Space Complexity of Stack Automata Models

This paper examines several measures of space complexity on variants of stack automata: non-erasing stack automata and checking stack automata. These measures capture the minimum stack size required to accept any word in a language (weak measure), the maximum stack size used in any accepting computation on any accepted word (accept measure), and the maximum stack size used in any computation (strong measure). We give a detailed characterization of the accept and strong space complexity measures for checking stack automata. Exactly one of three cases can occur: the complexity is either bounded by a constant, behaves (up to small technicalities explained in the paper) like a linear function, or it grows arbitrarily larger than the length of the input word. However, this result does not hold for non-erasing stack automata; we provide an example when the space complexity grows with the square root of the input length. Furthermore, an investigation is done regarding the best complexity of any machine accepting a given language, and on decidability of space complexity properties

On the Commutative Equivalence of Context-Free Languages

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

Priorities, Promoters and Inhibitors in Deterministic Non-Cooperative P Systems

Membrane systems (with symbol objects) are distributed controlled multiset processing systems. Non-cooperative P systems with either promoters or inhibitors (of weight not restricted to one) are known to be computationally complete. Since recently, it is known that the power of the deterministic subclass of such systems is subregular. We present new results on the weight of promoters and inhibitors, as well as for characterizing the systems with priorities only

Evaluating Matrix Circuits

The circuit evaluation problem (also known as the compressed word problem) for finitely generated linear groups is studied. The best upper bound for this problem is $\mathsf{coRP}$, which is shown by a reduction to polynomial identity testing. Conversely, the compressed word problem for the linear group $\mathsf{SL}_3(\mathbb{Z})$ is equivalent to polynomial identity testing. In the paper, it is shown that the compressed word problem for every finitely generated nilpotent group is in $\mathsf{DET} \subseteq \mathsf{NC}^2$. Within the larger class of polycyclic groups we find examples where the compressed word problem is at least as hard as polynomial identity testing for skew arithmetic circuits

Spatially resolved stress measurements in materials with polarization-sensitive optical coherence tomography: image acquisition and processing aspects

We demonstrate that polarization-sensitive optical coherence tomography (PS-OCT) is suitable to map the stress distribution within materials in a contactless and non-destructive way. In contrast to transmission photoelasticity measurements the samples do not have to be transparent but can be of scattering nature. Denoising and analysis of fringe patterns in single PS-OCT retardation images are demonstrated to deliver the basis for a quantitative whole-field evaluation of the internal stress state of samples under investigation.Comment: 10 pages, 6 figures; Copyright: Blackwell Publishing Ltd 2008; The definitive version is available at: www.blackwell-synergy.co

An FPTAS for Stochastic Unbounded Min-Knapsack Problem

In this paper, we study the stochastic unbounded min-knapsack problem ($\textbf{Min-SUKP}$). The ordinary unbounded min-knapsack problem states that: There are $n$ types of items, and there is an infinite number of items of each type. The items of the same type have the same cost and weight. We want to choose a set of items such that the total weight is at least $W$ and the total cost is minimized. The \prob~generalizes the ordinary unbounded min-knapsack problem to the stochastic setting, where the weight of each item is a random variable following a known distribution and the items of the same type follow the same weight distribution. In \prob, different types of items may have different cost and weight distributions. In this paper, we provide an FPTAS for $\textbf{Min-SUKP}$, i.e., the approximate value our algorithm computes is at most $(1+\epsilon)$ times the optimum, and our algorithm runs in $poly(1/\epsilon,n,\log W)$ time.Comment: 24 page

Meta-heuristically seeded genetic algorithm for independent job scheduling in grid computing

Grid computing is an infrastructure which connects geographically distributed computers owned by various organizations allowing their resources, such as computational power and storage capabilities, to be shared, selected, and aggregated. Job scheduling problem is one of the most difficult tasks in grid computing systems. To solve this problem efficiently, new methods are required. In this paper, a seeded genetic algorithm is proposed which uses a meta-heuristic algorithm to generate its initial population. To evaluate the performance of the proposed method in terms of minimizing the makespan, the Expected Time to Compute (ETC) simulation model is used to carry out a number of experiments. The results show that the proposed algorithm performs better than other selected techniques

Scheduling Games with Machine-Dependent Priority Lists

We consider a scheduling game 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 characterize four classes of instances in which a pure Nash equilibrium (NE) is guaranteed to exist, and show, by means of an example, that none of these characterizations can be relaxed. We then bound the performance of Nash equilibria for each of these classes with respect to the makespan of the schedule and the sum of completion times. We also analyze the computational complexity of several problems arising in this model. For instance, we prove that it is NP-hard to decide whether a NE exists, and that even for instances with identical machines, for which a NE is guaranteed to exist, it is NP-hard to approximate the best NE within a factor of $2-\frac{1}{m}-\epsilon$ for all $\epsilon>0$. In addition, we study a generalized model in which players' strategies are subsets of resources, each having its own priority list over the players. We show that in this general model, even unweighted symmetric games may not have a pure NE, and we bound the price of anarchy with respect to the total players' costs.Comment: 19 pages, 2 figure

Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata

After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors whose acceptance condition depends on the states of all cells in the automaton. We prove a time hierarchy theorem for sublinear-time ACA classes, analyze their intersection with the regular languages, and, finally, establish strict inclusions in the parallel computation classes $\mathsf{SC}$ and (uniform) $\mathsf{AC}$. As an addendum, we introduce and investigate the concept of a decider ACA (DACA) as a candidate for a decider counterpart to (acceptor) ACAs. We show the class of languages decidable in constant time by DACAs equals the locally testable languages, and we also determine $\Omega(\sqrt{n})$ as the (tight) time complexity threshold for DACAs up to which no advantage compared to constant time is possible.Comment: 16 pages, 2 figures, to appear at DLT 202

Control Words of String Rewriting P Systems

P systems with controlled computations have been introduced and investigated in the recent past, by assigning labels to the rules in the regions of the P system and guiding the computations by control words. Here we consider string rewriting cell-like transition P system with label assigned rules working in acceptor mode and compare the obtained family of languages of control words over the rule labels with certain well-known language families. An application to chain code picture generation is also pointed out