Dense Complete Set For NP

A sparse language is a formal language such that the number of strings of length $n$ is bounded by a polynomial function of $n$. We create a class with the opposite definition, that is a class of languages that are dense instead of sparse. We define a dense language on $m$ as a formal language (a set of binary strings) where there exists a positive integer $n_{0}$ such that the counting of the number of strings of length $n \geq n_{0}$ in the language is greater than or equal to $2^{n - m}$ where $m$ is a real number and $0 < m \leq 1$. We call the complexity class of all dense languages on $m$ as $DENSE(m)$. We prove that there exists an $\textit{NP--complete}$ problem that belongs to $DENSE(m)$ for every possible value of $0 < m \leq 1$.

Dense Complete Set For NP

A sparse language is a formal language such that the number of strings of length $n$ is bounded by a polynomial function of $n$. We create a class with the opposite definition, that is a class of languages that are dense instead of sparse. We define a dense language on $m$ as a formal language (a set of binary strings) where there exists a positive integer $n_{0}$ such that the counting of the number of strings of length $n \geq n_{0}$ in the language is greater than or equal to $2^{n - m}$ where $m$ is a real number and $0 < m \leq 1$. We call the complexity class of all dense languages on $m$ as $DENSE(m)$. We prove that there exists an $\textit{NP--complete}$ problem that belongs to $DENSE(m)$ for every possible value of $0 < m \leq 1$.

Succinct Encoding of Binary Strings Representing Triangulations

We consider the problem of designing a succinct data structure for representing the connectivity of planar triangulations. The main result is a new succinct encoding achieving the information-theory optimal bound of 3.24 bits per vertex, while allowing efficient navigation. Our representation is based on the bijection of Poulalhon and Schaeffer (Algorithmica, 46(3):505–527, 2006) that defines a mapping between planar triangulations and a special class of spanning trees, called PS-trees. The proposed solution differs from previous approaches in that operations in planar triangulations are reduced to operations in particular parentheses sequences encoding PS-trees. Existing methods to handle balanced parentheses sequences have to be combined and extended to operate on such specific sequences, essentially for retrieving matching elements. The new encoding supports extracting the d neighbors of a query vertex in O(d) time and testing adjacency between two vertices in O(1) time. Additionally, we provide an implementation of our proposed data structure. In the experimental evaluation, our representation reaches up to 7.35 bits per vertex, improving the space usage of state-of-the-art implementations for planar embeddings.

Alternate Lucas Cubes

We introduce alternate Lucas cubes, a new family of graphs designed as an alternative for the well known Lucas cubes. These interconnection networks are subgraphs of Fibonacci cubes and have a useful fundamental decomposition similar to the one for Fibonacci cubes. The vertices of alternate Lucas cubes are constructed from binary strings that are encodings of Lucas representation of integers. As well as ordinary hypercubes, Fibonacci cubes and Lucas cubes, alternate Lucas cubes have several interesting structural and enumerative properties. In this paper we study some of these properties. Specifically, we give the fundamental decomposition giving the recursive structure, determine the number of edges, number of vertices by weight, the distribution of the degrees; as well as the properties of induced hypercubes, [Formula: see text]-cube polynomials and maximal hypercube polynomials. We also obtain the irregularity polynomials of this family of graphs, determine the conditions for Hamiltonicity, and calculate metric properties such as the radius, diameter, and the center.

Formal Logic of Cellular Automata

This paper develops a formal logic, named L CA , targeting modeling of one-dimensional binary cellular automata. We first develop the syntax of L CA , then give semantics to L CA in the domain of all binary strings. Then the elementary cellular automata and four-neighborhood binary cellular automata are shown as models of the logic. These instances point out that there are other models of L CA . Finally it is proved that any one-dimensional binary cellular automaton is a model of the proposed logic.

Reversible and Plausibly Deniable Covert Channels in One-Time Passwords Based on Hash Chains

Covert channels enable stealthy communications over innocent appearing carriers. They are increasingly applied in the network context. However, little work is available that exploits cryptographic primitives in the networking context to establish such covert communications. We present a covert channel between two devices where one device authenticates itself with Lamport’s one-time passwords based on a cryptographic hash function. Our channel enables plausible deniability jointly with reversibility and is applicable in different contexts, such as traditional TCP/IP networks, CPS/IoT communication, blockchain-driven systems and local inter-process communications that apply hash chains. We also present countermeasures to detect the presence of such a covert channel, which are non-trivial because hash values are random-looking binary strings, so that deviations are not likely to be detected. We report on experimental results with MD5 and SHA-3 hash functions for two covert channel variants running in a localhost setup. In particular, we evaluate the channels’ time performance, conduct statistical tests using the NIST suite and run a test for matching hash values between legitimate and covert environments to determine our channels’ stealthiness.

Secure Digital Databases using Watermarking based on English-Character Attributes

Introduction: The single space and the double space (DS). In this procedure, an image is used to watermark a digital database, where the image bytes are divided into binary strings that block the text attributes of the selected database, we proposed an algorithm to defend against four common database attacks. Objective: Perform the watermark is Embedding and makes extraction of the watermark. We also describe the principal of the Embedding and extraction the watermark. Methods: The procedure to extract the watermark does not require knowledge of the original database that does not carry the same watermark. This feature is extremely important because it allows the discovery of a watermark in a copy of the original database, regardless of the subsequent updates to the asset. The extraction procedure is a direct reflection of the procedure used to embed the watermark is six steps. Results: Using new algorithm ability to develop a database watermark that would make it difficult for an attacker to remove or change the watermark without discovering the value of the object. To be judged effective, the database algorithm had to be able to create a strong enough watermark that could sustain the security of the database in the face of the following four types of attack: deletion of a sub-dataset, addition of a sub-dataset. Conclusion: The performance of the proposed algorithm was assessed in respect of its ability to defend the database against four common attacks for all tuples selection.