International Journal of Foundations of Computer Science

Mateescu et al (2000) introduced an interesting new tool, called Parikh matrix, to study in terms of subwords, the numerical properties of words over an alphabet. The Parikh matrix gives more information than the well-known Parikh vector of a word which counts only occurrences of symbols in a word. In this note a property of two words u, υ, called "ratio property", is introduced. This property is a sufficient condition for the words uυ and υu to have the same Parikh matrix. Thus the ratio property gives information on the M–ambiguity of certain words and certain sets of words. In fact certain regular, context-free and context-sensitive languages that have the same set of Parikh matrices are exhibited. In the study of fair words, Cerny (2006) introduced another kind of matrix, called the p–matrix of a word. Here a "weak-ratio property" of two words u, υ is introduced. This property is a sufficient condition for the words uυ and υu to have the same p–matrix. Also the words uυ and υu are fair whenever u, υ are fair and have the weak ratio property.

Weighted multioperator tree automata (for short: wmta) are finite-state bottom-up tree automata in which the transitions are weighted with an operation taken from some multioperator monoid. A wmta recognizes a tree series which is a mapping from the set of trees to some commutative monoid. We prove that every wmta recognizable tree series can be decomposed into a relabeling tree transformation, a recognizable tree language, and a tree series computed by a homomorphism wmta; vice versa, the composition of an arbitrary relabeling tree transformation, a recognizable tree language, and a tree series computed by a homomorphism wmta yields a wmta recognizable tree series. We use this characterization result for specific multioperator monoids and prove (1) a new decomposition of polynomial bottom-up tree series transducers over semirings and (2) a new characterization of tree series which are recognizable by weighted tree automata over semirings, in terms of projections of local tree languages.

In scheduling with controllable processing times the actual processing time of each job is to be chosen from the interval between the smallest (compressed or fully crashed) value and the largest (decompressed or uncrashed) value. In the problems under consideration, the jobs are processed on a single machine and the quality of a schedule is measured by two functions: the maximum cost (that depends on job completion times) and the total compression cost. Our main model is bicriteria and is related to determining an optimal trade-off between these two objectives. Additionally, we consider a pair of associated single criterion problems, in which one of the objective functions is bounded while the other one is to be minimized. We reduce the bicriteria problem to a series of parametric linear programs defined over the intersection of a submodular polyhedron with a box. We demonstrate that the feasible region is represented by a so-called base polyhedron and the corresponding problem can be solved by the greedy algorithm that runs two orders of magnitude faster than known previously. For each of the associated single criterion problems, we develop algorithms that deliver the optimum faster than it can be deduced from a solution to the bicriteria problem.

Ciliates are unicellular organisms having two types of functionally different nuclei: micronucleus and macronucleus. Gene assembly transforms a micronucleus into a macronucleus, thereby transforming each gene from its micronuclear form to its macronuclear form. Within a formal intramolecular model of gene assembly based on strings, the notion of reduction graph represents the macronuclear form of a gene, including byproducts, given only a description of the micronuclear form of that gene. For a more abstract model of gene assembly based on graphs, one cannot, in general, define the notion of reduction graphs. We show that if we restrict ourselves to the so-called realistic overlap graphs (which correspond to genes occurring in nature), then the notion of reduction graph can be defined in a manner equivalent to the string model. This allows one to carry over from the string model to the graph model several results that rely on the notion of reduction graph.

In this paper we extend the conditions of dynamic team constitution in simple eco–grammar systems, motivated by the bottom–up–clustering algorithm. The relationships of simple eco–grammar systems formed according to the newly introduced conditions to each other as well as to certain language classes of the Chomsky hierarchy and L systems are established. We prove that any recursively enumerable language can be obtained as the intersection of a regular language and the language of simple eco–grammar systems where the active teams are organized according to different conditions of team constitution. We also propose some further research directions.

Let L ≥ 1, ε > 0 be real numbers, (M, d) be a finite metric space and (N, ρ) be a metric space. A query to a metric space consists of a pair of points and asks for the distance between these points. We study the number of queries to metric spaces (M, d) and (N, ρ) needed to decide whether (M, d) is L-bilipschitz embeddable into (N, ρ) or ∊-far from being L-bilipschitz embeddable into N, ρ). When (M, d) is ∊-far from being L-bilipschitz embeddable into (N, ρ), we allow an o(1) probability of error (i.e., returning the wrong answer "L-bilipschitz embeddable"). However, no error is allowed when (M, d) is L-bilipschitz embeddable into (N, ρ). That is, algorithms with only one-sided errors are studied in this paper. When |M| ≤ |N| are both finite, we give an upper bound of on the number of queries for determining with one-sided error whether (M, d) is L-bilipschitz embeddable into (N, ρ) or ∊-far from being L-bilipschitz embeddable into (N, ρ). For the special case of finite |M| = |N|, the above upper bound evaluates to . We also prove a lower bound of Ω(|N|^3/2) for the special case when |M| = |N| are finite and L = 1, which coincides with testing isometry between finite metric spaces. For finite |M| = |N|, the upper and lower bounds thus match up to a multiplicative factor of at most , which depends only sublogarithmically in |N|. We also investigate the case when (N, ρ) is not necessarily finite. Our results are based on techniques developed in an earlier work on testing graph isomorphism.

This paper discusses the terminating derivation mode in cooperating distributed grammar systems where components are forbidding grammars instead of context-free grammars. Such systems are called forbidding cooperating distributed grammar systems, and it is demonstrated that the number of their components can be reduced to two without changing the generative power and that these systems are computationally complete. Without erasing productions, however, these systems are less powerful than context-sensitive grammars.

We study the problem of scheduling independent unit-time parallel jobs on hypercubes. A parallel job has to be scheduled between its release time and deadline on a subcube of processors. The objective is to maximize the number of early jobs. Jobs' intervals of feasibility have to be nested. We provide a polynomial time algorithm for the problem.

A convertible authenticated encryption scheme allows a designated receiver to retrieve an authenticated ciphertext and convert the authenticated ciphertext into an ordinary signature. The receiver can prove the dishonesty of the sender to anyone if the sender repudiates his/her signature. Recently, many researchers have proposed convertible authenticated encryption schemes based on cryptological algorithms. In this paper, the authors shall present a new convertible authenticated encryption scheme based on the ElGamal cryptosystem. The proposed scheme is more efficient than Wu-Hsu's scheme in terms of computational complexity.

In this paper, we present efficient geometric algorithms for the discrete constrained 1-D K-means clustering problem and extend our solutions to the continuous version of the problem. One key clustering constraint we consider is that the maximum difference in each cluster cannot be larger than a given threshold. These constrained 1-D K-means clustering problems appear in various applications, especially in intensity-modulated radiation therapy (IMRT). Our algorithms improve the efficiency and accuracy of the heuristic approaches used in clinical IMRT treatment planning.