Reliability of interconnection networks is important to design multiprocessor systems. The extra edge connectivity and component edge connectivity are two parameters for the reliability evaluation. The [Formula: see text]-extra edge connectivity [Formula: see text] is the cardinality of the minimum extra edge cut [Formula: see text] such that [Formula: see text] is not connected and each component of [Formula: see text] has at least [Formula: see text] vertices. The [Formula: see text]-component edge connectivity [Formula: see text] of a graph [Formula: see text] is the minimum edge number of a set [Formula: see text] such that [Formula: see text] is not connected and [Formula: see text] has at least [Formula: see text] components. In this paper, we find the relation of extra edge connectivity and component edge connectivity for regular networks. As an application, we determine the component edge connectivity of BC networks, [Formula: see text]-ary [Formula: see text]-cubes, enhanced hypercubes.

For a simple, undirected graph [Formula: see text], a function [Formula: see text] which satisfies the following conditions is called an outer-independent total Roman dominating function (OITRDF) of [Formula: see text] with weight [Formula: see text]. (C1) For all [Formula: see text] with [Formula: see text] there exists a vertex [Formula: see text] such that [Formula: see text] and [Formula: see text], (C2) The induced subgraph with vertex set [Formula: see text] has no isolated vertices and (C3) The induced subgraph with vertex set [Formula: see text] is independent. For a graph [Formula: see text], the smallest possible weight of an OITRDF of [Formula: see text] which is denoted by [Formula: see text], is known as the outer-independent total Roman domination number of [Formula: see text]. The problem of determining [Formula: see text] of a graph [Formula: see text] is called minimum outer-independent total Roman domination problem (MOITRDP). In this article, we show that the problem of deciding if [Formula: see text] has an OITRDF of weight at most [Formula: see text] for bipartite graphs and split graphs, a subclass of chordal graphs is NP-complete. We also show that MOITRDP is linear time solvable for connected threshold graphs and bounded treewidth graphs. Finally, we show that the domination and outer-independent total Roman domination problems are not equivalent in computational complexity aspects.

In this paper, we study the fault-tolerant capability of hypercubes with respect to the hamiltonian property based on the concept of forbidden faulty sets. We show, with the assumption that each vertex is incident with at least three fault-free edges, that an [Formula: see text]-dimensional hypercube contains a fault-free hamiltonian cycle, even if there are up to [Formula: see text] edge faults. Moreover, we give an example to show that the result is optimal with respect to the number of edge faults tolerated.

The Cramer-Shoup (CS) like cryptosystem based on index exchangeable family (IEF) construction is a novel scheme introduced in Asiaccs 2016 by Li et al. Its versatility was illustrated by building two public key encryption (PKE) schemes, a cramer-shoup encryption scheme based on IEFs, as well as an outsourcing technique based on non-abelian analog. However, the two schemes are not secure over the recommended linear group of Li et al. For them, we provide a new key-recovery attack by solving a linear equation respectively. Furthermore, we peel off complex encryption and decryption processes and propose more than three different attack methods. Finally, we give a corresponding example to illustrate the correctness of our attack methods. Our attack methods break an instance of claiming 80 bit security less than one minute under a personal computer.

We examine the accepting state complexity, i.e., the minimal number of accepting states of deterministic finite automata for languages resulting from unary and binary operations on languages with accepting state complexity given as a parameter. This is a continuation of the work of [J. Dassow: On the number of accepting states of finite automata, J. Autom., Lang. Comb., 21, 2016]. We solve most of the open problems mentioned thereof. In particular, we consider the operations of intersection, symmetric difference, right and left quotients, reversal, and permutation (on finite languages), where we obtain precise ranges of accepting state complexities. We also consider symmetric difference on unary finite languages where we obtain a non-contiguous range of accepting state complexities.

It is well known that reversible finite automata do not accept all regular languages, that reversible pushdown automata do not accept all deterministic context-free languages, and that reversible queue automata are less powerful than deterministic real-time queue automata. It is of significant interest from both a practical and theoretical point of view to close these gaps. We here extend these reversible models by a preprocessing unit which is basically a reversible injective and length-preserving finite state transducer. It turns out that preprocessing the input using such weak devices increases the computational power of reversible deterministic finite automata to the acceptance of all regular languages, whereas for reversible pushdown automata the accepted family of languages lies strictly in between the reversible deterministic context-free languages and the real-time deterministic context-free languages. For reversible queue automata the preprocessing of the input leads to machines that are stronger than real-time reversible queue automata, but less powerful than real-time deterministic (irreversible) queue automata. Moreover, it is shown that the computational power of all three types of machines is not changed by allowing the preprocessing finite state transducer to work irreversibly. Finally, we examine the closure properties of the family of languages accepted by such machines.

Optimal codebooks meeting the Welch bound with equality are desirable in many areas, such as direct spread code division multiple access communications, compressed sensing and so on. However, it is difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly meeting the Welch bound. In this paper, we introduce a generic construction of codebooks using generalized bent functions from [Formula: see text] to [Formula: see text], where [Formula: see text] is a prime and [Formula: see text] is a positive integer with [Formula: see text]. With this construction, we obtain two new families of codebooks nearly meeting the Welch bound. These codebooks have new parameters and could have a small alphabet size. In particular, a class of regular generalized bent functions from [Formula: see text] to [Formula: see text] is presented.

We prove some new theorems in additive number theory, using novel techniques from automata theory and formal languages. As an example of our method, we prove that every natural number [Formula: see text] is the sum of at most three natural numbers whose base-[Formula: see text] representation has an equal number of [Formula: see text]’s and [Formula: see text]’s.

The intersection problem for finite semigroups asks, given a set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. In previous work, it was shown that is problem is [Formula: see text]-complete. We introduce compressibility measures as a useful tool to classify the complexity of the intersection problem for certain classes of finite semigroups. Using this framework, we obtain a new and simple proof that for groups and for commutative semigroups, the problem (as well as the variant where the languages are represented by finite automata) is contained in [Formula: see text]. We uncover certain structural and non-structural properties determining the complexity of the intersection problem for varieties of semigroups containing only trivial submonoids. More specifically, we prove [Formula: see text]-hardness for classes of semigroups having a property called unbounded order and for the class of all nilpotent semigroups of bounded order. On the contrary, we show that bounded order and commutativity imply decidability in poly-logarithmic time on alternating random-access Turing machines with a single alternation. We also establish connections to the monoid variant of the problem.

In this paper, firstly we extend the polynomial quotient modulo an odd prime [Formula: see text] to its general case with modulo [Formula: see text] and [Formula: see text]. From the new quotient proposed, we define a class of [Formula: see text]-periodic binary threshold sequences. Then combining the Legendre symbol and Euler quotient modulo [Formula: see text] together, with the condition of [Formula: see text], we present exact values of the linear complexity for [Formula: see text], and all the possible values of the linear complexity for [Formula: see text]. The linear complexity is very close to the period and is of desired value for cryptographic purpose. Our results extend the linear complexity results of the corresponding [Formula: see text]-periodic binary sequences in earlier work.