pseudo-codewords
Venue: arXiv cs.IT 2007
Year: 2007

Belief Propagation (BP) and Linear Programming (LP) decodings of Low Density Parity Check (LDPC) codes are discussed. We summarize results of instanton/pseudo-codeword approach developed for analysis of the error-floor domain of the codes. Instantons are special, code and decoding specific, configurations of the channel noise contributing most to the Frame-Error-Rate (FER). Instantons are decoded into pseudo-codewords. Instanton/pseudo-codeword with the lowest weight describes the largest Signal-to-Noise-Ratio (SNR) asymptotic of FER, while the whole spectra of the low weight instantons is descriptive of the FER vs SNR profile in the extended error-floor domain. First, we describe a general optimization method that allows to find the instantons for any coding/decoding. Second, we introduce LP-specific pseudo-codeword search algorithm that allows efficient calculations of the pseudo-codeword spectra. Finally, we discuss results of combined BP/LP error-floor exploration experiments for two model codes.
Shape preservation behavior of spline curves
Venue: arXiv cs.GR 2007
Year: 2007

Shape preservation behavior of a spline consists of criterial conditions for preserving convexity, inflection, collinearity, torsion and coplanarity shapes of data polgonal arc. We present our results which acts as an improvement in the definitions of and provide geometrical insight into each of the above shape preservation criteria. We also investigate the effect of various results from the literature on various shape preservation criteria. These results have not been earlier refered in the context of shape preservation behaviour of splines. We point out that each curve segment need to satisfy more than one shape preservation criteria. We investigate the conflict between different shape preservation criteria 1)on each curve segment and 2)of adjacent curve segments. We derive simplified formula for shape preservation criteria for cubic curve segments. We study the shape preservation behavior of cubic Catmull-Rom splines and see that, though being very simple spline curve, it indeed satisfy all the shape preservation criteria.
The Suspension Calculus and its Relationship to Other Explicit Treatments of Substitution in Lambda Calculi
Venue: arXiv cs.LO 2007
Year: 2007

The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs. Supporting such a data structure in an implementation is made difficult by the complexity of the substitution operation relative to lambda terms. In this paper we present the suspension calculus, an explicit treatment of meta level binding in the lambda calculus. We prove properties of this calculus which make it a suitable replacement for the lambda calculus in implementation. Finally, we compare the suspension calculus with other explicit treatments of substitution.
On the variance of subset sum estimation
Venue: arXiv cs.DS 2007
Year: 2007

For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. Mathematically, we are dealing with a set of weighted items and want to support queries to arbitrary subset sums. With unit weights, we can compute subset sizes which together with the previous sums provide the subset averages. The question addressed here is which sampling scheme we should use to get the most accurate subset sum estimates. We present a simple theorem on the variance of subset sum estimation and use it to prove variance optimality and near-optimality of subset sum estimation with different known sampling schemes. This variance is measured as the average over all subsets of any given size. By optimal we mean there is no set of input weights for which any sampling scheme can have a better average variance. Such powerful results can never be established experimentally. The results of this paper are derived mathematically. For example, we show that appropriately weighted systematic sampling is simultaneously optimal for all subset sizes. More standard schemes such as uniform sampling and probability-proportional-to-size sampling with replacement can be arbitrarily bad. Knowing the variance optimality of different sampling schemes can help deciding which sampling scheme to apply in a given context.
Graph Splicing System
Venue: arXiv cs.DM 2007
Year: 2007

The string splicing was introduced by Tom Head which stands as an abstract model for the DNA recombination under the influence of restriction enzymes. The complex chemical process of three dimensional molecules in three dimensional space can be modeled using graphs. The graph splicing systems which were studied so far, can only be applied to a particular type of graphs which could be interpreted as linear or circular graphs. In this paper, we take a different and a novel approach to splice two graphs and introduce a splicing system for graphs that can be applied to all types of graphs. Splicing two graphs can be thought of as a new operation, among the graphs, that generates many new graphs from the given two graphs. Taking a different line of thinking, some of the graph theoretical results of the splicing are studied.
Efficient First-Order Temporal Logic for Infinite-State Systems
Venue: arXiv cs.LO 2007
Year: 2007

In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for this form of specification and tractable enough for practical deductive verification. Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex properties such as liveness and fairness properties. These aspects appear difficult for many other approaches to infinite-state verification.
Genetic Representations for Evolutionary Minimization of Network Coding Resources
Venue: arXiv cs.NE 2007
Year: 2007

We demonstrate how a genetic algorithm solves the problem of minimizing the resources used for network coding, subject to a throughput constraint, in a multicast scenario. A genetic algorithm avoids the computational complexity that makes the problem NP-hard and, for our experiments, greatly improves on sub-optimal solutions of established methods. We compare two different genotype encodings, which tradeoff search space size with fitness landscape, as well as the associated genetic operators. Our finding favors a smaller encoding despite its fewer intermediate solutions and demonstrates the impact of the modularity enforced by genetic operators on the performance of the algorithm.
Hadwiger and Helly-type theorems for disjoint unit spheres
Venue: arXiv cs.CG 2007
Year: 2007

We prove Helly-type theorems for line transversals to disjoint unit balls in $\R^{d}$. In particular, we show that a family of $n \geq 2d$ disjoint unit balls in $\R^d$ has a line transversal if, for some ordering $\prec$ of the balls, any subfamily of 2d balls admits a line transversal consistent with $\prec$. We also prove that a family of $n \geq 4d-1$ disjoint unit balls in $\R^d$ admits a line transversal if any subfamily of size $4d-1$ admits a transversal.
The Fibers and Range of Reduction Graphs in Ciliates
Venue: arXiv cs.LO 2007
Year: 2007

The biological process of gene assembly has been modeled based on three types of string rewriting rules, called string pointer rules, defined on so-called legal strings. It has been shown that reduction graphs, graphs that are based on the notion of breakpoint graph in the theory of sorting by reversal, for legal strings provide valuable insights into the gene assembly process. We characterize which legal strings obtain the same reduction graph (up to isomorphism), and moreover we characterize which graphs are (isomorphic to) reduction graphs.
Deciding k-colourability of $P_5$-free graphs in polynomial time
Venue: arXiv cs.DS 2007
Year: 2007

The problem of computing the chromatic number of a $P_5$-free graph is known to be NP-hard. In contrast to this negative result, we show that determining whether or not a $P_5$-free graph admits a $k$-colouring, for each fixed number of colours $k$, can be done in polynomial time. If such a colouring exists, our algorithm produces it.
Hierarchical Unambiguity
Venue: arXiv cs.CC 2007
Year: 2007

We develop techniques to investigate relativized hierarchical unambiguous computation. We apply our techniques to generalize known constructs involving relativized unambiguity based complexity classes (UP and \mathcal{UP}) to new constructs involving arbitrary higher levels of the relativized unambiguous polynomial hierarchy (UPH). Our techniques are developed on constraints imposed by hierarchical arrangement of unambiguous nondeterministic polynomial-time Turing machines, and so they differ substantially, in applicability and in nature, from standard methods (such as the switching lemma [Hastad, Computational Limitations of Small-Depth Circuits, MIT Press, 1987]), which play roles in carrying out similar generalizations. Aside from achieving these generalizations, we resolve a question posed by Cai, Hemachandra, and Vyskoc [J. Cai, L. Hemachandra, and J. Vyskoc, Promises and fault-tolerant database access, In K. Ambos-Spies, S. Homer, and U. Schoening, editors, Complexity Theory, pages 101-146. Cambridge University Press, 1993] on an issue related to nonadaptive Turing access to UP and adaptive smart Turing access to \mathcal{UP}.
The DFAs of Finitely Different Languages
Venue: arXiv cs.CC 2007
Year: 2007

Two languages are "finitely different" if their symmetric difference is finite. We consider the DFAs of finitely different regular languages and find major structural similarities. We proceed to consider the smallest DFAs that recognize a language finitely different from some given DFA. Such "f-minimal" DFAs are not unique, and this non-uniqueness is characterized. Finally, we offer a solution to the minimization problem of finding such f-minimal DFAs.
Nash equilibria in Voronoi games on graphs
Venue: arXiv cs.GT 2007
Year: 2007

In this paper we study a game where every player is to choose a vertex (facility) in a given undirected graph. All vertices (customers) are then assigned to closest facilities and a player's payoff is the number of customers assigned to it. We show that deciding the existence of a Nash equilibrium for a given graph is NP-hard which to our knowledge is the first result of this kind for a zero-sum game. We also introduce a new measure, the social cost discrepancy, defined as the ratio of the costs between the worst and the best Nash equilibria. We show that the social cost discrepancy in our game is Omega(sqrt(n/k)) and O(sqrt(kn)), where n is the number of vertices and k the number of players.
A probabilistic analysis of a leader election algorithm
Venue: arXiv cs.DS 2007
Year: 2007

A {\em leader election} algorithm is an elimination process that divides recursively into tow subgroups an initial group of n items, eliminates one subgroup and continues the procedure until a subgroup is of size 1. In this paper the biased case is analyzed. We are interested in the {\em cost} of the algorithm, i.e. the number of operations needed until the algorithm stops. Using a probabilistic approach, the asymptotic behavior of the algorithm is shown to be related to the behavior of a hitting time of two random sequences on [0,1].
Exploring k-Colorability
Venue: arXiv cs.CC 2007
Year: 2007

An introductory paper to the graph k-colorability problem.
Feasible reactivity in a synchronous pi-calculus
Venue: arXiv cs.LO 2007
Year: 2007

Reactivity is an essential property of a synchronous program. Informally, it guarantees that at each instant the program fed with an input will `react' producing an output. In the present work, we consider a refined property that we call ` feasible reactivity'. Beyond reactivity, this property guarantees that at each instant both the size of the program and its reaction time are bounded by a polynomial in the size of the parameters at the beginning of the computation and the size of the largest input. We propose a method to annotate programs and we develop related static analysis techniques that guarantee feasible reactivity for programs expressed in the S-pi-calculus. The latter is a synchronous version of the pi-calculus based on the SL synchronous programming model.