Let R=𝔽q+u𝔽q, where q is a power of a prime number p and u2=0. A triple cyclic code of length (r,s,t) over R is a set that can be partitioned into three parts that any cyclic shift of the coordinates of the three parts leaves the code invariant. These codes can be viewed as R[x]-submodules of R[x]/〈xr−1〉×R[x]/〈xs−1〉×R[x]/〈xt−1〉. In this paper, we study the generator polynomials and the minimum generating

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

In this paper, we give a proof of Parikh’s semilinear theorem via Dickson’s lemma. It is notable that our proof provides a clear separation between properties derived from Dickson’s lemma and tree decomposition for context-free grammars.

The interconnetion network plays an important role in a parallel system. To avoid the edge number of the interconnect network scaling rapidly with the increase of dimension and achieve a good balance of hardware costs and properties, this paper presents a new interconnection network called exchanged 3-ary n-cube (E3C). Compared with the 3-ary n-cube structures, E3C shows better performance in terms

The problem of the commutative equivalence of context-free and regular languages is studied. Conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated.

We consider the problem of fault-tolerant parallel search on an infinite line by n robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed 1 and can communicate wirelessly among themselves. However, among the n robots, there are f robots that exhibit byzantine faults. A faulty robot can fail to report the target even

Evaluating the importance of nodes for complex networks is an important part of invulnerability research. In this paper, node importance analysis is conducted in wheel-related networks by a method of evaluating node importance by node contraction based on network agglomeration in communication networks. Both degrees and positions of nodes are considered with this method. This method was also proved

We define a new strict and computable hierarchy for the family of automaton semigroups, which reflects the various asymptotic behaviors of the state-activity growth. This hierarchy extends that given by Sidki for automaton groups, and also gives new insights into the latter. Its exponential part coincides with a notion of entropy for some associated automata. We prove that the Order Problem is decidable

Linearizability is a commonly accepted consistency condition for concurrent objects. Filipović et al. show that linearizability is equivalent to observational refinement. However, linearizability does not permit concurrent objects to share memory spaces with their client programs. We show that linearizability (or observational refinement) can be broken even though a client program of an object accesses

Complementary prism graphs arise from the disjoint union of a graph G and its complement Ḡ by adding the edges of a perfect matching joining pairs of corresponding vertices of G and Ḡ. Classical graph problems such as Clique and Independent Set were proved to be NP-complete on such a class of graphs. In this work, we study the complexity of both problems on complementary prism graphs from the parameterized

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 n-dimensional hypercube contains a fault-free hamiltonian cycle, even if there are up to (4n−13) edge faults. Moreover, we give an example to

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

The inclusion problem is one of the common problems in real-time systems. The general form of this problem is undecidable; however, the time-bounded verification of inclusion problem is decidable for timed automata. In this study, we propose a new discretization technique to verify the inclusion problem. The proposed technique is applied to a non-Zeno timed automaton with an upper bound that does not

Large scale multiprocessor systems or multicomputer systems, taking interconnection networks as underlying topologies, have been widely used in the big data era. Fault tolerance is becoming an essential attribute in multiprocessor systems as the number of processors is getting larger. A connected graph G is called strong Menger (edge) connected if, for any two distinct vertices u and v, there are min{dG(u)

Let G be an undirected graph. An H-structure-cut (resp. H-substructure-cut) of G is a set of subgraphs of G, if any, whose deletion disconnects G, where the subgraphs deleted are isomorphic to a certain graph H (resp. where for any T′ of the subgraphs deleted, there is a subgraph T of G, isomorphic to H, such that T′ is a subgraph of T). G is superH|M-connected (resp. super sub-H|M-connected) if the

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

We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way — for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current software systems of formal language objects do not have a mechanism to define such objects. We define transducers in which transition labels involve what we call set specifications

The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a top-down interpretation of tree automata. In this paper, we propose new constructions based on Gluskov’s one and on the one by Ilie and Yu using a bottom-up interpretation. One of the main goals of this technique is to consider as a next step the links

Non-self-embedding grammars are a restriction of context-free grammars which does not allow to describe recursive structures and, hence, which characterizes only the class of regular languages. A double exponential gap in size from non-self-embedding grammars to deterministic finite automata is known. The same size gap is also known from constant-height pushdown automata and 1-limited automata to deterministic

Techniques are developed for creating new and general language families of only semilinear languages, and for showing families only contain semilinear languages. It is shown that for language families ℒ that are semilinear full trios, the smallest full AFL containing ℒ that is also closed under intersection with languages in NCM (where NCM is the family of languages accepted by NFAs augmented with

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

In this paper we address the question of synchronizing random automata in the critical settings of almost-group automata. Group automata are automata where all letters act as permutations on the set of states, and they are not synchronizing (unless they have one state). In almost-group automata, one of the letters acts as a permutation on n−1 states, and the others as permutations. We prove that this

The state complexity of a regular language Lm is the number m of states in a minimal deterministic finite automaton (DFA) accepting Lm. The state complexity of a regularity-preserving binary operation on regular languages is defined as the maximal state complexity of the result of the operation where the two operands range over all languages of state complexities ≤m and ≤n, respectively. We determine

Watson–Crick jumping finite automata work on tapes which are double stranded sequences of symbols similar to that of Watson–Crick automata. The double stranded sequence is scanned in a discontinuous manner. That is, after reading a double stranded string, the automata can jump over some subsequence and continue scanning depending on the rule. Some variants of such automata are 1-limited, No state,

A double occurrence word (DOW) is a word in which every symbol appears exactly twice. We define the symbol separation of a DOW w to be the number of letters between the two copies of a symbol, and the separation of w to be the sum of separations over all symbols in w. We then analyze relationship among size, reducibility and separation of DOWs. Specifically, we provide tight bounds of separations of

Diagnosability is an important factor in multiple-processor systems defined as the maximum number of faulty nodes that a system can recognize. In this paper, we propose a new form of diagnosability called non-inclusive diagnosability that requires all faulty sets to be non-inclusive. Furthermore, we study the non-inclusive diagnosability of hypercubes under the MM* model for n≥1.

The Steiner tree problem is one of the fundamental and classical problems in combinatorial optimization. In this paper we study this problem in the CONGESTED CLIQUE model (CCM) [29] of distributed computing. For the Steiner tree problem in the CCM, we consider that each vertex of the input graph is uniquely mapped to a processor and edges are naturally mapped to the links between the corresponding

The identification of node importance in complex networks is of theoretical and practical significance for improving network robustness and invulnerability. In this paper, the importance of each node is evaluated and important nodes are identified in cycles and related networks by node contraction method based on network agglomeration. This novel method considers both the degree and the position of

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 >25 is the sum of at most three natural numbers whose base-2 representation has an equal number of 0’s and 1’s.

We consider one of the weakest variants of cost register automata over a tropical semiring, namely copyless cost register automata over ℕ with updates using min and increments. We show that this model can simulate, in some sense, the runs of counter machines with zero-tests. We deduce that a number of problems pertaining to that model are undecidable, namely equivalence, upperboundedness, and semilinearity

We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric. We then consider three particular automata models (finite automata, transducers and automata weighted by integers here called sum-automata) and instantiate the generic logic for each of them. We

We consider an extension of tree automata on infinite trees that can use equality and disequality constraints between direct subtrees of a node. Recently, it has been shown that the emptiness problem for these kind of automata with a parity acceptance condition is decidable and that the corresponding class of languages is closed under Boolean operations. In this paper, we show that the class of languages

Motivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Černý conjecture by studying the primitivity phenomenon for sets of nonnegative matrices having neither zero-rows nor zero-columns. We formulate the primitivity process in the setting of a two-player probabilistic game and we make use of convex optimization

We continue our investigation [S. Beier, M. Holzer: Properties of right one-way jumping finite automata. In Proc. 20th DCFS, LNCS, 2018] on (right) one-way jumping finite automata (ROWJFAs), a variant of jumping automata, which is an automaton model for discontinuous information processing. Here we focus on decision problems for ROWJFAs. It turns out that most problems such as, e.g., emptiness, finiteness

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 PSPACE-complete. We introduce compressibility measures as a useful tool to classify the complexity of the intersection problem for certain classes

Transducers constitute a fundamental extension of automata. The class of regular word functions has recently emerged as an important class of word-to-word functions, characterized by means of (functional, or unambiguous, or deterministic) two-way transducers, copyless streaming string transducers, and MSO-definable graph transformations. A fundamental result in language theory is Kleene’s Theorem,

We investigate the problem of finding the visible pieces of a scene of objects from a specified viewpoint. In particular, we are interested in the design of an efficient hidden surface removal algorithm for a scene comprised of iso-oriented rectangles. We propose an algorithm where given a set of n iso-oriented rectangles we report all visible surfaces in O((n+k)logn) time and linear space, where k

Proxy Re-Encryption (PRE) is a cryptographic primitive that allows a proxy to turn an Alice’s ciphertext into a Bob’s ciphertext on the same plaintext. All of the PRE schemes are public key encryption and semantic security. Deterministic Public Key Encryption (D-PKE) provides an alternative to randomized public key encryption in various scenarios where the latter exhibits inherent drawbacks. In this

In this paper, firstly we extend the polynomial quotient modulo an odd prime p to its general case with modulo pr and r≥1. From the new quotient proposed, we define a class of pr+1-periodic binary threshold sequences. Then combining the Legendre symbol and Euler quotient modulo pr together, with the condition of 2p−1≢1(modp2), we present exact values of the linear complexity for p≡±3(mod8), and all

Forest algebras are defined for investigating languages of forests [ordered sequences] of unranked trees, where a node may have more than two [ordered] successors. They consist of two monoids, the horizontal and the vertical, with an action of the vertical monoid on the horizontal monoid, and a complementary axiom of faithfulness. A pseudovariety is a class of finite algebras of a given signature,

This paper proves that almost every n-vertex graph has the property that the multiset of its induced subgraphs on 3log2n vertices is sufficient to determine it up to isomorphism. That is, the probability that there exists two n-vertex graphs with the same multiset of 3log2n-vertex induced subgraphs goes to zero as n goes to infinity.

Parikh matrices as an extension of Parikh vectors are useful tools in arithmetizing words by numbers. This paper presents a further study of Parikh matrices by restricting the corresponding words to terms formed over a signature. Some M-equivalence preserving rewriting rules for such terms are introduced. A characterization of terms that are only M-equivalent to themselves is studied for binary signatures

Hypercubes and Fibonacci cubes are classical models for interconnection networks with interesting graph theoretic properties. We consider k-Fibonacci cubes, which we obtain as subgraphs of Fibonacci cubes by eliminating certain edges during the fundamental recursion phase of their construction. These graphs have the same number of vertices as Fibonacci cubes, but their edge sets are determined by a

A closed string contains a proper factor occurring as both a prefix and a suffix but not elsewhere in the string. Closed strings were introduced by Fici (WORDS 2011) as objects of combinatorial interest. This paper addresses a new problem by extending the closed string problem to the k-closed string problem, for which a level of approximation is permitted up to a number of Hamming distance errors,

Given a convex polygon with n vertices, we study the problem of identifying a triangle with its smallest side as large as possible among all the triangles that can be drawn inside the polygon. We show that at least one of the vertices of such a triangle must coincide with a vertex of the polygon. We also propose an O(n2) time algorithm to compute such a triangle inside the given convex polygon.

Connectivity and diagnosability are important parameters in measuring the reliability and fault-tolerance of an interconnection network G. The g-extra conditional faulty set F is a faulty vertex set such that every component of G−F has at least g+1 vertices. The g-extra connectivity κg(G) of a connected graph G is the minimum cardinality of a g-extra conditional faulty set F of G such that G−F is disconnected

Let a,k∈ℕ. By 1a:=a and ka:=ak−1a, we denote the k th iterate of the exponential function x↦ax evaluated at a, also known as tetration. We demonstrate how an algorithm for evaluating tetration modulo natural numbers N could be used to compute the prime factorization of N and provide heuristic arguments for the efficiency of this reduction. Additionally, we prove that the problem of computing the squarefree

We bring into attention the interplay between model theory of committed graphs (1-regular graphs) and their palindromic characteristic in the domain of formal languages. We prove some model theoretic properties of committed graphs and then give a characterization of them in the formal language domain using palindromes. We show in the first part of the paper that the theory of committed graphs and the

Frequency-hopping sequences (FHSs) with favorite partial Hamming correlation properties are intensively needed in many synchronization and multiple-access systems. Strictly optimal FHS sets are a kind of FHS sets which has optimal Hamming correlation for any correlation window. In this paper, firstly we present simplified representations of the generalized Lempel–Greenberger bound on the partial Hamming

One of the most essential classes of problems related to formal languages is the membership problem (also called word problem), i.e., to decide whether a given input word belongs to the language specified, e.g., by a generative grammar. For context-free languages the problem is solved efficiently by various well-known parsing algorithms. However, there are several important languages that are not context-free

Two-dimensional general row jumping finite automata were recently introduced as an interesting computational model for accepting two-dimensional languages. These automata are nondeterministic. They guess an order in which rows of the input array are read and they jump to the next row only after reading all symbols in the previous row. In each row, they choose, also nondeterministically, an order in

Multikey fully homomorphic encryption (MFHE) allows homomorphic operations between ciphertexts encrypted under different keys. In applications for secure multiparty computation (MPC) protocols, MFHE can be more advantageous than usual fully homomorphic encryption (FHE) since users do not need to agree with a common public key before the computation when using MFHE. In EUROCRYPT 2016, Mukherjee and

Let (n=pq,e=nβ) be an RSA public key with private exponent d=nδ, where p and q are large primes of the same bit size. At Eurocrypt 96, Coppersmith presented a polynomial-time algorithm for finding small roots of univariate modular equations based on lattice reduction and then succussed to factorize the RSA modulus. Since then, a series of attacks on the key equation ed−kϕ(n)=1 of RSA have been presented

In this paper, we consider a restricted covering problem, in which a convex polygon P with n vertices and an integer k are given, the objective is to cover the entire region of P using k congruent disks of minimum radius ropt, centered on the boundary of P. For k≥7 and any 𝜖>0, we propose an (1+7k+7𝜖k+𝜖)-factor approximation algorithm for this problem, which runs in O((n+k)(|logropt|+log⌈1𝜖⌉))

In 2013, the revelation of Edward Snowden rekindled cryptographic researchers’ interest in subversion attacks. Since then, many works have been carried out to explore the power of subversion attacks and feasible effective countermeasures as well. In this work, we investigate the study of subversion attacks against cloud auditing protocol, which has been well-known as useful primitive for secure cloud

Certificateless cryptosystems have attracted great interests in cryptographic research since its invention. Because compared with traditional public key cryptosystems or identity-based cryptosystems, they could not only simplify the certificate management, but also alleviate the key escrow problem. In certificateless cryptosystems, user revocation is a challenging issue. To address this issue, one

The topology properties of multi-processors interconnection networks are important to the performance of high performance computers. The hypercube network Qn has been proved to be one of the most popular interconnection networks. The n-dimensional locally twisted cube LTQn is an important variant of Qn. Fault diameter and wide diameter are two communication performance evaluation parameters of a network

We consider the maximum common connected edge subgraph problem and the maximum common connected induced subgraph problem for simple graphs with labeled vertices (or labeled edges). The former is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs. The latter is to find a common connected induced subgraph with the maximum number

This work answers some questions proposed by Bottoni, Labella, and Mitrana (Theoretical Computer Science 682, 2017) regarding the prefix–suffix reduction on words. The operation is defined as a reduction by one half of every square that is present as either a prefix or a suffix of a word, leading thus to a finite set of words associated to the starting one. The iterated case considers consecutive applications

In this paper we consider a new variant of Networks of Polarized Evolutionary Processors (NPEP) named Generalized Networks of Evolutionary Polarized Processors (GNPEP) and propose them as solvers of combinatorial optimization problems. Unlike the NPEP model, GNPEP uses its numerical evaluation over the processed data from a quantitative perspective, hence this model might be more suitable to solve