Truly stateless, optimal dynamic partial order reduction

Dynamic partial order reduction (DPOR) verifies concurrent programs by exploring all their interleavings up to some equivalence relation, such as the Mazurkiewicz trace equivalence. Doing so involves a complex trade-off between space and time. Existing DPOR algorithms are either exploration-optimal (i.e., explore exactly only interleaving per equivalence class) but may use exponential memory in the size of the program, or maintain polynomial memory consumption but potentially explore exponentially many redundant interleavings. In this paper, we show that it is possible to have the best of both worlds: exploring exactly one interleaving per equivalence class with linear memory consumption. Our algorithm, TruSt, formalized in Coq, is applicable not only to sequential consistency, but also to any weak memory model that satisfies a few basic assumptions, including TSO, PSO, and RC11. In addition, TruSt is embarrassingly parallelizable: its different exploration options have no shared state, and can therefore be explored completely in parallel. Consequently, TruSt outperforms the state-of-the-art in terms of memory and/or time.

Partial Order Games

We introduce a non-cooperative game model in which players’ decision nodes are partially ordered by a dependence relation, which directly captures informational dependencies in the game. In saying that a decision node v is dependent on decision nodes v1,…,vk, we mean that the information available to a strategy making a choice at v is precisely the choices that were made at v1,…,vk. Although partial order games are no more expressive than extensive form games of imperfect information (we show that any partial order game can be reduced to a strategically equivalent extensive form game of imperfect information, though possibly at the cost of an exponential blowup in the size of the game), they provide a more natural and compact representation for many strategic settings of interest. After introducing the game model, we investigate the relationship to extensive form games of imperfect information, the problem of computing Nash equilibria, and conditions that enable backwards induction in this new model.

LR-Preinvex Interval-Valued Functions and Riemann–Liouville Fractional Integral Inequalities

Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called LR-preinvex interval-valued functions (LR-preinvex I-V-Fs) and to establish Hermite–Hadamard type inequalities for LR-preinvex I-V-Fs using partial order relation (≤p). Furthermore, we demonstrate that our results include a large class of new and known inequalities for LR-preinvex interval-valued functions and their variant forms as special instances. Further, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.

Identifying Influential SLD Authoritative Name Servers on the Internet

DNS plays an important role on the Internet. The addressing of most applications depends on the proper operation of DNS. The root servers and the top-level domain servers are relied upon by many domains on the Internet, and their security affects the whole Internet. As a result, more attention has been paid to the security of servers at these two levels. However, the security of second-level domains and their servers also needs to be brought to the forefront. This paper focuses on showing the complex resolving dependencies and identifying influential name servers for second-level domains. We start by detecting domain name resolution paths and building up a name dependency graph. Then we construct domain name resolution networks of different numbers and sizes, which are connected by a certain number of domain name resolution graphs. On this basis, the network is analyzed from the perspective of complex network analysis, and a multi-indicators node importance evaluation method based on partial order is proposed to identify the influential name servers of the network. Once these name servers are not properly configured and fail or are compromised by DDoS attacks, it will cause resolution failure for a wide range of domain names.

Further Results of the TTT Transform Ordering of Order n

To compare the variability of two random variables, we can use a partial order relation defined on a distribution class, which contains the anti-symmetry. Recently, Nair et al. studied the properties of total time on test (TTT) transforms of order n and examined their applications in reliability analysis. Based on the TTT transform functions of order n, they proposed a new stochastic order, the TTT transform ordering of order n (TTT-n), and discussed the implications of order TTT-n. The aim of the present study is to consider the closure and reversed closure of the TTT-n ordering. We examine some characterizations of the TTT-n ordering, and obtain the closure and reversed closure properties of this new stochastic order under several reliability operations. Preservation results of this order in several stochastic models are investigated. The closure and reversed closure properties of the TTT-n ordering for coherent systems with dependent and identically distributed components are also obtained.