Theoretical Computer Science

DNA computing, or, more generally, molecular computing, is an exciting fast developing interdisciplinary area. Research in this area concerns theory, experiments, and applications of DNA computing. In this paper, we demonstrate the theoretical developments by discussing a number of selected topics. We also give an introduction to the basic structure of DNA and the basic DNA processing tools.

We survey and extend the work on the paradigm called "computing by observing". Its central feature is that one considers the behavior of an evolving system as the result of a computation. To this purpose an external observer records this behavior. In this way, several computational trade-offs between the observer and the observed system can be determined. It has turned out that the observed behavior of computationally simple systems can be very complex, when an appropriate observer is used. For example, a restricted version of context-free grammars with regular observers suffices to obtain computational completeness. As a second instantiation presented here, we apply an observer to sticker systems, an abstract model of DNA computing. Finally, we introduce and investigate the case where the observers can read only one measure of the observed system (e.g., mass or temperature) modeling in this way, limitations in the observation of real physical systems. Finally a research perspective on the topic is presented.

In this paper, a structural property of the set of lozenge tilings of a 2n-gon is highlighted. We introduce a simple combinatorial value called Hamming-distance, which is a lower bound for the flipdistance (i.e. the number of necessary local transformations involving three lozenges) between two given tilings. It is here proven that, for n ≤ 4, the flip-distance between two tilings is equal to the Hamming-distance. Conversely, for n ≥ 6, We show that there is some deficient pairs of tilings for which the flip connection needs more flips than the combinatorial lower bound indicates.

We consider a scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine. The input is a set of n jobs J = {J 1 , . . . , J n }. Each job, J j , is associated with an interval [s j , c j ] along which it should be processed. Also given is the parallelism parameter g ≥ 1, which is the maximal number of jobs that can be processed simultaneously by a single machine. Each machine operates along a contiguous time interval, called its busy interval, which contains all the intervals corresponding to the jobs it processes. The goal is to assign the jobs to machines such that the total busy time of the machines is minimized.

Data exchange is the problem of taking data structured under a source schema and creating an instance of a target schema that reflects the source data as accurately as possible. In this paper, we address foundational and algorithmic issues related to the semantics of data exchange and to the query answering problem in the context of data exchange. These issues arise because, given a source instance, there may be many target instances that satisfy the constraints of the data exchange problem.

We examine questions involving nondeterministic finite automata where all states are final, initial, or both initial and final. First, we prove hardness results for the nonuniversality and inequivalence problems for these NFAs. Next, we characterize the languages accepted. Finally, we discuss some state complexity problems involving such automata.

We consider the complexity of the traveling tournament problem, which is a well-known benchmark problem in tournament timetabling. The problem was supposed to be computationally hard ever since its proposal in 2001. Recently, the first NP-completeness proof has been given for the variant of the problem were no constraints on the number of consecutive home games or away games of a team are considered. The complexity of the original traveling tournament problem including these constraints, however, is still open. In this paper, we show that this variant of the problem is strongly NP-complete when the upper bound on the maximal number of consecutive away games is set to 3.

For a given graph G over n vertices, let OPT G denote the size of an optimal solution in G of a particular minimization problem (e.g., the size of a minimum vertex cover). A randomized algorithm will be called an α-approximation algorithm with an additive error for this minimization problem, if for any given additive error parameter > 0 it computes a value OPT such that, with probability at least 2/3, it holds that OPT G ≤ OPT ≤ α · OPT G + n .

In combinatorics and analysis of algorithms a Poisson version of a problem (henceforth called Poisson model or poissonization) is often easier to solve than the original one, which we name here the Bernoulli model. Poissonization is a technique that replaces the original input (e.g., think of balls thrown into urns) by a Poisson process (e.g., think of balls arriving according to a Poisson process into urns). More precisely, analytical Poisson transform maps a sequence (e.g., characterizing the Bernoulli model) into a generating function of a complex variable. However, after poissonization one must depoissonize in order to translate the results of the Poisson model into the original (i.e., Bernoulli) model. We present in this paper several analytical depoissonization results that fall into the following general scheme: If the Poisson transform has an appropriate growth in the complex plane, then an asymptotic expansion of the sequence can be expressed in terms of the Poisson transform and its derivatives evaluated on the real line. Not surprisingly, actual formulations of depoissonization results depend on the nature of the growth of the Poisson transform, and thus we have polynomial and exponential depoissonization theorems. Normalization (e.g., as in the central limit theorem) introduces another twist that led us to formulate the so{called diagonal depoissonization theorems. Finally, we illustrate our results on numerous examples from combinatorics and the analysis of algorithms and data structures (e.g., combinatorial assemblies, digital trees, multiaccess protocols, probabilistic counting, selecting a leader, data compression, etc.).

A 1-planar graph is a graph that can be embedded in the plane with at most one crossing per edge. It is known that testing 1-planarity of a graph is NP-complete. In this paper, we consider maximal 1-planar graphs. A graph G is maximal 1-planar if addition of any edge destroys 1-planarity of G. We first study combinatorial properties of maximal 1-planar embeddings. In particular, we show that in a maximal 1-planar embedding, the graph induced by the non-crossing edges is spanning and biconnected. Using the properties, we show that the problem of testing maximal 1-planarity of a graph G can be solved in linear time, if a rotation system Φ (i.e., the circular ordering of edges for each vertex) is given. We also prove that there is at most one maximal 1-planar embedding ξ of G that is consistent with the given rotation system Φ. Our algorithm also produces such an embedding in linear time, if it exists.

We investigate the complexity of subclasses of Presburger arithmetic, i.e., the first-order theory of natural numbers with addition. The subclasses are defined by restricting the quantifier prefix to finite lists Q , . . .(I,. For all m 3 2 we find formula classes, defined by prefixes with m + 1 alternations and m + 5 quantifiers, which are Z:P,-respectively I&complete. For m = 1, the class of 3WV-formulas is shown to be NP-complete. For m = 0 and for all natural numbers t, the class of 3'-formulas is known to be in P. Thus we have a nice characterisation of the polynomial-time hierarchy by classes of Presburger formulas. Finally, the NP-completeness of the 3VV-class is used to prove that for certain formulas there exist no equivalent quantifier-free formulas of polynomial length.

This paper is aimed at exploring the hidden fundamental computational property of natural language that has been so elusive that it has made all attempts to characterize its real computational property ultimately fail. Earlier natural language was thought to be context-free. However, it was gradually realized that this does not hold much water given that a range of natural language phenomena have been found as being of non-context-free character that they have almost scuttled plans to brand natural language contextfree. So it has been suggested that natural language is mildly context-sensitive and to some extent context-free. In all, it seems that the issue over the exact computational property has not yet been solved. Against this background it will be proposed that this exact computational property of natural language is perhaps the N-th dimension of language, if what we mean by dimension is nothing but universal (computational) property of natural language.

In this paper, we generalize the Ski-Rental Problem to the Bahncard Problem which is an online problem of practical relevance for all travelers. The Bahncard is a railway pass of the Deutsche Bundesbahn (the German railway company) which entitles its holder to a 50% price reduction on nearly all train tickets. It costs 240 DM, and it is valid for 12 months. Similar bus or railway passes can be found in many other countries. For the common traveler, the decision at which time to buy a Bahncard is a typical online problem, because she usually does not know when and where she will travel next. We show that the greedy algorithm applied by most travelers and clerks at ticket o ces is not better in the worst case than the trivial algorithm which never buys a Bahncard. We present two optimal deterministic online algorithms, an optimistic one and a pessimistic one. We further give a lower bound for randomized online algorithms and present an algorithm which we conjecture to be optimal; a proof of the conjecture is given for a special case of the problem. It turns out that the optimal competitive ratio only depends on the price reduction factor (50% for the German Bahncard Problem), but does not depend on the price or validity period of a Bahncard.

The matching problem asks for a large set of disjoint edges in a graph. It is a problem that has received considerable attention in both the sequential and self-stabilizing literature. Previous work has resulted in self-stabilizing algorithms for computing a maximal ( 1 2 -approximation) matching in a general graph, as well as computing a 2 3 -approximation on more specific graph types. In the following we present the first selfstabilizing algorithm for finding a 2 3 -approximation to the maximum matching problem in a general graph. We show that our new algorithm stabilizes in at most exponential time under a distributed adversarial daemon, and O(n 2 ) rounds under a distributed fair daemon, where n is the number of nodes in the graph.

In this paper, we consider smooth words over 2-letter alphabets {a, b}, where a, b are integers having same parity, with 0 < a < b. We show that all are recurrent and that the closure of the set of factors under reversal holds for odd alphabets only. We provide a linear time algorithm computing the extremal words, w.r.t. lexicographic order. The minimal word is an infinite Lyndon word if and only if either a = 1 and b are odd, or a, b are even. A connection is established between generalized Kolakoski words and maximal infinite smooth words over even 2-letter alphabets revealing new properties for some of the generalized Kolakoski words. Finally, the frequency of letters in extremal words is 1/2 for even alphabets, and for a = 1 with b odd, the frequency of b's is 1/( √ 2b − 1 + 1).

The efficiency of the αβ-algorithm as a minimax search procedure can be attributed to its effective pruning at so-called cut-nodes; ideally only one move is examined there to establish the minimax value. This paper explores the benefits of investing additional search effort at cut-nodes by also expanding some of the remaining moves. Our results show a strong correlation between the number of promising move alternatives at cut-nodes and a new principal variation emerging. Furthermore, a new forward-pruning method is introduced that uses this additional information to ignore potentially futile subtrees. We also provide experimental results with the new pruning method in the domain of chess.

In this work, we address the problem of locally estimating the size of a Peerto-Peer (P2P) network using local information. We present a novel approach for estimating the size of a peer-to-peer (P2P) network, fitting the sum of new neighbors discovered at each iteration of a breadth-first search (BFS) with a logarithmic function, and then using Lambert’s W function to solve a root of a ln(n)+b−n = 0, where n is the network size. With rather little computation, we reach an estimation error of at most 10 percent, only allowing the BFS to iterate to the third level.

Benchmarking graph-oriented database workloads and graph-oriented database systems are increasingly becoming relevant in analytical Big Data tasks, such as social network analysis. In graph data, structure is not mainly found inside the nodes, but especially in the way nodes happen to be connected, i.e. structural correlations. Because such structural correlations determine join fan-outs experienced by graph analysis algorithms and graph

We model and study arbitrage across sponsored search markets, created by search engines. We identify and focus on traffic arbitrage and click arbitrage by auctioneers. We derive and characterize equilibria of such arbitrage behaviors across multiple markets.

The aim of this work is to show how one can study varieties of associative algebras using computer algebra. The Nonstandard point of view to describe the irreducible components is well adapted to computer algebra. It leads to algorithms which are implemented under Mathematica Software. We give a package which helps to describe the irreducible components of the n-dimensional unitary associative algebras and nilpotent algebras. We also compute under Mathematics the second cohomology group and the set of invariant scalar products over an algebra. As illustration, the procedures are applied in this paper to study the 3-dimensional associative algebras.

We present an axiom system ACP, for communicating processes with silent actions ('z-steps'). The system is an extension of ACP, Algebra of Communicating Processes, with Milner's z-laws and an explicit abstraction operator. By means of a model of finite acyclic process graphs for ACP, syntactic properties such as consistency and conservativity over ACP are proved. Furthermore, the Expansion Theorem for ACP is shown to carry over to ACP~. Finally, termination of rewriting terms according to the ACP~ axioms is proved using the method of recursive path orderings.

This paper is placed in a formal framework in which the interdisciplinary study of natural language is conducted by integrating linguistics, computer science and biology. It provides an overview of the field of research, conveying the main biological ideas that have influenced research in linguistics. Our work highlights the main methods of molecular computing that have been applied to the processing and study of the structure of natural language: DNA computing, membrane computing and networks of evolutionary processors. Moreover, some new challenges and lines of research for the future are pointed out, that can provide important improvements in the understanding of natural language as a structure and a human capacity.

The literature on membrane computing describes several variants of P systems whose complexity classes C are "closed under exponentiation", that is, they satisfy the inclusion P C ⊆ C, where P C is the class of problems solved by polynomial-time Turing machines with oracles for problems in C. This closure automatically implies closure under many other operations, such as regular operations (union, concatenation, Kleene star), intersection, complement, and polynomial-time mappings, which are inherited from P. Such results are typically proved by showing how elements of a family of P systems Π can be embedded into P systems simulating Turing machines, which exploit the elements of Π as subroutines. Here we focus on the latter construction, abstracting from the technical details which depend on the specific variant of P system, in order to describe a general strategy for proving closure under exponentiation.

A distributed selection algorithm and its expected communication complexity, Theoretical Computer Science 100 (1992) 1855204. We consider the distributed K-selection problem defined as follows: a set S of n elements is distributed among d processors and an originator processor wants to know the value of the Kth smallest element in S. The goal is to obtain an algorithm that minimizes the communication activities among the processors. We propose an algorithm whose expected communication complexity is O(log log n) whereas the worst-case complexity is O(log n); in the point-to-point model, this yields an 0 (d log log n) upper bound on the expected number of messages for distributed selection.

We introduce a new kind of abstract machine based on the chemical metaphor used in the l? language of Ban%tre & al. States of a machine are chemical solutions where floating molecules can interact according to reaction rules. Solutions can be stratified by encapsulating subsolutions within membranes that force reactions to occur locally. We illustrate the use of this model by describing the operational semantics of the TCCS and CCS process calculi. We also show how to extract a higher-order concurrent &calculus out of the basic concepts of the chemical abstract machine.

We study the properties of the set of binary strings with the relation \the Kolmogorov complexity of x conditional to y is small". We prove that there are pairs of strings which have no greatest common lower bound with respect to this pre-order. We present several examples when the greatest common lower bound exists but its complexity is much less than mutual information (extending G acs and K orner result 2]).

In this paper we discusses the relationship between the known classes P and NP. We show that the difficulties in solving problem "P versus NP' have methodological in nature. An algorithm for solving any problem is sensitive to even small changes in its formulation. As we will shown in the paper, these difficulties are exactly in the formulation of some problems of the class NP.

Leo, .I., A general context-free parsing algorithm running in linear time on every LR(k) grammar without using lookahead, Theoretical Computer Scic 2s; 82 :'13?1) ;tLiiti A new general context-free parsing algorithm is pre<.ented which runs in linear time and space on every LR( k) grammar without using any lookahead and without making use of the LR property. Most of the existing implementations of tabular parsing algorithms, including those using lookahead, can easily be adapted to this new algorithm without a noteworthy loss of efficiency. For some natural right recursive grammars both the time and space complexity will be improved from n( n') to O(n). This makes this algorithm not only of theoretical but probably of practical interest as well.

We study the dynamical behavior of D-dimensional linear cellular automata over Zm. We provide an easy-to-check necessary and sufficient condition for a D-dimensional linear cellular automata over Zm to be ergodic and topologically transitive. As a byproduct, we get that for linear cellular automata ergodicity is equivalent to topological transitivity. Finally, we prove that for 1-dimensional linear cellular automata over

This chapter is devoted to introducing the theories of interval algebra to people who are interested in applying the interval methods to uncertainty analysis in science and engineering. In view of this purpose, we shall introduce the key concepts of the algebraic theories of intervals that form the foundations of the interval techniques as they are now practised, provide a historical and epistemological background of interval mathematics and uncertainty in science and technology, and finally describe some typical applications that clarify the need for interval computations to cope with uncertainty in a wide variety of scientific disciplines.

Keywords. Interval mathematics, Uncertainty, Quantitative Knowledge, Reliability, Complex interval arithmetic, Machine interval arithmetic, Interval automatic differentiation, Computer graphics, Ray tracing, Interval root isolation.

Recommended Citation:

Hend Dawood. Interval Mathematics as a Potential Weapon against Uncertainty. In S. Chakraverty, editor, Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems. chapter 1, pages 1-38. IGI Global, Hershey, PA, 2014. ISBN 978-1-4666-4991-0.

The final publication is available at IGI Global via http://dx.doi.org/10.4018/978-1-4666-4991-0.ch001

Recently, it has been recognizedthat phase transitions play an important role in the proba- bilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that leadto close ties between computer science andstatistical physics. This review aims at presenting the tools andconcepts d esignedby physicists to d eal with optimization or decision problems in a language accessible

The use of social networking websites has increased since last few decades. The social networking sites such as Twitter, Facebook, LinkedIn and YouTube are sources of human interaction, where the users are allowed to create and share their activities, thoughts and opinions pertaining to different subjects. These sites have not only connected large user populations but have also captured massive information associated with their daily interactions in the form of Big Data. This data provides unprecedented information about human behavior and social interactions. It makes it possible to understand who the users are, what their interests are and what they need. This information is vital for businesses to target potential consumers or seek customer opinions in the event of diversification as a business strategy. Thus, this work analyzes social media data to predict significant personality traits, i.e. qualities or characteristics specific to an individual, using the Big Five Model. The predictions can be applied to various domains like business intelligence, marketing, sociology and psychology. A parallelism between an individual’s personality traits and his/her linguistic information is explored for analytics.

Arithmetic functions related to number representation systems exhibit various periodicity phenomena. For instance, a well known theorem of Delange expresses the total number of ones in the binary representations of the rst n integers in terms of a periodic fractal function.

The author of this article is a theoretical physicist and computer scientist, who has no background in literature or creative writing. Nor did he intend to write a book on poetry. This book entitled: “About Love” came as Divine Inspiration. The writing was so captivating, majestic, fascinating and effortlessly magical. The poems came to him during the draft of his book Digital Physics: The Meaning of the Holographic Universe and Its Implications beyond Theoretical Physics. During the writing, he started asking himself many questions, particularly about where do our ideas come from? Is there a universe of ideas out there that we have access to it? Indeed, he is aware that some of our thoughts originate from the books we read, from school, society and the environment surrounding us, but that perhaps does not answer the question. The facts before his eyes say that not all our ideas come from society or learning.

Keywords: computes, digital, discrimination, divine, happiness, injustice, inspiration, love, multiverse, physics, Platonism, struggle, togetherness, universe.

In this paper the problem of the number of fixed points for an RSA algorithm is considered. This is an important question from the point of view of any cryptosystem. We have estimated the expected value of this number for randomly chosen RSA parameters. It turned out that it is O(ln2n), and the probability of finding such a point is O(ln2n/n). Thus, these values are really negligible, which had been intuitively expected.

In this paper we consider several types of equations on words, motivated by the attempt of characterizing the class of polyominoes that tile the plane by translation in two distinct ways. Words coding the boundary of these polyominoes satisfy an equation whose solutions are in bijection with a subset of the solutions of equations of the form ABA˜B˜≡XYX˜Y˜. It turns

It is widely yxlievk Lhat showing a pro"jlem to be NP-completc is tantamount to proving its computational intractability. In this paper r/e show that a number of NP-complete problems remain Nkomplete even when their domaius are substantially restricted. First we show the completeness of Simple Max Cut (Max Cut with edge weights restricted to value l), and, as a corollary, the completeness af the Optimal Linear Arrangement problem. We then show that even if the domains of the Node Cover and Directed Hamiltonian Path problems :are restricted tc planar graphs, the two problems remain N&complete, and that these and other graph problems remain NBcompHete even when their domains are restricted to graphs with low node degrees. For Graph 3=Colorability, Node Cover, and Undirected Wamiltonian Circui t, we determine essentially the lowest possible upper bounds on node degree for which the problems remsin NBcomplete.

An extended overview of the organic and inorganic phase composition of biomass was conducted. Some general considerations and problems related to phase composition of biomass as a solid fuel were discussed initially. Then, reference peer-reviewed data including contents of cellulose, hemicellulose, lignin and bulk extractives of 93 varieties of biomass were used and grouped for their comparison and classification. Additionally, reference peer-reviewed data and own investigations for various minor organic components and minerals, and modes of element occurrence identified in biomass were also applied and organised to describe the biomass systematically. It was found that the phase distinctions among the specified natural and anthropogenic (technogenic) biomass groups, subgroups and varieties are significant and relate to different biomass sources and origin. The phase composition of biomass is highly variable due to the extremely high variations of structural components and different genetic types (authigenic, detrital and technogenic) of inorganic matter. The technogenic biomass group is quite complicated as a result of incorporation of various non-biomass materials during biomass processing. It was identified that the biomass phase composition is significantly different from that of coal. Correlations and associations among phase and chemical characteristics were studied to find some major trends and important relationships occurring in the natural biomass system. Certain leading associations related to the occurrence, content and origin of elements and phases in biomass were identified and discussed, namely: (1) CAH (mainly as authigenic cellulose, hemicellulose, lignin and organic extractives); (2) SiAAlAFeANaATi (mostly as detrital silicates and oxyhydroxides, excluding authigenic opal); (3) CaAMgAMn (commonly as authigenic oxalates and carbonates); and (4) NAKASAPACl (normally as authigenic phosphates, sulphates, chlorides and nitrates). Finally, it was emphasised that these important associations have potential applications and can be used for initial classifications or prediction and indicator purposes connected with future advanced and sustainable processing of biomass to biofuels and chemical feedstock.