Validating Arbitrarily Large Network Protocol Compositions with Finite Computation

Formal tools like finite-state model checkers have proven useful in verifying the correctness of systems of bounded size and for hardening single system components against arbitrary inputs. However, conventional applications of these techniques are not well suited to characterizing emergent behaviors of large compositions of processes. In this paper, we present a methodology by which arbitrarily large compositions of components can, if sufficient conditions are proven concerning properties of small compositions, be modeled and completely verified by performing formal verifications upon only a finite set of compositions. The sufficient conditions take the form of reductions, which are claims that particular sequences of components will be causally indistinguishable from other shorter sequences of components. We show how this methodology can be applied to a variety of network protocol applications, including two features of the HTTP protocol, a simple active networking applet, and a proposed web cache consistency algorithm. We also doing discuss its applicability to framing protocol design goals and to representing systems which employ non-model-checking verification methodologies. Finally, we briefly discuss how we hope to broaden this methodology to more general topological compositions of network applications.

Adaptive Weighing Designs for Keyword Value Computation

Attributing a dollar value to a keyword is an essential part of running any profitable search engine advertising campaign. When an advertiser has complete control over the interaction with and monetization of each user arriving on a given keyword, the value of that term can be accurately tracked. However, in many instances, the advertiser may monetize arrivals indirectly through one or more third parties. In such cases, it is typical for the third party to provide only coarse-grained reporting: rather than report each monetization event, users are aggregated into larger channels and the third party reports aggregate information such as total daily revenue for each channel. Examples of third parties that use channels include Amazon and Google AdSense. In such scenarios, the number of channels is generally much smaller than the number of keywords whose value per click (VPC) we wish to learn. However, the advertiser has flexibility as to how to assign keywords to channels over time. We introduce the channelization problem: how do we adaptively assign keywords to channels over the course of multiple days to quickly obtain accurate VPC estimates of all keywords? We relate this problem to classical results in weighing design, devise new adaptive algorithms for this problem, and quantify the performance of these algorithms experimentally. Our results demonstrate that adaptive weighing designs that exploit statistics of term frequency, variability in VPCs across keywords, and flexible channel assignments over time provide the best estimators of keyword VPCs.

Determining Acceptance Possibility for a Quantum Computation is Hard for PH

It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation.

Determining Acceptance Possibility for a Quantum Computation is Hard for the Polynomial Hierarchy

It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation value at the end of a quantum computation. This result is achieved by showing that the complexity class NQP of Adleman, Demarrais, and Huang, a quantum analog of NP, is equal to the counting class coC=P.

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.