Showing papers in "International Journal of Foundations of Computer Science in 2004"
TL;DR: It is proved that there exist periodic words having the maximum number of palindromes as in the case of Sturmian words, by providing a simple and easy to check condition.
Abstract: We study the problem of constructing infinite words having a prescribed finite set P of palindromes. We first establish that the language of all words with palindromic factors in P is rational. As a consequence we derive that there exists, with some additional mild condition, infinite words having P as palindromic factors. We prove that there exist periodic words having the maximum number of palindromes as in the case of Sturmian words, by providing a simple and easy to check condition. Asymmetric words, those that are not the product of two palindromes, play a fundamental role and an enumeration is provided.
106 citations
TL;DR: The paper investigates inequalities between the numbers of different (scattered) subword occurrences and gives various characterizations for Parikh matrices in the case where the matrix determines the word uniquely.
Abstract: The paper investigates inequalities between the numbers of different (scattered) subword occurrences. The Parikh matrix recently introduced is an efficient tool. We give various characterizations for Parikh matrices. Of special interest is the case where the matrix determines the word uniquely. We investigate such matrix unambiguous words. The considerations are extended to concern languages. Several open problems and problem areas are indicated.
56 citations
TL;DR: It is shown that the clique-width of gem- and co-gem-free graphs is at most 16.5%, which is fundamental for the recently introduced concept ofClique- width of graphs which extends the famous concept of treewidth.
Abstract: The P4 is the induced path of four vertices. The gem consists of a P4 with an additional universal vertex being completely adjacent to the P4, and the co-gem is its complement graph. Gem- and co-gem-free graphs generalize the popular class of cographs (i. e. P4-free graphs). The tree structure and algebraic generation of cographs has been crucial for several concepts of graph decomposition such as modular and homogeneous decomposition. Moreover, it is fundamental for the recently introduced concept of clique-width of graphs which extends the famous concept of treewidth. It is well-known that the cographs are exactly those graphs of clique-width at most 2. In this paper, we show that the clique-width of gem- and co-gem-free graphs is at most 16.
54 citations
TL;DR: A quantum authentication scheme is presented in this paper that creates auxiliary EPR pairs to interact with the identification token by a complete Bell state measurement and is proved to be secure.
Abstract: A quantum authentication scheme is presented in this paper. Two parties share Einstein-Podolsky-Rosen(EPR) pairs previously as the identification token. They create auxiliary EPR pairs to interact with the identification token. Then the authentication is accomplished by a complete Bell state measurement. This scheme is proved to be secure. If no errors and eavesdroppers exist in the transmission, the identification token is unchanged after the authentication. So it can be reused.
52 citations
TL;DR: This paper shows a DNA representation of n binary numbers of m bits, and proposes a procedure to assign the bits of that representation to DNA molecules.
Abstract: In this paper, we consider procedures for logic and arithmetic operations with DNA molecules. We first show a DNA representation of n binary numbers of m bits, and propose a procedure to assign the...
36 citations
TL;DR: In this paper, it was shown that the infinite binary word "cube" can be replaced by any fractional power > 5/2, and the analogous problem where "4" is replaced by a fixed integer.
Abstract: In 1976, Dekking showed that there exists an infinite binary word that contains neither squares yy with |y|≥4 nor cubes xxx. We show that 'cube' can be replaced by any fractional power > 5/2. We also consider the analogous problem where '4' is replaced by any integer. This results in an interesting and subtle hierarchy.
33 citations
TL;DR: This work defines COSMOS, the Cluster-based, heterOgeneouSMOdel for Sensor networks, which assumes a hierarchical network architecture comprising of a large number of low cost sensors with limited computation capability, and fewer number of powerful clusterheads, uniformly distributed in a two dimensional terrain.
Abstract: In-network collaborative computation is essential for implementation of a large number of sensor applications We approach the problem of computation in sensor networks from a parallel and distributed system's perspective We define COSMOS, the Cluster-based, heterOgeneouSMOdel for Sensor networks The model abstracts the key features of the class of cluster-based sensor applications It assumes a hierarchical network architecture comprising of a large number of low cost sensors with limited computation capability, and fewer number of powerful clusterheads, uniformly distributed in a two dimensional terrain The sensors are organized into single hop clusters, each managed by a distinct clusterhead The clusterheads are organized in a mesh-like topology All sensors in a cluster are time synchronized, whereas the clusterheads communicate asynchronously The sensors are assumed to have multiple power states and a wakeup mechanism to facilitate power management To illustrate algorithm design using our model, we discuss implementation of algorithms for sorting and summing in sensor networks
30 citations
TL;DR: A deeper insight is gained into the properties of episturmian words and a matrix formula for computing the number of representations of an integer in such a system similar to the Ostrowski ones is given.
Abstract: Episturmian words, which include the Arnoux-Rauzy sequences, are infinite words on a finite alphabet generalizing the Sturmian words and sharing many of their same properties. This was studied in previous papers. Here we gain a deeper insight into these properties. This leads in particular to consider numerations systems similar to the Ostrowski ones and to give a matrix formula for computing the number of representations of an integer in such a system. We also obtain a complete answer to the question: if an episturmian word is morphic, which shifts of it, if any, also are morphic ?
30 citations
TL;DR: A survey of the two problems that allow to investigate evolutionary mechanisms at work in tandem repeats and an alignment of the sequences having minimal cost are presented.
Abstract: Local repetitions in genomes are called tandem repeats. A tandem repeat contains multiple, but slightly different copies of a repeated unit. It changes over time as the copies are altered by mutations, when additional copies are created by amplification of an existing copy, or when a copy is removed by contraction. Theses changes let tandem repeats evolve dynamically. From this statement follow two problems. TANDEM REPEAT HISTORY aims at recovering the history of amplifications and mutations that produced the tandem repeat sequence given as input. Given the tandem repeat sequences at the same genomic location in two individuals and a cost function for amplifications, contractions, and mutations, the purpose of TANDEM REPEAT ALLELE ALIGNMENT is to find an alignment of the sequences having minimal cost. We present a survey of these two problems that allow to investigate evolutionary mechanisms at work in tandem repeats.
29 citations
TL;DR: This paper presents several threshold schemes that are generalizations of Shamir's secret sharing scheme such that only authorized people can reconstruct the secret from their shares.
Abstract: A secret sharing scheme is a system designed to share a piece of information or the secret among a group of people such that only authorized people can reconstruct the secret from their shares. Since Blakley and Shamir proposed threshold secret sharing schemes in 1979 independently, many secret sharing schemes have been constructed. In this paper, we present several threshold schemes that are generalizations of Shamir's secret sharing scheme.
29 citations
TL;DR: It is observed that the length of any word guaranteeing minimal image cannot be less than |A|^(n-1), and some known results of automata theory immediately lead to an alternative construction which yields a simpler word that guarantees minimal image.
Abstract: Given a positive integer n and a finite alphabet A, a word w over A is said to guarantee minimal image if, for every homomorphism f from the free monoid A* over A into the monoid of all transformations of an n-element set, the range of the transformation wf has the minimum cardinality among the ranges of all transformations of the form vf where v runs over A*. Although the existence of words guaranteeing minimal image is pretty obvious, the problem of their explicit description is very far from being trivial. Sauer and Stone in 1991 gave a recursive construction for such a word w but the length of the word resulting from that construction was doubly exponential (as a function of n). We first show that some known results of automata theory immediately lead to an alternative construction which yields a simpler word that guarantees minimal image: it has exponential length, more precisely, its length is O(|A|^(n^3-n)). Then using a different approach, we find a word guaranteeing minimal image similar to that of Sauer and Stone but of the length O(|A|^(n^2-n)). On the other hand, we observe that the length of any word guaranteeing minimal image cannot be less than |A|^(n-1).
TL;DR: An FPGA-based implementation of an instance-specific hardware which accelerates the CKY (Cocke-Kasami- Younger) parsing of context-free grammars and attains an astonishing speed-up factor of up to 3,700 over traditional software solutions.
Abstract: The main contribution of this paper is an FPGA-based implementation of an instance-specific hardware which accelerates the CKY (Cocke-Kasami- Younger) parsing of context-free grammars. Given a context-free grammar G and a string x, the CKY parsing determines whether G derives x. We developed a hardware generator that creates a Verilog HDL source to perform the CKY parsing for any fixed context-free grammar G. The generated source is embedded in an FPGA using the design software provided by the FPGA vendor. The results show that our instance-specific hardware solution attains an astonishing speed-up factor of up to 3,700 over traditional software solutions.
TL;DR: A variant of the CRBT (collection of red-black trees) data structure proposed earlier for dynamic router-tables is formulated, and experiments indicate that a supernode implementation of the ACRBT usually has better search performance than does the traditional one-element-per-node implementation.
Abstract: Internet (IP) packet forwarding is typically done by finding the longest prefix in a router table that matches the packet's destination address. Although significant effort has been devoted to the development of data structures for static and dynamic router-tables for random packet-access-patterns, considerably less effort has been expended in the development of such structures for bursty access-patterns (i.e., streams of packets in which destination addresses repeat frequently within localized windows of packets). In this paper, we first formulate a variant, ACRBT (alternative collection of red-black trees), of the CRBT (collection of red-black trees) data structure proposed earlier for dynamic router-tables. By replacing the red-black trees used in the ACRBT with splay trees, we obtain the CST (collection of splay trees) structure in which search, insert, and delete take O(log n) amortized time per operation, where n is the number of prefixes in the router table. By replacing the front end of the CST with biased skip lists, we obtain the BSLPT (biased skip lists with prefix trees) structure in which search, insert, and delete take O(log n) expected time. The CST and BSLPT structures are designed so as to perform much better when the access pattern is bursty than when it is not. Experimental results using real IPv4 routing databases and synthetically generated search sequences as well as trace sequences are presented. For extremely bursty access patterns, the CST structure is best. Otherwise, the ACRBT is recommended. Our experiments also indicate that a supernode implementation of the ACRBT usually has better search performance than does the traditional one-element-per-node implementation.
TL;DR: The first distributed algorithm on general graphs for the Minimum Degree Spanning Tree problem is presented, it works for named asynchronous arbitrary networks and achieves O(|V|) time complexity and O(||E|) message complexity.
Abstract: In this paper we present the first distributed algorithm on general graphs for the Minimum Degree Spanning Tree problem. The problem is NP-hard in sequential. Our algorithm give a Spanning Tree of a degree at most 1 from the optimal. The resulting distributed algorithm is asynchronous, it works for named asynchronous arbitrary networks and achieves O(|V|) time complexity and O(|V||E|) message complexity.
TL;DR: It is shown that the extended ZPC-structure can be built in linear time w.r.t. the size of the -expression and that the associated position automaton can be deduced from it in quadratic time.
Abstract: In this article we generalize concepts of the position automaton and ZPC-structure to the regular -expressions. We show that the extended ZPC-structure can be built in linear time w.r.t. the size of the -expression and that the associated position automaton can be deduced from it in quadratic time.
TL;DR: This paper presents in this paper fast algorithms for the 3-D dominance reporting and counting problems, and generalize the results to the d-dimensional case.
Abstract: We present in this paper fast algorithms for the 3-D dominance reporting and counting problems, and generalize the results to the d-dimensional case. Our 3-D dominance reporting algorithm achieves O(log n/loglog n+f) query time using O(n log∊ n) space, where f is the number of points satisfying the query and ∊>0 is an arbitrarily small constant. For the 3-D dominance counting problem (which is equivalent to the 3-D range counting problem), our algorithm runs in O((log n/loglog n)2) time using O(n log1+∊n/loglog n) space.
TL;DR: An algorithm for minimizing the total completion time in O(n6c) time (for sufficiently large c) is designed, which improves the best previous time bound of O(nc(c-1)) given by Brucker et al [1].
Abstract: We study the scheduling problem on a batch machine which is capable of processing a batch of jobs at a time. For a batch machine of capacity c, we designed an algorithm for minimizing the total completion time in O(n6c) time (for sufficiently large c). This improves the best previous time bound of O(nc(c-1)) given by Brucker et al [1]. We also designed a new algorithm with running time .
TL;DR: This work addresses the unrelated parallel machines model and presents the first known fully polynomial time approximation scheme, when the number of machines is fixed, and shows that FIFO is an on-line algorithm with a (3-2/m)-competitive ratio.
Abstract: We investigate the max flow time scheduling problem in the off-line and on-line setting. We prove positive and negative theoretical results. In the off-line setting, we address the unrelated parallel machines model and present the first known fully polynomial time approximation scheme, when the number of machines is fixed. In the on-line setting and when the machines are identical, we analyze the First In First Out (FIFO) heuristic when preemption is allowed. We show that FIFO is an on-line algorithm with a (3-2/m)-competitive ratio. Finally, we present two lower bounds on the competitive ratio of deterministic on-line algorithms.
TL;DR: A lower bound of competitive ratio (1+θ)·k/(θ·k+2) for the on-line k-truck problem is given, where θ is the ratio of cost of the loaded truck and the empty truck on the same distance, and a relevant lower bound for theOn- line k-taxi problem followed naturally.
Abstract: In this paper, some results concerning the k-truck problem are produced. Firstly, the algorithms and their complexity concerning the off-line k-truck problem are discussed. Following that, a lower bound of competitive ratio (1+θ)·k/(θ·k+2) for the on-line k-truck problem is given, where θ is the ratio of cost of the loaded truck and the empty truck on the same distance, and a relevant lower bound for the on-line k-taxi problem followed naturally. Thirdly, based on the Position Maintaining Strategy (PMS), some new results which are slightly better than those of [11] for general cases are obtained. For example, a c-competitive or (c/θ+1/θ+1)-competitive algorithm for the on-line k-truck problem depending on the value of θ, where c is the competitive ratio of some algorithm to a relevant k-server problem, is developed. The Partial-Greedy Algorithm (PG) is used as well to solve this problem on a line with n nodes and is proved to be a (1+(n-k)/θ)-competitive algorithm for this case. Finally, the concepts of the on-line k-truck problem are extended to obtain a new variant: Deeper On-line k-Truck Problem (DTP). We claim that results of PMS for the STP (Standard Truck Problem) hold for the DTP.
TL;DR: It is shown that for any integer k≥3, binary morphisms which are not k-power-free, but which are (k+1)-power- free and generate k- power-free infinite words are possible.
Abstract: After giving an overview about morphisms and k-power-freeness (k∈IN), we present several conjectures, and partially solve one of those by giving, for any integer k≥3, binary morphisms which are not k-power-free, but which are (k+1)-power-free and generate k-power-free infinite words.
TL;DR: A complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word, and de Bruijn words, well known for their high subword complexity, are shown to have almost highest repetition complexity.
Abstract: With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, R(w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu…u of the same subword u of w are stored as (u,n). The repetition complexity has interesting relations with well-known complexity measures, such as subword complexity, SUB, and Lempel-Ziv complexity, LZ. We have always R(w)≥LZ(w) and could even be that the former is linear while the latter is only logarithmic; e.g., this happens for prefixes of certain infinite words obtained by iterated morphisms. An infinite word α being ultimately periodic is equivalent to: (i) , (ii) , and (iii) . De Bruijn words, well known for their high subword complexity, are shown to have almost highest repetition complexity; the precise complexity remains open. R(w) can be computed in time and it is open, and probably very difficult, to find fast algorithms.
TL;DR: In this article, it was shown that all languages of infinite pictures which are accepted row by row by Buchi or Choueka automata reading words of length ω2 are Buchi recognized by a finite tiling system, but the converse is not true.
Abstract: In a recent paper, Altenbernd, Thomas and Wohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the Buchi and Muller ones, firstly used for infinite words. The authors asked for comparing the tiling system acceptance with an acceptance of pictures row by row using an automaton model over ordinal words of length ω2. We give in this paper a solution to this problem, showing that all languages of infinite pictures which are accepted row by row by Buchi or Choueka automata reading words of length ω2 are Buchi recognized by a finite tiling system, but the converse is not true. We give also the answer to two other questions which were raised by Altenbernd, Thomas and Wohrle, showing that it is undecidable whether a Buchi recognizable language of infinite pictures is E-recognizable (respectively, A-recognizable).
TL;DR: This work improves the known bounds on the number of pairwise non-isomorphic minimal deterministic finite automata (DFAs) on n states which accept finite languages.
Abstract: We improve the known bounds on the number of pairwise non-isomorphic minimal deterministic finite automata (DFAs) on n states which accept finite languages. The lower bound constructions are iterative approaches which yield recurrence relations.
TL;DR: These algorithms are based on a method of ordering the vertices and edges by traversing a spanning tree of a graph in a bottom-up fashion and are the first linear-time algorithm to 5-list-total-color subcubic graphs.
Abstract: We present efficient algorithms for three coloring problems on subcubic graphs. (A subcubic graph has maximum degree at most three.) The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. The second algorithm is the first randomized EREW PRAM algorithm for the same problem. It uses O(n/log n) processors and runs in O(log n) time with high probability, where n is the number of vertices of the graph. The third algorithm is the first linear-time algorithm to 5-total-color subcubic graphs. The fourth algorithm generalizes this to get the first linear-time algorithm to 5-list-total-color subcubic graphs. Our sequential algorithms are based on a method of ordering the vertices and edges by traversing a spanning tree of a graph in a bottom-up fashion. Our parallel algorithm is based on a simple decomposition principle for subcubic graphs.
TL;DR: In this article, the authors defined the number of productions and number of symbols as measures of descriptional complexity for tabled interactionless Lindenmayer systems and their special cases and investigated the decrease of the descriptional complexities if we go from a family to another one which has a larger generative capacity.
Abstract: We define the number of productions and the number of symbols as measures of descriptional complexity for tabled interactionless Lindenmayer systems and their special cases. We investigate the decrease of the descriptional complexities if we go from a family to another one which has a larger generative capacity.
TL;DR: By limiting levels of the hierarchy to two, this work will establish the analytically optimal hierarchical configurations for two popular interconnection networks: mesh and hypercube and present heuristic algorithms for multiple-level hierarchical partitions.
Abstract: We study hierarchical configuration of distributed systems for achieving optimized system performance A distributed system consists of a collection of local processes which are distributed over a network of processors, and work in a cooperative manner to fulfill various tasks A hierarchical approach is to group and organize the distributed processes into a logical hierarchy of multiple levels, so as to coordinate the local computation/control activities to improve the overall system performance It has been proposed as an effective way to solve various problems in distributed computing, such as distributed monitoring, resource scheduling, and network routing The optimization problem considered in this paper is concerned with finding an optimal hierarchical partition of the processors, so that the total traffic flow over the network is minimized The problem in its general form has been known to be NP-hard Therefore, we just focus on distributed computing jobs which require collecting and processing information from all processors By limiting levels of the hierarchy to two, we will establish the analytically optimal hierarchical configurations for two popular interconnection networks: mesh and hypercube Based on analytical results, partitioning algorithms are proposed to achieve minimal communication cost (network traffic flow) We will also present and discuss heuristic algorithms for multiple-level hierarchical partitions
TL;DR: Some combinatorial properties of two-dimensional words over a given finite alphabet, which are related to the number of occurrences in them of words of a fixed size, are considered.
Abstract: We consider some combinatorial properties of two-dimensional words (or pictures) over a given finite alphabet, which are related to the number of occurrences in them of words of a fixed size (m,n). In particular a two-dimensional word (briefly, 2D-word) is called (m,n)-full if it contains as factors (or subwords) all words of size (m,n). An (m,n)-full word such that any word of size (m,n) occurs in it exactly once is called a de Bruijn word of order (m,n). A 2D-word w is called (m,n)-uniform if the difference in the number of occurrences in w of any two words of size (m,n) is at most 1. A 2D-word is called uniform if it is (m,n)-uniform for all m,n>0. In this paper we extend to the two-dimensional case some results relating the notions above which were proved in the one-dimensional case in a preceding article. In this analysis the study of repeated factors in a 2D-word plays an essential role. Finally, some open problems and conjectures are discussed.
TL;DR: A simple algorithm to determine if there is a member in within edit distanced of a given query string q of length m, which takes time O(dmd+1) in the RAM model, independent of n, and requires O(dm) additional space.
Abstract: Let be a dictionary consisting of n binary strings of length m each, represented as a trie. The usual d-query asks if there exists a string in within Hamming distance d of a given binary query string q. We present a simple algorithm to determine if there is a member in within edit distanced of a given query string q of length m. The method takes time O(dmd+1) in the RAM model, independent of n, and requires O(dm) additional space. We also generalize the results for the case of the problem over a larger alphabet.
TL;DR: This work presents a new data structure to support orthogonal range max queries on a datacube that requires query time and O((c2n)d) storage and is asymptotically optimal when d is constant independent of n.
Abstract: We present a new data structure to support orthogonal range max queries on a datacube. For a d-dimensional datacube with size n in each dimension where d≤c3log log n/log(log* n), our structure requires query time and O((c2n)d) storage where c1, c2 and c3 are constants independent of d and n; and log* n is the minimum number of repeated logarithms it takes to reduce the value n to at most 2. Hence our data structure is asymptotically optimal when d is constant independent of n.
TL;DR: In this paper, a fuzzy version of Symport/Antiport membrane systems is introduced and their rules are endowed with threshold functions that determine whether a rule can be applied or not to a given set of objects, depending of the degree of accuracy of these objects to the reactives specified in the rule.
Abstract: In this paper we introduce a fuzzy version of symport/antiport membrane systems. Our fuzzy membrane systems handle possibly inexact copies of reactives and their rules are endowed with threshold functions that determine whether a rule can be applied or not to a given set of objects, depending of the degree of accuracy of these objects to the reactives specified in the rule. We prove that these fuzzy membrane systems generate exactly the recursively enumerable finite-valued fuzzy subsets of ℕ.