Uniform Membership Research Articles

The central tree property and algorithmic problems on subgroups of free groups

Abstract We study the average case complexity of the Uniform Membership Problem for subgroups of free groups, and we show that it is orders of magnitude smaller than the worst case complexity of the best known algorithms. This applies to subgroups given by a fixed number of generators as well as to subgroups given by an exponential number of generators. The main idea behind this result is to exploit a generic property of tuples of words, called the central tree property. An application is given to the average case complexity of the Relative Primitivity Problem, using Shpilrain’s recent algorithm to decide primitivity, whose average case complexity is a constant depending only on the rank of the ambient free group.

The new detection of blue straggler stars in 50 open clusters using Gaia DR3

Context. The particularly abundant presence of blue straggler stars (BSS) in Galactic open clusters offers favorable conditions for detailed studies on the statistical properties and the origin of the blue straggler population. With the help of Gaia DR3, the number of identified open clusters continuously increases, and the determination of star cluster members is more reliable. Aims. We performed a more thorough search for BSS in newly found open clusters based on Gaia data. Methods. We implemented a uniform membership determination for over one thousand newly identified open clusters with larger sky coverage based on the astrometric and photometric data from Gaia DR3. The membership probabilities of stars were assigned by the pyUPMASK algorithm. Then we estimated the physical parameters of these clusters by isochrone fitting on their CMDs and picked out BSS in the specific region of these CMDs. Results. We identified 138 BSS that had not been reported before in 50 open clusters. Conclusions. Compared with recent catalogs that present more than 1500 BSS in 339 open clusters, our new catalog increased the number of BSS in Galactic open clusters by about 10%, and the number of open clusters with BSS by nearly 17%. In the future, more accurate abundance measurements are anticipated to better probe the origin of BSS in open clusters.

Nuclear Supplier Group (NSG) Membership and Mainstreaming Non-NPT Nuclear Weapon State (NWS): Case Study of Pakistan and India

This article examines the possibility of devising membership criteria for the Non-NPT Nuclear Weapons States (NWS) (India, Pakistan and Israel) in the Nuclear Suppliers Group (NSG). The question whether membership should be granted to these nuclear outliers or not should be determined after considering the nuclear history, their overall approach towards the Nuclear Non-Proliferation Regime (NPR) of these states and the debate on the proposed applicability of uniform membership criteria. There is a possibility of mainstreaming these states because some are emerging nuclear energy markets and others have the potential to become future markets. Furthermore, they do have nuclear weapons, therefore, it is vital to incorporate them in the existing export controls regimes to inhibit horizontal proliferation by implementing stringent measures. This study investigates policy recommendations for the international community to incorporate the Non-NPT nuclear weapon countries in the NSG. The paper concludes that a positive upshot of such a step would be granting membership to the mentioned states and such an unbiased approach would diminish global nuclear proliferation concerns.

Membership Problem for Two-Dimensional General Row Jumping Finite Automata

Two-dimensional general row jumping finite automata were recently introduced as an interesting computational model for accepting two-dimensional languages. These automata are nondeterministic. They guess an order in which rows of the input array are read and they jump to the next row only after reading all symbols in the previous row. In each row, they choose, also nondeterministically, an order in which segments of the row are read. In this paper, we study the membership problem for these automata. We show that each general row jumping finite automaton can be simulated by a nondeterministic Turing machine with space bounded by the logarithm. This means that the fixed membership problems for such automata are in NL, and so in P. On the other hand, we show that the uniform membership problem is NP-complete.

Application of Fuzzy Logic in the Ranking of Academic Institutions

For the development of any organization, evaluation of performance is an important task. To analyze the performance, Das et al. introduced a ranking framework based on fuzzy logic. That framework compared the current NIRF system of Indian Institutions with the fuzzy logic-based Mamdani system, KSM index. In that study, uniform membership functions are not taken. This study will focus on the ranking system based on Mamdani and Sugeno with fuzzy triangular numbers as input values of membership functions. Also, the updated results are compared with existing NIRF systems and considered Top 20 institutions of India for the year 2019 as per NIRF.

A Practical Algorithm for the Uniform Membership Problem of Labeled Multidigraphs of Tree-Width 2 for Spanning Tree Automata

This paper presents a practical algorithm for the uniform membership problem of labeled multidigraphs of tree-width at most 2 for spanning tree automata. Though the theoretical existence of a linear-time algorithm for the membership problem for graphs of bounded tree-width was shown in the previous study, the implementation of the linear-time algorithm is expected to be impractical because it requires the construction of a finite-state automaton whose size is super-exponential in the size of the tree automaton and the tree-width of graphs. In addition, the tree automaton itself should be a part of the input in practical situations.

The monoid of queue actions

We model the behavior of a fifo-queue as a monoid of transformations that are induced by sequences of writing and reading. We describe this monoid by means of a confluent and terminating semi-Thue system and study some of its basic algebraic properties such as conjugacy. Moreover, we show that while several properties concerning its rational subsets are undecidable, their uniform membership problem is $${{\mathsf {N}}}{{\mathsf {L}}}$$ -complete. Furthermore, we present an algebraic characterization of this monoid’s recognizable subsets. Finally, we prove that it is not Thurston-automatic.

Membership Problem in groups acting freely on [formula omitted]-trees

Groups acting freely on Zn-trees (Zn-free groups) play a key role in the study of non-archimedean group actions. Following Stallingsʼ ideas, we develop graph-theoretic techniques to investigate subgroup structure of Zn-free groups. As an immediate application of the presented method, we give an effective solution to the Uniform Membership Problem and the Power Problem in Zn-free groups.

A performance-enhancement algorithm for the part-machine grouping problem

This paper introduces a novel meta-heuristic algorithm called a “performance-enhancement algorithm”, to solve the part-machine grouping problem. The process of applying the algorithm begins with allocating the parts and machines randomly into different clusters and assigning each of them a uniform initial membership index to each cluster. Each of the parts and machines are then placed in different clusters in turn, and the fitness function is recorded in order to adjust the membership index. Finally, each part and machine is reallocated to the cluster with the highest membership index to get the algorithm ready for next generation. To evaluate the solution quality of this type of grouping scheme, four indexes (total bond energy, exceptional elements, machine utilization, and grouping efficacy) are used as the performance measure of the proposed algorithm. The algorithm has been applied to solve several well-cited problems, and the computational results show that the novel algorithm is effective in finding the best solution and revolution ability.

A Fuzzy Traffic Controller Considering the spillback on the Multiple Crossroads

In this paper, we propose a fuzzy traffic controller of Sugeno`s fuzzy model so as to model the nonlinear characteristics of controlling the traffic light. It use a degree of the traffic congestion of the preceding roads as an input so that it can cope with traffic congestion appropriately, which causes the loss of fuel and our discomfort. First, in order to construct fuzzy traffic controller of Sugeno`s fuzzy model, we model the control process of the traffic light by using Mamdani`s fuzzy model, which has the uniform membership functions of the same size and shape. Second, we make Mamdani`s fuzzy model with the non-uniform membership functions so that it can exactly reflect the knowledge of experts and operators. Last, we construct the fuzzy traffic controller of Sugeno`s fuzzy model by learning from the input/output data, which is retrieved from Mamdani`s fuzzy model with the non-uniform membership functions. We compared and analyzed the fixed traffic light controller, the fuzzy traffic controller of Mamdani`s fuzzy model and the fuzzy traffic controller of Sugeno`s fuzzy model by using the delay time and the proportion of the entered vehicles to the occurred vehicles. As a result of comparison, the fuzzy traffic controller of Sugeno`s fuzzy model showed the best performance.

Coxeter Groups, 2-Completion, Perimeter Reduction and Subgroup Separability

We show that all groups in a very large class of Coxeter groups are locally quasiconvex and have a uniform membership problem solvable in quadratic time. If a group in the class satisfies a further hypothesis it is subgroup separable and relevant homomorphisms are also calculable in quadratic time. The algorithm also decides if a finitely generated subgroup has finite index.

The complexity of membership for deterministic growing context-sensitive grammars∗

In this note, we present an interesting P-complete problem concerning growing context-sensitive grammars, a proper subclass of the context-sensitive grammars. We show that uniform membership for forward deterministic growing context-sensitive grammars is P-complete. As a consequence, we obtain a simple proof for the NP-completeness of the uniform membership problem for growing context- sensitive grammars.

Membership problems for regular and context-free trace languages

Trace languages have been introduced in order to describe the behaviour of concurrent systems in the same way as usual formal languages do for sequential system. They can be defined as subsets of a free partially commutative monoid and a theory of trace languages can be developed, generalizing the usual formal languages theory. In this paper, the time complexity of membership problems for regular and context-free trace languages is investigated. It is proved that the membership problem for context free trace languages can be solved in time O ( BM ( n α )), where α is the dimension of the greatest clique of the concurrency relation C and BM ( n ) is the time required for multiplying two arbitrary n × n boolean matrices. For regular trace languages, our method gives an algorithm which requires O ( n α ) time. Finally, the uniform membership problem is shown to be NP-complete.

Microfoundations of pressure group competition

The core of the model is the explicit microeconomic investigation of pressure group formation, activity, and interaction. At the first stage we envisage two groups consisting of those individuals who are willing to pay for an increase or a decrease, respectively, of some public good relative to the government proposal. Each of these groups play noncooperative lobby-formation game and forms, under certain conditions, a lobbying organization being financed out of uniform membership dues. At the second stage the competition among these lobbies is again modelled as a noncooperative game.