Code Graph Research Articles

Partially balanced network designs and graph codes generation

<abstract> <p>Partial balanced incomplete block designs have a wide range of applications in many areas. Such designs provide advantages over fully balanced incomplete block designs as they allow for designs with a low number of blocks and different associations. This paper introduces a class of partially balanced incomplete designs. We call it partially balanced network designs (PBNDs). The fundamentals and properties of PBNDs are studied. We are concerned with modeling PBNDs as graph designs. Some direct constructions of small PBNDs and generalized PBNDs are introduced. Besides that, we show that our modeling yields an effective utilization of PNBDs in constructing graph codes. Here, we are interested in constructing graph codes from bipartite graphs. We have proved that these codes have good characteristics for error detection and correction. In the end, the paper introduces a novel technique for generating new codes from already constructed codes. This technique results in increasing the ability to correct errors.</p> </abstract>

Looking for Criminal Intents in JavaScript Obfuscated Code

The majority of websites incorporate JavaScript for client-side execution in a supposedly protected environment. Unfortunately, JavaScript has also proven to be a critical attack vector for both independent and state-sponsored groups of hackers. On the one hand, defenders need to analyze scripts to ensure that no threat is delivered and to respond to potential security incidents. On the other, attackers aim to obfuscate the source code in order to disorient the defenders or even to make code analysis practically impossible. Since code obfuscation may also be adopted by companies for legitimate intellectual-property protection, a dilemma remains on whether a script is harmless or malignant, if not criminal. To help analysts deal with such a dilemma, a methodology is proposed, called JACOB, which is based on five steps, namely: (1) source code parsing, (2) control flow graph recovery, (3) region identification, (4) code structuring, and (5) partial evaluation. These steps implement a sort of decompilation for control flow fattened code, which is progressively transformed into something that is close to the original JavaScript source, thereby making eventual code analysis possible. Most relevantly, JACOB has been successfully applied to uncover unwanted user tracking and fingerprinting in e-commerce websites operated by a well-known Chinese company.

Locating and identifying codes in dihedral graphs

The smallest cardinalities of identifying and locating codes in dihedral graphs are studied in this paper which is the first step to study these codes in general networks.

Improving Text-to-Code Generation with Features of Code Graph on GPT-2

Code generation, as a very hot application area of deep learning models for text, consists of two different fields: code-to-code and text-to-code. A recent approach, GraphCodeBERT uses code graph, which is called data flow, and showed good performance improvement. The base model architecture of it is bidirectional encoder representations from transformers (BERT), which uses the encoder part of a transformer. On the other hand, generative pre-trained transformer (GPT)—another multiple transformer architecture—uses the decoder part and shows great performance in the multilayer perceptron model. In this study, we investigate the improvement of code graphs with several variances on GPT-2 to refer to the abstract semantic tree used to collect the features of variables in the code. Here, we mainly focus on GPT-2 with additional features of code graphs that allow the model to learn the effect of the data stream. The experimental phase is divided into two parts: fine-tuning of the existing GPT-2 model, and pre-training from scratch using code data. When we pre-train a new model from scratch, the model produces an outperformed result compared with using the code graph with enough data.

Trapping Sets of Quantum LDPC Codes

Iterative decoders for finite length quantum low-density parity-check (QLDPC) codes are attractive because their hardware complexity scales only linearly with the number of physical qubits. However, they are impacted by short cycles, detrimental graphical configurations known as trapping sets (TSs) present in a code graph as well as symmetric degeneracy of errors. These factors significantly degrade the decoder decoding probability performance and cause so-called error floor. In this paper, we establish a systematic methodology by which one can identify and classify quantum trapping sets (QTSs) according to their topological structure and decoder used. The conventional definition of a TS from classical error correction is generalized to address the syndrome decoding scenario for QLDPC codes. We show that the knowledge of QTSs can be used to design better QLDPC codes and decoders. Frame error rate improvements of two orders of magnitude in the error floor regime are demonstrated for some practical finite-length QLDPC codes without requiring any post-processing.

On the Cayleyness of Praeger-Xu graphs

This paper discusses a family of graphs, called Praeger-Xu graphs and denoted PX(n,k) here, introduced by C.E. Praeger and M.-Y. Xu in 1989. These tetravalent graphs are distinguished by having large symmetry groups; their vertex-stabilizers can be arbitrarily larger than the number of vertices in the graph. This paper does the following: (1) exhibits a connection between vertex-transitive groups of symmetries in a Praeger-Xu graph and certain linear codes, (2) characterizes those linear codes, (3) characterizes Praeger-Xu graphs PX(n,k) which are Cayley, (4) shows that every PX(n,k) is quasi-Cayley, and (5) constructs an infinite family of Praeger-Xu graphs in which a smallest vertex-transitive group of symmetries has arbitrarily large vertex-stabiliser.

Quadratic residue codes, rank three groups and PBIBDs

The automorphism group of the Zetterberg code Z of length 17 (also a quadratic residue code) is a rank three group whose orbits on the coordinate pairs determine two strongly regular graphs equivalent to the Paley graph attached to the prime 17. As a consequence, codewords of a given weight of Z are the characteristic vectors of the blocks of a PBIBD with two associate classes of cyclic type. More generally, this construction of PBIBDs is extended to quadratic residue codes of length \(\equiv 1 \pmod {8},\) to the adjacency codes of triangular and lattice graphs, and to the adjacency codes of various rank three graphs. A remarkable fact is the existence of 2-designs held by the quadratic residue code of length 41 for code weights 9 and 10.

Graph-state representation of the toric code

Given their potential for fault-tolerant operations, topological quantum states are currently a focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer codes that are equivalent to the celebrated toric code. While every stabilizer state maps to a graph state under local Clifford operations, the graphs associated with topological stabilizer codes remain unknown. We show that the toric code graph is composed of only two kinds of subgraphs: star graphs (which encode Greenberger-Horne-Zeilinger states) and half graphs. The topological order is identified with the existence of multiple star graphs, which reveals a connection between the repetition and toric codes. The graph structure readily yields a log-depth quantum circuit for state preparation, assuming geometrically nonlocal gates, which can be reduced to a constant depth including ancillae and measurements at the cost of increasing the circuit width. The results provide a graph-theoretic framework for the investigation of topological order and the development of topological error correction codes.

Fast and Effective Retrieval for Large Multimedia Collections

The indexing and retrieval of multimedia content is generally implemented by employing feature graphs. These graphs typically contain a significant number of nodes and edges to reflect the level of detail in feature detection. A higher level of detail increases the effectiveness of the results, but also leads to more complex graph structures. However, graph traversal-based algorithms for similarity are quite inefficient and computationally expensive, especially for large data structures. To deliver fast and effective retrieval especially for large multimedia collections and multimedia big data, an efficient similarity algorithm for large graphs in particular is desirable. Hence, in this paper, we define a graph projection into a 2D space (Graph Code) and the corresponding algorithms for indexing and retrieval. We show that calculations in this space can be performed more efficiently than graph traversals due to the simpler processing model and the high level of parallelization. As a consequence, we demonstrate experimentally that the effectiveness of retrieval also increases substantially, as the Graph Code facilitates more levels of detail in feature fusion. These levels of detail also support an increased trust prediction, particularly for fused social media content. In our mathematical model, we define a metric triple for the Graph Code, which also enhances the ranked result representations. Thus, Graph Codes provide a significant increase in efficiency and effectiveness, especially for multimedia indexing and retrieval, and can be applied to images, videos, text and social media information.

New results of identifying codes in product graphs

For the vertex v of graph G and the subset N⊆V(G) of the vertex set, let IN(v)={N∩NG[v]}. If, for all vertices v’s of G, IN(v)’s are distinct non-empty sets, then N is said to be an identifying code and we indicate it by i(G). A graph G is called identifiable, if distinct vertices of this graph have distinct closed neighboods. In the current work, we investigate some upper bounds for the identifying code of given graph products.

Perfect t-codes in Cayley graphs of groups

A perfect [Formula: see text]-code in a graph [Formula: see text] is a subset [Formula: see text] of [Formula: see text] such that every vertex of [Formula: see text] is at a distance not more than [Formula: see text], to exactly one vertex of [Formula: see text]. In this paper, we present a new family of perfect [Formula: see text]-codes in Cayley graphs of groups. We proposed the role of the subgroups of a group to create perfect [Formula: see text]-codes by restricting the elements of the left transversal of the subgroups in the given group. Also, we introduce a new decoding algorithm for the all of perfect [Formula: see text]-codes in Cayley graphs. These codes are able to correct every [Formula: see text]-error pattern.

Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 20 important graph problems. We also present the interfaces, optimizations, and graph processing techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We have made the implementations developed in this work publicly-available as the Graph Based Benchmark Suite (GBBS).

Extremal absorbing sets in low-density parity-check codes

Absorbing sets are combinatorial structures in the Tanner graphs of low-density parity-check (LDPC) codes that have been shown to inhibit the high signal-to-noise ratio performance of iterative decoders over many communication channels. Absorbing sets of minimum size are the most likely to cause errors, and thus have been the focus of much research. In this paper, we determine the sizes of absorbing sets that can occur in general and left-regular LDPC code graphs, with emphasis on the range of $ b $ for a given $ a $ for which an $ (a,b) $-absorbing set may exist. We identify certain cases of extremal absorbing sets that are elementary, a particularly harmful class of absorbing sets, and also introduce the notion of minimal absorbing sets which will help in designing absorbing set removal algorithms.

Optimal Identifying Codes in Oriented Paths and Circuits

Identifying codes in graphs are related to the classical notion of dominating sets [1]. Since there first introduction in 1998 [2], they have been widely studied and extended to several application, such as: detection of faulty processor in multiprocessor systems, locating danger or threats in sensor networks. Let G=(V,E) an unoriented connected graph. The minimum identifying code in graphs is the smallest subset of vertices C, such that every vertex in V have a unique set of neighbors in C. In our work, we focus on finding minimum cardinality of an identifying code in oriented paths and circuits

Quantum stabilizer codes, lattices, and CFTs

There is a rich connection between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices and non-chiral CFTs. More specifically, real self-dual stabilizer codes can be associated with even self-dual Lorentzian lattices, and thus define Narain CFTs. We dub the resulting theories code CFTs and study their properties. T-duality transformations of a code CFT, at the level of the underlying code, reduce to code equivalences. By means of such equivalences, any stabilizer code can be reduced to a graph code. We can therefore represent code CFTs by graphs. We study code CFTs with small central charge c = n ≤ 12, and find many interesting examples. Among them is a non-chiral E8 theory, which is based on the root lattice of E8 understood as an even self-dual Lorentzian lattice. By analyzing all graphs with n ≤ 8 nodes we find many pairs and triples of physically distinct isospectral theories. We also construct numerous modular invariant functions satisfying all the basic properties expected of the CFT partition function, yet which are not partition functions of any known CFTs. We consider the ensemble average over all code theories, calculate the corresponding partition function, and discuss its possible holographic interpretation. The paper is written in a self-contained manner, and includes an extensive pedagogical introduction and many explicit examples.

Formulation and research of new fitness function in the genetic algorithm for maximum code coverage

In present paper we investigate an approach to intelligent support of the software white box testing process based on evolutionary paradigm. As part of this approach we solve the urgent problem of finding the optimal set of test data that provides maximum coverage of the code when it is used in the testing process. Traditionally, to solve this problem, an approach is used when the genetic algorithm is used to find the most adapted chromosome, which is a set of test data that ensures passage along the most complex (long) path in the code graph. Many data sets that provide maximum code coverage can be found by repeating this procedure multiple times with preliminary zeroing of the code operation weights corresponding to the chromosomes found earlier. Thus, the fitness function of the genetic algorithm has a simple form, but the process of finding all the data sets is quite long and non-optimal. In this paper, we study a different approach, when an additional component is initially included in the fitness function, which is responsible for the greatest possible difference in the paths of the population, along with a component responsible for the complexity of each path. The basic version of the algorithm is examined and it’s more effective modifications have been proposed to achieve the final goal of obtaining the optimal set of test data covering the flow graph in the least expensive way.

Hunting Vulnerable Smart Contracts via Graph Embedding Based Bytecode Matching

Smart contract vulnerabilities have attracted lots of concerns due to the resultant financial losses. Matching-based detection methods extrapolating known vulnerabilities to unknown have proven to be effective in other platforms. However, directly adopting the technique to smart contracts is obstructed by two issues, i.e., diversity of bytecode generation resulting from the rapid evolution of compilers and interference of noise code easily caused by the homogeneous business logics. To address the problems, we propose contract bytecode-oriented normalization and slicing techniques to augment bytecode matching. Specifically, we conduct data- and instruction-level normalizations to uniform the bytecode generated by different compilers, and enforce contract-specific slicing by tracking data- and control-flows with simulated bytecode executions to prune the noise code as far as possible. Based on the above techniques, we design an unsupervised graph embedding algorithm to encode the code graphs into quantitatively comparable vectors. The potentially vulnerable smart contracts can be identified by measuring the similarities between their vectors and known vulnerable ones. Our evaluations have shown the efficiency (0.47 seconds per contract on average), effectiveness (160 verified true positives) and high precision (91.95% for top-ranked). It is worth noting that, we also identify dozens of honeypot contracts, further demonstrating the capability of our method.

On subgroup perfect codes in Cayley graphs

A perfect code in a graph Γ=(V,E) is a subset C of V such that no two vertices in C are adjacent and every vertex in V∖C is adjacent to exactly one vertex in C. A subgroup H of a group G is called a subgroup perfect code of G if there exists a Cayley graph of G which admits H as a perfect code. Equivalently, H is a subgroup perfect code of G if there exists an inverse-closed subset A of G containing the identity element such that (A,H) is a tiling of G in the sense that every element of G can be uniquely expressed as the product of an element of A and an element of H. In this paper we obtain multiple results on subgroup perfect codes of finite groups, including a few necessary and sufficient conditions for a subgroup of a finite group to be a subgroup perfect code, a few results involving 2-subgroups in the study of subgroup perfect codes, and several results on subgroup perfect codes of metabelian groups, generalized dihedral groups, nilpotent groups and 2-groups.

Subgroup perfect codes in Cayley sum graphs

Let $$\Gamma $$ be a graph with vertex set V. If a subset C of V is independent in $$\Gamma $$ and every vertex in $$V\setminus C$$ is adjacent to exactly one vertex in C, then C is called a perfect code of $$\Gamma $$. Let G be a finite group and let S be a square-free normal subset of G. The Cayley sum graph of G with respect to S is a simple graph with vertex set G and two vertices x and y are adjacent if $$xy\in S$$. A subset C of G is called a perfect code of G if there exists a Cayley sum graph of G which admits C as a perfect code. In particular, if a subgroup of G is a perfect code of G, then the subgroup is called a subgroup perfect code of G. In this paper, we give a necessary and sufficient condition for a non-trivial subgroup of an abelian group with non-trivial Sylow 2-subgroup to be a subgroup perfect code of the group. This reduces the problem of determining when a given subgroup of an abelian group is a perfect code to the case of abelian 2-groups. As an application, we classify the abelian groups whose every non-trivial subgroup is a subgroup perfect code. Moreover, we determine all subgroup perfect codes of a cyclic group, a dihedral group and a generalized quaternion group.

Perfect codes in proper reduced power graphs of finite groups

Let Γ be a graph with vertex set A subset C of is a perfect code of Γ if C is an independent set such that every vertex in is adjacent to exactly one vertex in C. A subset T of is a total perfect code of Γ if every vertex of Γ is adjacent to exactly one vertex in T. Let G be a finite group. The proper reduced power graph of G is the undirected graph whose vertex set consists of all nonidentity elements, and two distinct vertices x and y are adjacent if or In this paper, we give a necessary and sufficient condition for a proper reduced power graph to contain a perfect code. In particular, we determine all perfect codes of a proper reduced power graph provided that the proper reduced power graph admits a perfect code. Moreover, we give some necessary conditions for a proper reduced power graph to contain a total perfect code. As applications, we determine the abelian groups and generalized quaternion groups whose proper reduced power graphs admit a total perfect code. We also characterize all finite groups whose proper reduced power graphs admit a total perfect code of size 2.