In digital systems such as fiber optical communications, the ratio between probability of errors of type 1→0 and 0→1 can be large. Practically, one can assume that only one type of error can occur. These errors are called asymmetric. Unidirectional errors differ from asymmetric type of errors; here both 1→0 and 0→1 type of errors are possible, but in any submitted codeword all the errors are of the

In this paper we consider Levin's notion of mutual information in infinite 0-1-sequences, as defined in Levin (1974) [6]. The respective information conservation inequalities were stated in that paper without proofs. Later some proofs appeared in the literature, however no proof of the probabilistic conservation inequality has been published yet. In this paper we prove that inequality and for the sake

We consider several computational problems related to conjugacy between subshifts of finite type, restricted to k-block codes: verifying a proposed k-block conjugacy, deciding if two shifts admit a k-block conjugacy, and reducing the representation size of a shift via a k-block conjugacy. We give a polynomial-time algorithm for verification, and show GI- and NP-hardness for deciding conjugacy and reducing

We consider the following online two-way trading problem: given some amount of money and a stock (security) of fluctuating prices, we want to perform a bounded number of speculative trades so as to make the most money. We assume a global fluctuation model, where global limits on the minimum and maximum possible prices are given. Previously, optimal algorithms were established in the deterministic case

We extend the notion of distributed decision in the framework of distributed network computing, inspired by both the polynomial hierarchy for Turing machines and recent results on so-called distributed graph automata. We show that, by using distributed decision mechanisms based on the interaction between a prover and a disprover, the size of the certificates distributed to the nodes for certifying

Given a CNF formula Φ with clauses C1,…,Cm and variables V={x1,…,xn}, a truth assignment a:V→{0,1} of Φ leads to a clause sequence σΦ(a)=(C1(a),…,Cm(a))∈{0,1}m where Ci(a)=1 if clause Ci evaluates to 1 under assignment a, otherwise Ci(a)=0. The set of all possible clause sequences carries a lot of information on the formula, e.g. SAT, MAX-SAT and MIN-SAT can be encoded in terms of finding a clause

Spanning trees T1,T2,…,Tk (k⩾2) in a network are called completely independent spanning trees (CISTs for short) if they are pairwise edge-disjoint and inner-node-disjoint. Particularly, if k=2, the two CISTs are called a dual-CIST. Hasunuma (2002) [8] proved that the problem of determining whether there exists a dual-CIST in a network is NP-complete. Tapolcai (2013) [20] showed that a dual-CIST has

In this paper, we consider the reconfiguration problem of integer linear systems. In this problem, we are given an integer linear system I and two feasible solutions s and t of I, and then asked to transform s to t by changing a value of only one variable at a time, while maintaining a feasible solution of I throughout. Z(I) for I is the complexity index introduced by Kimura and Makino (Discrete Applied

The status of a vertex v in a connected graph is the sum of the distances from v to all other vertices. The status sequence of a connected graph is the list of the statuses of all the vertices of the graph. In this paper we investigate the status sequences of trees. Particularly, we show that it is NP-complete to decide whether there exists a tree that has a given sequence of integers as its status

Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks. In particular, one needs to distinguish different networks and determine whether one network is contained in another. In this paper, we introduce cherry-picking networks, a class of networks that can be reduced by a so-called

Groups of automaton permutations over finite alphabets are considered. Finite automata over minimal possible alphabets that define amalgamated free products of finite cyclic groups are constructed. For any prime p the case of amalgamated free products of cyclic p-groups is considered. In this case it is shown that elements defined by constructed finite automata belong to p-Sylow subgroups of the group

The concept of the locating-chromatic number for graphs was introduced by Chartrand et al. (2002). In this paper, we propose an algorithm to determine the upper bound of the locating-chromatic number of any tree. This algorithm works much better than the one given by Furuya and Matsumoto (2019).

It is shown that conflict complexity of every total Boolean function, recently introduced in [1] to prove a composition theorem of randomized decision tree complexity, is at least a half of its block sensitivity. The paper proposes to compare conflict complexity with certificate complexity and explains why it could be interesting.

Bisimulation metrics are a successful instrument used to estimate the behavioural distance between probabilistic concurrent systems. They have been defined in both discrete and continuous state space models. However, the weak semantics approach, where non-observable actions are abstracted away, has been adopted only in the discrete case. In this paper we fill this gap and provide a weak bisimulation

We extend the notion of k-automatic sequences to Ostrowski-automatic sequences, and develop a procedure to computationally decide certain combinatorial and enumeration questions about such sequences that can be expressed as predicates in first-order logic. Our primary contribution is the design and implementation of an adder recognizing addition in a generalized Ostrowski numeration system. We also

The longest cycle problem is the problem of finding a cycle with maximal vertices in a graph. Although it is solvable in polynomial time on few trivial graph classes, the longest cycle problem is well known as NP-complete. A lot of efforts have been devoted to the longest cycle problem. To the best of our knowledge however, there are no polynomial algorithms that can solve any of the non-trivial graph

We propose a new design technique for constructing secret sharing schemes over a potentially infinite set of participants. Our findings leverage on a nice property of secret sharing schemes for finite sets of participants based on the chinese remainder theorem: the possibility of providing shares of different sizes to participants. We successful apply the technique to the (3,∞)-threshold access structure

The subspace approximation problem with outliers, for given n points in d dimensions x1,x2,…,xn∈Rd, an integer 1≤k≤d, and an outlier parameter 0≤α≤1, is to find a k-dimensional linear subspace of Rd that minimizes the sum of squared distances to its nearest (1−α)n points. More generally, the ℓp subspace approximation problem with outliers minimizes the sum of p-th powers of distances instead of the

Range partitioning is a typical and mostly used data partitioning method and has became a core operation in most of big data computing platforms. Given an input L of N data items admitting a total order, the goal of range partitioning is to divide the whole input into k ranges containing the same number of data items. There is a trivial lower bound Ω(N) for the exact partitioning algorithms, since

Diversity is a concept relevant to numerous domains of research varying from ecology, to information theory, and to economics, to cite a few. It is a notion that is steadily gaining attention in the information retrieval, network analysis, and artificial neural networks communities. While the use of diversity measures in network-structured data counts a growing number of applications, no clear and

BP maximization problem has many applications in machine learning and data science. It can be described as maximizing the sum of a suBmodular function and a suPermodular function(BP) under some constraints, where both functions are nonnegative and monotonic. In this paper, we consider two online cases. The first is a BP maximization problem subject to a uniform matroid constraint when the items arrive

The game of cops and robbers is a well-known game played on graphs. In this paper we consider the straight-ahead orientations of 4-regular quadrangulations of the torus and the Klein bottle and we prove that their cop number is bounded by a constant. We also show that the cop number of every k-regularly oriented toroidal grid is at most 13.

Among the challenges of the big data era, the analysis of high-dimensional data is still an open research area. As a result, several multidimensional projection techniques have been developed to reduce data dimensionality, becoming important visualization and visual analytics tools. In order to ensure the quality of projections, it is necessary to assess the low-dimensional embeddings by using different

Prefix normal words are binary words with the property that no factor has more 1s than the prefix of the same length. Finite prefix normal words were introduced in [Fici and Lipták, DLT 2011]. In this paper, we study infinite prefix normal words and explore their relationship to some known classes of infinite binary words. In particular, we establish a connection between prefix normal words and Sturmian

Whereas Perl-compatible regular expression matchers typically exhibit some variation of leftmost-greedy semantics, those conforming to the posix standard are prescribed leftmost-longest semantics. However, the posix standard leaves some room for interpretation, and Fowler and Kuklewicz have done experimental work to confirm differences between various posix matchers. The Boost library has an interesting

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. It is known that the length of the longest palindromic substrings (LPSs) of a given string T of length n can be computed in O(n) time by Manacher's algorithm [J. ACM '75]. In this paper, we consider the problem of finding the LPS after the string is edited

We seek constructions of general-purpose immunizers that take arbitrary cryptographic primitives, and transform them into ones that withstand a powerful “malicious but proud” adversary, who attempts to break security by possibly subverting the implementation of all algorithms (including the immunizer itself!), while trying not to be detected. This question is motivated by the recent evidence of cryptographic

The Burrows-Wheeler-Transform (BWT) is a reversible string transformation which plays a central role in text compression and is fundamental in many modern bioinformatics applications. The BWT is a permutation of the characters, which is in general better compressible and allows to answer several different query types more efficiently than the original string. It is easy to see that not every string

We consider the sum of digits functions for both base phi, and for the Zeckendorf expansion of the natural numbers. For both sum of digits functions we present morphisms on infinite alphabets such that these functions viewed as infinite words are letter-to-letter projections of fixed points of these morphisms. We characterize the first differences of both functions a) with generalized Beatty sequences

We consider graph-based hedonic games such as simple symmetric fractional hedonic games and social distance games, where a group of utility maximizing players have hedonic preferences over the players' set, and wish to be partitioned into clusters so that they are grouped together with players they prefer. The players are nodes in a connected graph and their preferences are defined so that shorter

In this paper, three impossible results for one-way permutations in the quantum world are obtained. The first one is the impossibility of fully black-box reduction from one-way permutations to one-way functions in a quantum setting. The two-oracle method is the main technique adopted in our proof that was originally proposed by Hsiao and Reyzin, and extended later to a quantum setting by Hosoyamada

We consider bounds for the temperatures of combinatorial games. Our first result gives an upper bound on the temperatures of the positions of a ruleset in terms of the lengths of the confusion intervals of these positions. We give an example to show that this bound is tight. Our second main result is a method to find a bound for the lengths of the confusion intervals. This pair of results constitutes

The equitable list tree-coloring model is an useful tool to formulate a structure decomposition problem on the complex network with some security considerations. In this paper, it is proved that the equitable list vertex arboricity of every graph with treewidth ω is at most ⌈Δ(G)/2⌉+ω−2 whenever Δ(G)≥4ω+1, and moreover, if such a graph does not contain K3,3 as a topological minor, then its equitable

Let Fk be the family of the binary words containing exactly k 0s. Ilić, Klavžar and Rho constructed an infinite subfamily of 2-isometric but not 3-isometric words among F2. Wei, Yang and Wang further found there are 2-isometric but not 3-isometric words among Fk for all k∈{2,5,6} and k≥8, and they conjectured that F1, F3, F4 and F7 are the only families in which there are not 2-isometric but not 3-isometric

The k-dimensional data center network with n-port switches, denoted by Dk,n, has been proposed for data centers as a server centric network structure. Wang et al. had proved that Dk,n is Hamiltonian-connected for k≥0 and n≥2 except for (k,n)=(1,2). In this paper, we prove that for any edge (u,v) in a complete subgraph Kn of Dk,n, there is a cycle of every length from 3 to |V(Dk,n)| passing through

We consider a scheduling game on parallel related machines, in which jobs try to minimize their completion time by choosing a machine to be processed on. Each machine uses an individual priority list to decide on the order according to which the jobs on the machine are processed. We prove that it is NP-hard to decide if a pure Nash equilibrium exists and characterize four classes of instances in which

We study interactive proof systems (IPSes) in a strong adversarial setting where the machines of honest parties might be corrupted and under control of the adversary. Our aim is to answer the following, seemingly paradoxical, questions: • Can Peggy convince Vic of the veracity of an NP statement, without leaking any information about the witness even in case Vic is malicious and Peggy does not trust

We introduce a notion of coded equivalence in one-sided topological Markov shifts. The notion is inspired by coding theory. One-sided topological conjugacy implies coded equivalence. We will show that coded equivalence implies continuous orbit equivalence of one-sided topological Markov shifts.

Collaborative text editing systems allow users to concurrently edit a shared document, inserting and deleting elements (e.g., characters or lines). There are a number of protocols for collaborative text editing, but so far there has been no abstract, high-level specification of their desired behavior, which is decoupled from their actual implementation. Several of these protocols have been shown not

In this paper we consider the digraph width measures directed path-width, directed tree-width, directed feedback vertex set number, directed feedback arc set number, cycle rank, DAG-depth, DAG-width and Kelly-width of recursively defined digraphs. While the minimization problem for these width measures is generally NP-hard, we prove that it is computable in linear time for all these parameters, except

The stable set associated to a given set S of nonerasing endomorphisms or substitutions is the set of all right infinite words that can be indefinitely desubstituted over S. This notion generalizes the notion of sets of fixed points of morphisms. It is linked to S-adicity and to property preserving morphisms. Two main questions are considered. Which known sets of infinite words are stable sets? Which

A hidden graph is a graph whose edge set is hidden. A distance oracle of a graph G is a black-box that receives two vertices of G and outputs the distance between the two vertices. Given a hidden graph, the reconstruction problem aims to identify the edges of the hidden graph by accessing a distance oracle, and the verification problem aims to check whether the hidden graph is equal to another given

An injective k-coloring of a graph G is a mapping f:V(G)→{1,2,…,k} such that for any two vertices v1,v2∈V(G), f(v1)≠f(v2) if N(v1)∩N(v2)≠∅. The injective chromatic number of a graph G, denoted by χi(G), is the smallest integer k such that G has an injective k-coloring. In this paper, we prove that for a Halin graph G, χi(G)≤Δ(G)+2. Moreover, χi(G)≤Δ(G)+1 if Δ(G)≥6. Also, we show that for a triangle-free

A generalisation of Scott's information systems [15] is presented that captures exactly all L-domains. The global consistency predicate in Scott's definition is relativised in such a way that there is a consistency predicate for each atomic proposition (token) saying which finite sets of such statements express information that is consistent with the given statement. It is shown that the states of

A well-designed task recommendation framework aims to protect the data quality as well as increase the task execution results. However, current crowdsourcing systems ignore the fact that there are few duplicate task expectations because of the budget limitation in realistic conditions. Besides, a practical crowdsourcing system needs to recommend new tasks without previous knowledge about the concrete

Streaming tree transducers with single-use restriction (STTsurs) were introduced by Alur and D'Antoni as an analyzable, executable, and expressive model for transforming unranked ordered trees in a single pass. The equivalence problem of STTsurs is decidable because their class is as expressive as the class of MSO-definable tree transformations. In this paper, we present streaming ranked-tree-to-string

In this paper, we propose an architecture of oritatami systems, a mathematical model of RNA cotranscriptional folding, with which one can simulate an arbitrary nondeterministic finite automaton (NFA) in a unified manner. The oritatami system is known to be Turing-universal but the simulation available so far requires 542 bead types and O(t4log2⁡t) steps in order to simulate t steps of a Turing machine

DS decomposition plays an important role in set function optimization problem, because there is DS decomposition for any set function. How to design an efficient and effective algorithm to solve maximizing DS decomposition is a heated problem. In this work, we propose a framework called Parameter Conditioned Greedy Algorithm which has a deterministic version and two random versions. In more detail

AGM's belief revision is one of the main paradigms in the study of belief change operations. Recently, several logics for belief and information change have been proposed in the literature and used to encode belief change operations in rich and expressive semantic frameworks. While the connections of AGM-like operations and their encoding in dynamic doxastic logics have been studied before by the work

In this paper we propose an algorithm for the approximate k-Nearest-Neighbors problem. According to the existing researches, there are two kinds of approximation criteria. One is the distance criterion, and the other is the recall criterion. All former algorithms suffer the problem that there are no theoretical guarantees for the two approximation criteria. The algorithm proposed in this paper unifies

Influence maximization (IM) is a widely studied problem in social networks, which aims at finding a seed set with limited size that can maximize the expected number of influenced users. However, existing studies haven't considered the matching relationship, which refers to such scenarios that influenced users seek matched partners among the influenced users, such as time matching with friends to watch

We are interested in regular expressions 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. Labelled graphs (transducers and automata) with alphabet-invariant and user-defined labels were

A two-dimensional automaton has a read-only input head that moves in four directions on a finite array of cells labeled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves, while a two-way two-dimensional automaton can only move downward and rightward. We show that the language emptiness problem for unary three-way nondeterministic two-dimensional

Supply energy to battery-powered sensor devices by deploying wireless chargers is a promising way to prolong the operation time of wireless sensor networks, and has attracted much attention recently. Existing works focus on maximizing the total received charging power of the network. However, this may face the unbalanced energy allocation problem, which is not beneficial to prolong the operation time

This paper proposes a dynamic approach of specification mining for Propositional Projection Temporal Logic (PPTL). To this end, a pattern library is built to collect some common temporal relation among events. Further, several algorithms of specification mining for PPTL are designed. With our approach, PPTL specifications are mined from a trace set of a target program by using patterns in the library

Given a two-dimensional array of symbols and a picture language over a finite alphabet, we investigate how to find rectangular subarrays that belong to the picture language. Two-dimensional pattern matching problems can be formulated by interpreting subarrays as matches and picture languages as patterns. We formulate four particular problems – finding maximum, minimum, any or all match(es) – and describe

In this work, we investigate online bicriteria algorithms that consider both coverage and cost in the team formation problem, which selects a set of experts with the objective of maximizing the difference of two set functions f−ℓ, where function f is non-negative normalized monotone approximately submodular, and function ℓ is non-negative linear. By exploiting the problem's combinatorial structure

Let V be a finite set of vertices in the plane and S be a finite set of polygonal obstacles, where the vertices of S are in V. We show how to construct a plane 2-spanner of the visibility graph of V with respect to S. As this graph can have unbounded degree, we modify it in three easy-to-follow steps, in order to bound the degree to 7 at the cost of slightly increasing the spanning ratio to 6.

An equitable tree-k-coloring of a graph is a vertex k-coloring such that each color class induces a forest and the size of any two color classes differ by at most one. In this work, we show that every interval graph G has an equitable tree-k-coloring for any integer k≥⌈(Δ(G)+1)/2⌉, solving a conjecture of Wu, Zhang and Li (2013) for interval graphs, and furthermore, give a linear-time algorithm for

This paper deals with the control problem of right linear grammars with unknown behaviors (RLUBs, for short) in which derivation behavior is not determined completely. In particular, we discuss on the size of control alphabets of control systems which regulate RLUBs in order to generate a target string only. We contribute to the reduction of control alphabet size from O(l) to O(log⁡l), where l is a