On the hardness of approximating label-cover

The Label-Cover problem, defined by S. Arora, L. Babai, J. Stern, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp. 724-733], serves as a starting point for numerous hardness of approximation reductions. It is one of six ‘canonical’ approximation problems in the survey of Arora and Lund [Hardness of Approximations, in: Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, 1996, Chapter 10]. In this paper we present a direct combinatorial reduction from low error-probability PCP [Proceedings of 31st ACM Symposium on Theory of Computing, 1999, pp. 29-40] to Label-Cover showing it NP-hard to approximate to within 2^{(logn)1−o(1)}. This improves upon the best previous hardness of approximation results known for this problem.We also consider the Minimum-Monotone-Satisfying-Assignment (MMSA) problem of finding a satisfying assignment to a monotone formula with the least number of 1's, introduced by M. Alekhnovich, S. Buss, S. Moran, T. Pitassi [Minimum propositional proof length is NP-hard to linearly approximate, 1998]. We define a hierarchy of approximation problems obtained by restricting the number of alternations of the monotone formula. This hierarchy turns out to be equivalent to an AND/OR scheduling hierarchy suggested by M.H. Goldwasser, R. Motwani [Lecture Notes in Comput. Sci., Vol. 1272, Springer-Verlag, 1997, pp. 307-320]. We show some hardness results for certain levels in this hierarchy, and place Label-Cover between levels 3 and 4. This partially answers an open problem from M.H. Goldwasser, R. Motwani regarding the precise complexity of each level in the hierarchy, and the place of Label-Cover in it.     

OPM/Web – Object-Process Methodology for Developing Web Applications

Web applications can be classified as hybrids between hypermedia and information systems. They have a relatively simple distributed architecture from the user viewpoint, but a complex dynamic architecture from the designer viewpoint. They need to respond to operation by an unlimited number of heterogeneously skilled users, address security and privacy concerns, access heterogeneous, up-to-date information sources, and exhibit dynamic behaviors that involve such processes as code transferring. Common system development methods can model some of these aspects, but none of them is sufficient to specify the large spectrum of Web application concepts and requirements. This paper introduces OPM/Web, an extension to the Object-Process Methodology (OPM) that satisfies the functional, structural and behavioral Web-based information system requirements. The main extensions of OPM/Web are adding properties of links to express requirements, such as those related to encryption; extending the zooming and unfolding facilities to increase modularity; cleanly separating declarations and instances of code to model code transferring; and adding global data integrity and control constraints to express dependence or temporal relations among (physically) separate modules. We present a case study that helps evaluate OPM/Web and compare it to an extension of the Unified Modeling Language (UML) for the Web application domain.     

Saving Space by Fully Exploiting Invisible Transitions

Checking that a given finite state program satisfies a linear temporal logic property suffers from the state explosion problem. Often the resulting lack of available memory is more significant than any time limitations. One way to cope with this is to reduce the state graph used for model checking. We present an algorithm for constructing a state graph that is a projection of the program's state graph. The algorithm maintains the transitions and states that affect the truth of the property to be checked. Especially in conjunction with known partial order reduction algorithms, we show a substantial reduction in memory over using partial order methods alone, both in the precomputation stage, and in the result presented to a model checker. The price of the space reduction is a single additional traversal of the graph obtained with partial order reduction. As part of our space-saving methods, we present a new way to exploit Holzmann's Bit Hash Table, which assists us in solving the revisiting problem.     

The effect of age-dependent increase in fat mass on peripheral insulin action is saturable

Insulin resistance and increased fat mass (FM) are common in human aging. We aimed to investigate the relationship between the age-dependent increase in FM and insulin resistance (by euglycemic hyperinsulinemic clamp technique), in a homogenous rodent model. The decline in insulin responsiveness was linear until late adulthood when body weight, FM, and epididymal fat reached a critical amount (r > .750, for all). Above this critical point, there was no further decline in insulin responsiveness with aging and with increased BW (p < .00001 for all spline curve analyses). This decline in insulin-mediated glucose uptake was accounted for by a decrease in whole body glycolytic rate with no change in the rate of glycogen synthesis. Thus, in this homogenous model, an early increase in FM is associated with impairment in insulin action until a critical FM is achieved, after which there is no additional insulin resistance with aging. We suggest that decreasing insulin responsiveness, in a heterogeneous group such as humans, will only occur within a specific accretion of visceral or total FM.