TINISAT in SAT-Race 2006

was started as part of an investigation of the effect of restart policies on clause learning (Huang 2006). The version entering the race, TINISAT 0.2, is written in about 760 lines of C++ including comments. The top-level procedure of the solver is given in Algorithm 1, which operates on an implicit CNF formula whose satisfiability is in question. The following components of a typical clause learning SAT solver can be identified in Algorithm 1: decision heuristic (selectLiteral), unit propagation (decide, assertLearnedClause), clause learning (learnClause, backtrack), restarts (restartPoint, backtrack). We note that TINISAT 0.2 uses the 1-UIP (Zhang et al. 2001) learning scheme, does not delete clauses, and does not use randomness. The functions involved have the following semantics: • selectLiteral uses some decision heuristic to select a free variable and then select one of its two literals, and returns it, or returns nil if no free variables exist. • decide increments the decision level, sets the given literal to true, and performs unit propagation; it returns true iff no empty clause is derived. • learnClause performs 1-UIP learning to derive an implicate of the CNF formula, and sets the assertion level (i) to 0 if the empty clause is derived, (ii) to 1 if a unit clause is derived, and otherwise (iii) to the second highest decision level among literals of the derived clause. • assertionLevel returns the assertion level, which ha

Hierarchical diagnosis of multiple faults

Due to large search spaces, diagnosis of combinational circuits is often practical for finding only single and double faults. In principle, system models can be compiled into a tractable representation (such as DNNF) on which faults of arbitrary cardinal

End-to-end Structure-Aware Convolutional Networks for Knowledge Base Completion

Knowledge graph embedding has been an active research topic for knowledge base completion, with progressive improvement from the initial TransE, TransH, DistMult et al to the current state-of-the-art ConvE. ConvE uses 2D convolution over embeddings and multiple layers of nonlinear features to model knowledge graphs. The model can be efficiently trained and scalable to large knowledge graphs. However, there is no structure enforcement in the embedding space of ConvE. The recent graph convolutional network (GCN) provides another way of learning graph node embedding by successfully utilizing graph connectivity structure. In this work, we propose a novel end-to-end Structure-Aware Convolutional Network (SACN) that takes the benefit of GCN and ConvE together. SACN consists of an encoder of a weighted graph convolutional network (WGCN), and a decoder of a convolutional network called Conv-TransE. WGCN utilizes knowledge graph node structure, node attributes and edge relation types. It has learnable weights that adapt the amount of information from neighbors used in local aggregation, leading to more accurate embeddings of graph nodes. Node attributes in the graph are represented as additional nodes in the WGCN. The decoder Conv-TransE enables the state-of-the-art ConvE to be translational between entities and relations while keeps the same link prediction performance as ConvE. We demonstrate the effectiveness of the proposed SACN on standard FB15k-237 and WN18RR datasets, and it gives about 10% relative improvement over the state-of-the-art ConvE in terms of HITS@1, HITS@3 and [email protected]: The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI 2019

Light Ring behind Wormhole Throat: Geodesics, Images and Shadows

The geodesics of the Ellis-Bronnikov wormhole with two parameters are studied. The asymmetric wormhole has only one light ring and one innermost stable circular orbit located on one side of the wormhole throat. Consequently, certain light rays can be reflected back by the wormhole. Additionally, the same wormhole can have different appearances on both sides of the throat. We present novel images of the wormhole with a light ring behind the throat in a scenario with an accretion disk as the light source and in a backlit wormhole scenario, which are distinct from the images of other compact objects and have the potential to be observed.Comment: 26 pages, 14 figures, add reference