OpenRaiser/Intern-Atlas huggingface dataset:
Deterministic Bayesian Logic
Venue: arXiv cs.LO 2007
Year: 2007

In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. This logic is shown to be non-trivial and is not reduced to classical propositions. The Bayesian conditional of DBL implies a definition of logical independence. Interesting results are derived about the interactions between the logical independence and the proofs. A model is constructed for the logic. Completeness results are proved. It is shown that any unconditioned probability can be extended to the whole logic DBL. The Bayesian conditional is then recovered from the probabilistic DBL. At last, it is shown why DBL is compliant with Lewis triviality.
Fast Distributed Algorithms for Computing Separable Functions
Venue: arXiv cs.NI 2007
Year: 2007

The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer, and ad-hoc networks. The task of computing separable functions, which can be written as linear combinations of functions of individual variables, is studied in this context. Known iterative algorithms for averaging can be used to compute the normalized values of such functions, but these algorithms do not extend in general to the computation of the actual values of separable functions. The main contribution of this paper is the design of a distributed randomized algorithm for computing separable functions. The running time of the algorithm is shown to depend on the running time of a minimum computation algorithm used as a subroutine. Using a randomized gossip mechanism for minimum computation as the subroutine yields a complete totally distributed algorithm for computing separable functions. For a class of graphs with small spectral gap, such as grid graphs, the time used by the algorithm to compute averages is of a smaller order than the time required by a known iterative averaging scheme.
On Coding for Reliable Communication over Packet Networks
Venue: arXiv cs.IT 2007
Year: 2007

We present a capacity-achieving coding scheme for unicast or multicast over lossy packet networks. In the scheme, intermediate nodes perform additional coding yet do not decode nor even wait for a block of packets before sending out coded packets. Rather, whenever they have a transmission opportunity, they send out coded packets formed from random linear combinations of previously received packets. All coding and decoding operations have polynomial complexity. We show that the scheme is capacity-achieving as long as packets received on a link arrive according to a process that has an average rate. Thus, packet losses on a link may exhibit correlation in time or with losses on other links. In the special case of Poisson traffic with i.i.d. losses, we give error exponents that quantify the rate of decay of the probability of error with coding delay. Our analysis of the scheme shows that it is not only capacity-achieving, but that the propagation of packets carrying "innovative" information follows the propagation of jobs through a queueing network, and therefore fluid flow models yield good approximations. We consider networks with both lossy point-to-point and broadcast links, allowing us to model both wireline and wireless packet networks.
Optimal Prefix Codes for Infinite Alphabets with Nonlinear Costs
Venue: arXiv cs.IT 2007
Year: 2007

Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a source code that is optimal in the sense of minimizing expected codeword length. For some applications, however, a source code should instead minimize one of a family of nonlinear objective functions, $β$-exponential means, those of the form $\log_a \sum_i p(i) a^{n(i)}$, where $n(i)$ is the length of the $i$th codeword and $a$ is a positive constant. Applications of such minimizations include a novel problem of maximizing the chance of message receipt in single-shot communications ($a<1$) and a previously known problem of minimizing the chance of buffer overflow in a queueing system ($a>1$). This paper introduces methods for finding codes optimal for such exponential means. One method applies to geometric distributions, while another applies to distributions with lighter tails. The latter algorithm is applied to Poisson distributions and both are extended to alphabetic codes, as well as to minimizing maximum pointwise redundancy. The aforementioned application of minimizing the chance of buffer overflow is also considered.
Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction
Venue: arXiv cs.IT 2007
Year: 2007

A simple scheme for communication over MIMO broadcast channels is introduced which adopts the lattice reduction technique to improve the naive channel inversion method. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. Simulation results show that the proposed scheme performs well, and as compared to the more complex methods (such as the perturbation method) has a negligible loss. Moreover, the proposed method is extended to the case of different rates for different users. The asymptotic behavior of the symbol error rate of the proposed method and the perturbation technique, and also the outage probability for the case of fixed-rate users is analyzed. It is shown that the proposed method, based on LLL lattice reduction, achieves the optimum asymptotic slope of symbol-error-rate (called the precoding diversity). Also, the outage probability for the case of fixed sum-rate is analyzed.
Finding Cliques of a Graph using Prime Numbers
Venue: arXiv cs.DS 2007
Year: 2007

This paper proposes a new algorithm for solving maximal cliques for simple undirected graphs using the theory of prime numbers. A novel approach using prime numbers is used to find cliques and ends with a discussion of the algorithm.
Incremental Redundancy Cooperative Coding for Wireless Networks: Cooperative Diversity, Coding, and Transmission Energy Gain
Venue: arXiv cs.IT 2007
Year: 2007

We study an incremental redundancy (IR) cooperative coding scheme for wireless networks. To exploit the spatial diversity benefit we propose a cluster-based collaborating strategy for a quasi-static Rayleigh fading channel model and based on a network geometric distance profile. Our scheme enhances the network performance by embedding an IR cooperative coding scheme into an existing noncooperative route. More precisely, for each hop, we form a collaborating cluster of M-1 nodes between the (hop) sender and the (hop) destination. The transmitted message is encoded using a mother code and partitioned into M blocks corresponding to the each of M slots. In the first slot, the (hop) sender broadcasts its information by transmitting the first block, and its helpers attempt to relay this message. In the remaining slots, the each of left-over M-1 blocks is sent either through a helper which has successfully decoded the message or directly by the (hop) sender where a dynamic schedule is based on the ACK-based feedback from the cluster. By employing powerful good codes (e.g., turbo codes, LDPC codes, and raptor codes) whose performance is characterized by a threshold behavior, our approach improves the reliability of a multi-hop routing through not only cooperation diversity benefit but also a coding advantage. The study of the diversity and the coding gain of the proposed scheme is based on a new simple threshold bound on the frame-error rate (FER) of maximum likelihood decoding. A average FER upper bound and its asymptotic (in large SNR) version are derived as a function of the average fading channel SNRs and the code threshold.
Twenty (or so) Questions: $D$-ary Length-Bounded Prefix Coding
Venue: arXiv cs.IT 2007
Year: 2007

Efficient optimal prefix coding has long been accomplished via the Huffman algorithm. However, there is still room for improvement and exploration regarding variants of the Huffman problem. Length-limited Huffman coding, useful for many practical applications, is one such variant, for which codes are restricted to the set of codes in which none of the $n$ codewords is longer than a given length, $l_{\max}$. Binary length-limited coding can be done in $O(n l_{\max})$ time and O(n) space via the widely used Package-Merge algorithm and with even smaller asymptotic complexity using a lesser-known algorithm. In this paper these algorithms are generalized without increasing complexity in order to introduce a minimum codeword length constraint $l_{\min}$, to allow for objective functions other than the minimization of expected codeword length, and to be applicable to both binary and nonbinary codes; nonbinary codes were previously addressed using a slower dynamic programming approach. These extensions have various applications -- including fast decompression and a modified version of the game ``Twenty Questions'' -- and can be used to solve the problem of finding an optimal code with limited fringe, that is, finding the best code among codes with a maximum difference between the longest and shortest codewords. The previously proposed method for solving this problem was nonpolynomial time, whereas solving this using the novel linear-space algorithm requires only $O(n (l_{\max}- l_{\min})^2)$ time, or even less if $l_{\max}- l_{\min}$ is not $O(\log n)$.
The Discrete Memoryless Multiple Access Channel with Confidential Messages
Venue: arXiv cs.IT 2007
Year: 2007

A multiple-access channel is considered in which messages from one encoder are confidential. Confidential messages are to be transmitted with perfect secrecy, as measured by equivocation at the other encoder. The upper bounds and the achievable rates for this communication situation are determined.
On the possible Computational Power of the Human Mind
Venue: arXiv cs.NE 2007
Year: 2007

The aim of this paper is to address the question: Can an artificial neural network (ANN) model be used as a possible characterization of the power of the human mind? We will discuss what might be the relationship between such a model and its natural counterpart. A possible characterization of the different power capabilities of the mind is suggested in terms of the information contained (in its computational complexity) or achievable by it. Such characterization takes advantage of recent results based on natural neural networks (NNN) and the computational power of arbitrary artificial neural networks (ANN). The possible acceptance of neural networks as the model of the human mind's operation makes the aforementioned quite relevant.
A synchronous pi-calculus
Venue: arXiv cs.LO 2007
Year: 2007

The SL synchronous programming model is a relaxation of the Esterel synchronous model where the reaction to the absence of a signal within an instant can only happen at the next instant. In previous work, we have revisited the SL synchronous programming model. In particular, we have discussed an alternative design of the model including thread spawning and recursive definitions, introduced a CPS translation to a tail recursive form, and proposed a notion of bisimulation equivalence. In the present work, we extend the tail recursive model with first-order data types obtaining a non-deterministic synchronous model whose complexity is comparable to the one of the pi-calculus. We show that our approach to bisimulation equivalence can cope with this extension and in particular that labelled bisimulation can be characterised as a contextual bisimulation.
Approximation Algorithms for Multi-Criteria Traveling Salesman Problems
Venue: arXiv cs.DS 2007
Year: 2007

In multi-criteria optimization problems, several objective functions have to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as the optimal solution. Instead, the aim is to compute a so-called Pareto curve of solutions. Since Pareto curves cannot be computed efficiently in general, we have to be content with approximations to them. We design a deterministic polynomial-time algorithm for multi-criteria g-metric STSP that computes (min{1 +g, 2g^2/(2g^2 -2g +1)} + eps)-approximate Pareto curves for all 1/2<=g<=1. In particular, we obtain a (2+eps)-approximation for multi-criteria metric STSP. We also present two randomized approximation algorithms for multi-criteria g-metric STSP that achieve approximation ratios of (2g^3 +2g^2)/(3g^2 -2g +1) + eps and (1 +g)/(1 +3g -4g^2) + eps, respectively. Moreover, we present randomized approximation algorithms for multi-criteria g-metric ATSP (ratio 1/2 + g^3/(1 -3g^2) + eps) for g < 1/sqrt(3)), STSP with weights 1 and 2 (ratio 4/3) and ATSP with weights 1 and 2 (ratio 3/2). To do this, we design randomized approximation schemes for multi-criteria cycle cover and graph factor problems.
Scheduling Algorithms for Procrastinators
Venue: arXiv cs.DS 2007
Year: 2007

This paper presents scheduling algorithms for procrastinators, where the speed that a procrastinator executes a job increases as the due date approaches. We give optimal off-line scheduling policies for linearly increasing speed functions. We then explain the computational/numerical issues involved in implementing this policy. We next explore the online setting, showing that there exist adversaries that force any online scheduling policy to miss due dates. This impossibility result motivates the problem of minimizing the maximum interval stretch of any job; the interval stretch of a job is the job's flow time divided by the job's due date minus release time. We show that several common scheduling strategies, including the "hit-the-highest-nail" strategy beloved by procrastinators, have arbitrarily large maximum interval stretch. Then we give the "thrashing" scheduling policy and show that it is a Θ(1) approximation algorithm for the maximum interval stretch.
Scheduling and Codeword Length Optimization in Time Varying Wireless Networks
Venue: arXiv cs.IT 2007
Year: 2007

In this paper, a downlink scenario in which a single-antenna base station communicates with K single antenna users, over a time-correlated fading channel, is considered. It is assumed that channel state information is perfectly known at each receiver, while the statistical characteristics of the fading process and the fading gain at the beginning of each frame are known to the transmitter. By evaluating the random coding error exponent of the time-correlated fading channel, it is shown that there is an optimal codeword length which maximizes the throughput. The throughput of the conventional scheduling that transmits to the user with the maximum signal to noise ratio is examined using both fixed length codewords and variable length codewords. Although optimizing the codeword length improves the performance, it is shown that using the conventional scheduling, the gap between the achievable throughput and the maximum possible throughput of the system tends to infinity as K goes to infinity. A simple scheduling that considers both the signal to noise ratio and the channel time variation is proposed. It is shown that by using this scheduling, the gap between the achievable throughput and the maximum throughput of the system approaches zero.
Weighted hierarchical alignment of directed acyclic graph
Venue: arXiv cs.DS 2007
Year: 2007

In some applications of matching, the structural or hierarchical properties of the two graphs being aligned must be maintained. The hierarchical properties are induced by the direction of the edges in the two directed graphs. These structural relationships defined by the hierarchy in the graphs act as a constraint on the alignment. In this paper, we formalize the above problem as the weighted alignment between two directed acyclic graphs. We prove that this problem is NP-complete, show several upper bounds for approximating the solution, and finally introduce polynomial time algorithms for sub-classes of directed acyclic graphs.
A simple generalization of El-Gamal cryptosystem to non-abelian groups
Venue: arXiv cs.CR 2007
Year: 2007

In this paper we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the El-Gamal cryptosystem over finite fields can be built using the proposed groups and a set of automorphisms of these groups. We also show that the security of this proposed MOR cryptosystem is equivalent to the El-Gamal cryptosystem over finite fields.
An Analysis of Arithmetic Constraints on Integer Intervals
Venue: arXiv cs.AI 2007
Year: 2007

Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that reduce the variable domains. We compare these approaches using a set of benchmarks. For the most promising approach we provide results that characterize the effect of constraint propagation. This is a full version of our earlier paper, cs.PL/0403016.
Analysis of CDMA systems that are characterized by eigenvalue spectrum
Venue: arXiv cs.IT 2007
Year: 2007

An approach by which to analyze the performance of the code division multiple access (CDMA) scheme, which is a core technology used in modern wireless communication systems, is provided. The approach characterizes the objective system by the eigenvalue spectrum of a cross-correlation matrix composed of signature sequences used in CDMA communication, which enables us to handle a wider class of CDMA systems beyond the basic model reported by Tanaka. The utility of the novel scheme is shown by analyzing a system in which the generation of signature sequences is designed for enhancing the orthogonality.
Length-based cryptanalysis: The case of Thompson's Group
Venue: arXiv cs.CR 2007
Year: 2007

The length-based approach is a heuristic for solving randomly generated equations in groups which possess a reasonably behaved length function. We describe several improvements of the previously suggested length-based algorithms, that make them applicable to Thompson's group with significant success rates. In particular, this shows that the Shpilrain-Ushakov public key cryptosystem based on Thompson's group is insecure, and suggests that no practical public key cryptosystem based on this group can be secure.
Degrees of Freedom Region for the MIMO X Channel
Venue: arXiv cs.IT 2007
Year: 2007

We provide achievability as well as converse results for the degrees of freedom region of a MIMO $X$ channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels from each transmitter to each receiver. With M=1 antennas at each node, we find that the total (sum rate) degrees of freedom are bounded above and below as $1 \leqη_X^\star \leq {4/3}$. If $M>1$ and channel matrices are non-degenerate then the precise degrees of freedom $η_X^\star = {4/3}M$. Simple zero forcing without dirty paper encoding or successive decoding, suffices to achieve the ${4/3}M$ degrees of freedom. With equal number of antennas at all nodes, we explore the increase in degrees of freedom when some of the messages are made available to a transmitter or receiver in the manner of cognitive radio. With a cognitive transmitter we show that the number of degrees of freedom $η= {3/2}M$ (for $M>1$) on the MIMO $X$ channel. The same degrees of freedom are obtained on the MIMO $X$ channel with a cognitive receiver as well. In contrast to the $X$ channel result, we show that for the MIMO \emph{interference} channel, the degrees of freedom are not increased even if both the transmitter and the receiver of one user know the other user's message. However, the interference channel can achieve the full $2M$ degrees of freedom if \emph{each} user has either a cognitive transmitter or a cognitive receiver. Lastly, if the channels vary with time/frequency then the $X$ channel with single antennas $(M=1)$ at all nodes has exactly 4/3 degrees of freedom with no shared messages and exactly 3/2 degrees of freedom with a cognitive transmitter or a cognitive receiver.
A linear algebra approach to the differentiation index of generic DAE systems
Venue: arXiv cs.SC 2007
Year: 2007

The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper bounds for the regularity of the Hilbert-Kolchin function and the order of the ideal associated to the DAE systems under consideration, not depending on characteristic sets. Some quantitative and algorithmic results concerning differential transcendence bases and induced equivalent explicit ODE systems are also established.
From Invariants to Canonization in Parallel
Venue: arXiv cs.CC 2007
Year: 2007

A function $f$ of a graph is called a complete graph invariant if the isomorphism of graphs $G$ and $H$ is equivalent to the equality $f(G)=f(H)$. If, in addition, $f(G)$ is a graph isomorphic to $G$, then $f$ is called a canonical form for graphs. Gurevich proves that graphs have a polynomial-time computable canonical form exactly when they have a polynomial-time computable complete invariant. We extend this equivalence to the polylogarithmic-time model of parallel computation for classes of graphs with bounded rigidity index and for classes of graphs with small separators. In particular, our results apply to three representative classes of graphs embeddable into a fixed surface, namely, to 5-connected graphs, to 3-connected graphs admitting a polyhedral embedding, and 3-connected graphs admitting a large-edge-width embedding. Another application covers graphs with bounded treewidth. Since in the latter case an NC complete-invariant algorithm is known, we conclude that graphs of bounded treewidth have a canonical form (and even a canonical labeling) computable in NC.
Streaming Maximum-Minimum Filter Using No More than Three Comparisons per Element
Venue: arXiv cs.DS 2007
Year: 2007

The running maximum-minimum (max-min) filter computes the maxima and minima over running windows of size w. This filter has numerous applications in signal processing and time series analysis. We present an easy-to-implement online algorithm requiring no more than 3 comparisons per element, in the worst case. Comparatively, no algorithm is known to compute the running maximum (or minimum) filter in 1.5 comparisons per element, in the worst case. Our algorithm has reduced latency and memory usage.