Computational Complexity

ONCE UPON A TIME there was a system administrator A of a computer network who , wanting to secure a area of the network, utilized what he called an heavy complexity Enigma Turing machine TM e to create or find passwords. The specifications of this Turing machine TM e were that it decided an exptime-complete complexity language of passwords L pe such that for each word length n, there existed exactly one password p n with word-length |p n |=n.

In this paper, graphs called overtrees are introduced and studied. These are connected graphs that contain a single simple cycle. Such graphs are connected graphs following the trees in terms of the number of edges. An overtree can be obtained from a tree by adding an edge to connect two non-adjacent vertices of a tree. The same class of graphs can also be defined as a class of graphs obtained from trees by replacing one vertex of the tree with a simple cycle. The main characteristics of overtrees are n, which is the number of vertices, and k, which is the number of vertices of a simple cycle (3 ≤ k ≤ n). A formula for the chromatic polynomial of an overtree is obtained, which is determined by the characteristics n and k only. As a consequence, it is obtained the formula for the chromatic function of a graph which is built from a tree by replacing some of its vertices (possibly all) with simple cycles of arbitrary length. It follows from these formulas that any overtree with an even-length cycle is two-colored, and with an odd-length cycle is three-colored. The same is true for graphs obtained from trees by replacing some vertices with simple cycles.

Cognitive radio is an emerging technology that aims for efficient spectrum usage. Cognitive radios have been proposed as a solution to the spectrum underutilization problem and have been proven to increase spectrum efficiency whilst providing opportunities for futuristic technologies. However, in this we are analyzing the performance of the cognitive radio based on cooperative spectrum sensing. Performance can be studied through by the energy and throughput setup. In the energy efficient setup, the number of cooperating cognitive radios is minimized for a k-out-of-N fusion rule with a constraint on the probability of detection and false alarm while in the throughput optimization setup, we maximize the throughput of the cognitive radio network, by deriving the optimal reporting time in a sensing time frame which is proportional to the number of cognitive users, subject to a constraint on the probability of detection. It is shown that both problems can be simplified to line search pro...

In this paper, we propose a new One-Way Hash Algorithm, which is also obtains better efficiency and security, compared with a particular conventional hash algorithm, Hash algorithm can be used to determine if two values are equal, a hash function maps keys to small values[1]. DILH algorithm using linear combination of matrices to find non-invertible matrix, that takes advantage about of the compact representation of a set of numbers in a matrix, and fast calculations. IndexTerms computational complexity, cryptography, hashing, collision, oneway algorithm, DILH, non-invertable matrix.

Cognitive Radio (CR) can be defined as a technology that allows users to change the transmission parameters as required to increase the spectrum efficiency. Because of this mechanism, some threats emerge. Two major threats are found in CR. The first is the Primary User Emulation Attack (PUEA), where the attacker is able to transmit at a forbidden time slot effectively, emulating the signals of the primary user. This makes all the system users believe that the spectrum is occupied by a good primary user.  The second threat is known as the spectrum sensing data falsification attack (SSDF). In this case, the attackers send false observation information, intentionally or unintentionally, to the fusion center (FC), causing it to make the wrong decision. In this study, the scheme presented  was based on a users' reputation for secure spectrum access in cognitive radio networks. Each Secondary User (SU) performs local sensing and then forwards the sensing results to the main fusion cen...

It is shown that a full-dimensional polytope P is uniquely determined by its r-dimensional fibre polytopes when $$r \ge 2$$ r ≥ 2 . Further, if $$r \ge 4$$ r ≥ 4 and the r-dimensional fibre polytopes are zonotopes, then P itself must be a zonotope.

In this article we analyze the internal structure of bare universal and negative quantifiers in Italian varieties, taking into consideration both synchronic and diachronic variation. It is proposed that bare quantifiers are not standard QPs with a null DP restrictor, but deficient items where the Q-portion is paired with a classifier expressing the [+/− human]-feature, more specifically a special type of light noun. Items of this type are overtly realized in languages like English and in some Italian varieties. The overt realization of these items appears to be related to the surface position of the QP, as is crucially shown by some varieties that allow both variants. The paper also discusses some cases where these classifiers are still lexically ambiguous between a full noun and a light noun.

We focus on the random generation of SAT instances that have properties similar to real-world instances. It is known that many industrial instances, even with a great number of variables, can be solved by a clever solver in a reasonable amount of time. This is not possible, in general, with classical randomly generated instances. We provide a different generation model of SAT instances, called scale-free random SAT instances. This is based on the use of a non-uniform probability distribution P(i)∼i−β to select variable i, where β is a parameter of the model. This results in formulas where the number of occurrences k of variables follows a power-law distribution P(k)∼k−δ, where δ=1+1/β. This property has been observed in most real-world SAT instances. For β=0, our model extends classical random SAT instances. We prove the existence of a SAT–UNSAT phase transition phenomenon for scale-free random 2-SAT instances with β<1/2 when the clause/variable ratio is m/n=1−2β(1−β)2. We also p...

Let γ (G) denote the cardinality of a minimum dominating set of a graph G. A well-known upper bound for γ (G), due to Berge (1962), states that for any graph G of order n and maximum degree∆, γ (G)≤ n−∆. Similarly, Hedetniemi and Laskar (1984) proved γc (G)≤ ...

The Symmetric Primal-Dual Symplex Pivot Decision Strategy (spdspds) is a novel iterative algorithm to solve linear programming problems. A symplex pivoting operation is considered simply as an exchange between a basic (dependent) variable and a non-basic (independent) variable, in the Goldman-Tucker Compact-Symmetric-Tableau (CST) which is a unique symmetric representation common to both the primal as well as the dual of a linear programming problem in its standard canonical form. From this viewpoint, the classical simplex pivoting operation of Dantzig may be considered as a restricted special case.