Membership Problem Research Articles

Determining solubility for finitely generated groups of PL homeomorphisms

The set of finitely generated subgroups of the group P L + ( I ) PL_+(I) of orientation-preserving piecewise-linear homeomorphisms of the unit interval includes many important groups, most notably R. Thompson’s group F F . Here, we show that every finitely generated subgroup G > P L + ( I ) G>PL_+(I) is either soluble, or contains an embedded copy of the finitely generated, non-soluble Brin-Navas group B B , affirming a conjecture of the first author from 2009. In the case that G G is soluble, we show the derived length of G G is bounded above by the number of breakpoints of any finite set of generators. We specify a set of ‘computable’ subgroups of P L + ( I ) PL_+(I) (which includes R. Thompson’s group F F ) and give an algorithm which determines whether or not a given finite subset X X of such a computable group generates a soluble group. When the group is soluble, the algorithm also determines the derived length of ⟨ X ⟩ \langle X\rangle . Finally, we give a solution of the membership problem for a particular family of finitely generated soluble subgroups of any computable subgroup of P L + ( I ) PL_+(I) .

On the size of partial derivatives and the word membership problem

On the size of partial derivatives and the word membership problem

Critical Relations of Crowns in Critical Times of Coronavirus Depression

The critical relations are the building blocks of the relational clone of a relational structure with respect to the relational operations intersection and direct product. In this paper we describe the critical relations of crowns. As a consequence, we obtain that the subpower membership problem for any crown is polynomial-time solvable.

Decidability Questions for Insertion Systems and Related Models

Insertion systems or insertion grammars are a generative formalism in which words can only be generated by starting with some axioms and by iteratively inserting strings subject to certain contexts of a fixed maximal length. It is known that languages generated by such systems are always context sensitive and that the corresponding language classes are incomparable with the regular languages. On the other hand, it is possible to generate non-semilinear languages with systems having contexts of length two. Here, we study decidability questions for insertion systems. On the one hand, it can be seen that emptiness and universality are decidable. Moreover, the fixed membership problem is solvable in deterministic polynomial time. On the other hand, the usually studied decidability questions such as, for example, finiteness, inclusion, equivalence, regularity, inclusion in a regular language, and inclusion of a regular language turn out to be undecidable. Interestingly, the latter undecidability results can be carried over to other models which are basically able to handle the mechanism of inserting strings depending on contexts. In particular, new undecidability results are obtained for pure grammars, restarting automata, clearing restarting automata, and forgetting automata.

In the Implementation of State Educational Standards Based on Competency Approach in Mathematics the Problem of Membership and Continuity

This article provides information on the problem of continuity and continuity in the teaching of mathematics and the extent to which it is provided in education. The concepts of continuity and continuity in education are explained in terms of topics in mathematics. The consistent, sequential, coherent placement of mathematical knowledge and its delivery to students is demonstrated by explaining the topics. This means that if a sequence is not maintained in any subject, that is, if the acquired knowledge does not complement the initial knowledge, if it is not enriched in content, if it is not interconnected, it does not form a certain understanding in the student and shows the effectiveness of such teaching. Also, factors influencing the implementation of state educational standards based on the competency approach introduced in our schools have been developed.

Complexity thresholds in inclusion logic

Inclusion logic differs from many other logics of dependence and independence in that it can only describe polynomial-time properties. In this article we examine more closely connections between syntactic fragments of inclusion logic and different complexity classes. Our focus is on two computational problems: maximal subteam membership and the model checking problem for a fixed inclusion logic formula. We show that very simple quantifier-free formulae with one or two inclusion atoms generate instances of these problems that are complete for (non-deterministic) logarithmic space and polynomial time. We also present a safety game for the maximal subteam membership problem and use it to investigate this problem over teams in which one variable is a key. Furthermore, we relate our findings to consistent query answering over inclusion dependencies, and present a fragment of inclusion logic that captures non-deterministic logarithmic space in ordered models.

Barriers and Facilitators of Community-Based Health Insurance Policy Renewal in Low- and Middle-Income Countries: A Systematic Review.

PurposeA growing number of low- and middle-income countries are implementing small-scale community-based health insurance schemes to tackle the burdens posed by direct out-of-pocket payments. Apart from a few successful experiences, such schemes suffer from the problem of persistent low membership which could be attributed to either initial low enrollment or low renewal rate. However, there is a lack of comprehensive information on the factors that influence subscribers’ policy renewal decisions. Hence, we systematically synthesize information to answer the review question ”what are the barriers and facilitators of community-based health insurance policy renewal in low and middle-income countries?”.MethodsWe searched PubMed, Scopus, and Hinari electronic databases in line with the PRISMA guidelines. Our search was limited to studies published from January 2005 to February 2020 in the English language. Additional studies and grey literature were searched using Google Scholar. We included quantitative, qualitative, and mixed-method studies in the review. We assessed the methodological quality of the studies using standardized appraisal tools. The findings were synthesized inductively using a thematic analysis approach.ResultsOur searches retrieved 2386 records among which 27 were included in the review. The thematic synthesis identified six major themes that influence the decision to renew scheme policy: socio-demographic factors; scheme-related awareness and understanding; participation in scheme and other voluntary groupings, need and benefit factors; health-care quality; and scheme operation and policy.ConclusionLower socioeconomic status, poor quality of health care, lack of benefit from the scheme, lack of trust in scheme management, and dissatisfaction with scheme services are important barriers for community-based health insurance policy renewal. Better education, understanding the principles of the scheme, active participation in the scheme, and long-term illness experience of member households facilitate renewal decisions. These are important areas of intervention for governments and other relevant stakeholders to retain members and maintain the sustainability of the schemes.RegistrationThe review protocol was registered in PROSPERO international prospective register of systematic reviews (ID = CRD42020168971).

Towards efficient verification of population protocols

Population protocols are a well established model of computation by anonymous, identical finite-state agents. A protocol is well-specified if from every initial configuration, all fair executions of the protocol reach a common consensus. The central verification question for population protocols is the well-specification problem: deciding if a given protocol is well-specified. Esparza et al. have recently shown that this problem is decidable, but with very high complexity: it is at least as hard as the Petri net reachability problem, which is TOWER-hard, and for which only algorithms of non-primitive recursive complexity are currently known. In this paper we introduce the class { WS}^3 of well-specified strongly-silent protocols and we prove that it is suitable for automatic verification. More precisely, we show that { WS}^3 has the same computational power as general well-specified protocols, and captures standard protocols from the literature. Moreover, we show that the membership and correctness problems for { WS}^3 reduce to solving boolean combinations of linear constraints over {mathbb {N}}. This allowed us to develop the first software able to automatically prove correctness for all of the infinitely many possible inputs.

New results on the prefix membership problem for one-relator groups

In this paper we prove several results regarding decidability of the membership problem for certain submonoids in amalgamated free products and HNN extensions of groups. These general results are then applied to solve the prefix membership problem for a number of classes of one-relator groups which are low in the Magnus–Moldavanskiĭ hierarchy. Since the prefix membership problem for one-relator groups is intimately related to the word problem for one-relator special inverse monoids in the E E -unitary case (as discovered in 2001 by Ivanov, Margolis and Meakin), these results yield solutions of the word problem for several new classes of one-relator special inverse monoids. In establishing these results, we introduce a new theory of conservative factorisations of words which provides a link between the prefix membership problem of a one-relator group and the group of units of the corresponding one-relator special inverse monoid. Finally, we exhibit the first example of a one-relator group, defined by a reduced relator word, that has an undecidable prefix membership problem.

A Dynamic Membership Group-Based Multiple-Data Aggregation Scheme for Smart Grid

In the smart grid, meters report their real-time electricity consumption data to a utility supplier, and the utility supplier can adjust its supply accordingly. However, adversaries can infer users' privacy behaviors based on publicly transferred real-time electricity consumption data. Data aggregation schemes protect users' privacy from being leaked. We find two major problems are unsolved: 1) meter failure problem and 2) dynamic membership problem. To solve these problems, we designed a dynamic membership group-based multiple-data aggregation scheme. First, a group-based key establishment scheme is proposed, meters are divided into groups, meters in a group build keys to encrypt their data, the meter failure problem is alleviated. If one group has broken meters, the other groups will not be affected. Second, the dynamic join, dynamic leave, and meter replacement techniques are proposed, and the dynamic membership is achieved by allowing meters to update their keys. The simulation results show a meter's computation cost and communication cost are the minima among the related works, which makes the proposed scheme more suitable for the IoT scenario. Besides, we designed a data encoding method and a data retrieve method, we designed two attacks: 1) “bilinear map pairing attack” and 2) “zero attack.”

Pledged into Harm: Sorority and Fraternity Members Face Increased Risk of Sexual Assault and Sexual Harassment

The purpose of this manuscript is to examine the risk of sexual exploitation (both assault and harassment) associated with sorority and fraternity membership on U.S. college campuses. The results from this study come from data collected through an online survey. Participants (N=883) at a large Pacific Northwestern university provided information related to their sorority or fraternity membership, experiences of sexual violence (i.e., assault and harassment), and alcohol use. We both replicated and extended past research. Corroborating prior research, Greek-affiliated students experienced higher rates of sexual assault than non-affiliated students. We extended past research by focusing on sexual harassment experiences within the Greek life culture. Both male and female Greek-affiliated students reported higher rates of sexual harassment particularly unwanted sexual attention, compared to their non-Greek-affiliated peers. We also found that both sorority membership and alcohol-related problems predicted unique variance in women’s exposure to nonconsensual sexual contact, attempted/completed rape, and unwanted sexual attention. Fraternity membership but not alcohol-related problems predicted unique variance in men’s exposure to nonconsensual sexual contact and unwanted sexual attention. Implications discussed include the short- and long-term consequences of Greek-affiliation, institutional betrayal, and addressing sexual exploitation within this culture. Also identified are limitations of the current study and future directions for research on sexual exploitation within Greek life.

ICS-GNN

Searching a community containing a given query vertex in an online social network enjoys wide applications like recommendation, team organization, etc. When applied to real-life networks, the existing approaches face two major limitations. First, they usually take two steps, i.e. , crawling a large part of the network first and then finding the community next, but the entire network is usually too big and most of the data are not interesting to end users. Second, the existing methods utilize hand-crafted rules to measure community membership, while it is very difficult to define effective rules as the communities are flexible for different query vertices. In this paper, we propose an Interactive Community Search method based on Graph Neural Network (shortened by ICS-GNN) to locate the target community over a subgraph collected on the fly from an online network. Specifically, we recast the community membership problem as a vertex classification problem using GNN, which captures similarities between the graph vertices and the query vertex by combining content and structural features seamlessly and flexibly under the guide of users' labeling. We then introduce a k -sized Maximum-GNN-scores (shortened by kMG ) community to describe the target community. We next discover the target community iteratively and interactively. In each iteration, we build a candidate subgraph using the crawled pages with the guide of the query vertex and labeled vertices, infer the vertex scores with a GNN model trained on the subgraph, and discover the kMG community which will be evaluated by end users to acquire more feedback. Besides, two optimization strategies are proposed to combine ranking loss into the GNN model and search more space in the target community location. We conduct the experiments in both offline and online real-life data sets, and demonstrate that ICS-GNN can produce effective communities with low overhead in communication, computation, and user labeling.

On the Complexity of the Clone Membership Problem

We investigate the complexity of the Boolean clone membership problem (CMP): given a set of Boolean functions $F$ and a Boolean function $f$, determine if $f$ is in the clone generated by $F$, i.e., if it can be expressed by a circuit with $F$-gates. Here, $f$ and elements of $F$ are given as circuits or formulas over the usual De Morgan basis. B\"ohler and Schnoor (2007) proved that for any fixed $F$, the problem is coNP-complete, with a few exceptions where it is in P. Vollmer (2009) incorrectly claimed that the full problem CMP is also coNP-complete. We prove that CMP is in fact $\Theta^P_2$-complete, and we complement B\"ohler and Schnoor's results by showing that for fixed $f$, the problem is NP-complete unless $f$ is a projection. More generally, we study the problem $B$-CMP where $F$ and $f$ are given by circuits using gates from $B$. For most choices of $B$, we classify the complexity of $B$-CMP as being $\Theta^P_2$-complete (possibly under randomized reductions), coDP-complete, or in P.

Two Problems for Solvable and Nilpotent Groups

Section 1 gives a brief review of known results on embeddings of solvable, nilpotent, and polycyclic groups in 2-generated groups from these classes, including the description of the author’s recently obtained solution to the Mikaelian–Ol’schanskii problem on embeddings of finitely generated solvable groups of derived length l in solvable groups of derived length l + 1 with a fixed small number of generators. Section 2 contains a somewhat more extensive review of known results on the rational subset membership problem for groups, including the presentation of the author’s recently obtained solution to the Laurie–Steinberg–Kambites–Silva–Zetsche problem of whether the membership problem is decidable for finitely generated submonoids of free nilpotent groups.

Operator Splitting for a Homogeneous Embedding of the Linear Complementarity Problem

We present a first-order quadratic cone programming algorithm that can scale to very large problem sizes and produce modest accuracy solutions quickly. Our algorithm returns primal-dual optimal solutions when available or certificates of infeasibility otherwise. It is derived by applying Douglas--Rachford splitting to a homogeneous embedding of the linear complementarity problem, which is a general set membership problem that includes quadratic cone programs (QCPs) as a special case. Each iteration of our procedure requires projecting onto a convex cone and solving a linear system with a fixed coefficient matrix. If a sequence of related problems are solved, then the procedure can easily be warm-started and make use of factorization caching of the linear system. We demonstrate on a range of public and synthetic datasets that for feasible problems our approach tends to be somewhat faster than applying operator splitting directly to the QCP, and in cases of infeasibility our approach can be significantly faster than alternative approaches based on diverging iterates. The algorithm we describe has been implemented in C and is available open-source in the solver SCS v3.0.

On the membership problem for finite automata over symmetric groups

Рассматриваются автоматы с переходами, помеченными произвольными перестановками. Язык такого автомата состоит из композиций перестановок по всем возможным допустимым цепочкам вычислений. Задача проверки принадлежности для конечных автоматов над симметрическими группами - это задача разрешимости, в которой для данного автомата и перестановки необходимо определить, принадлежит ли перестановка языку автомата. В данной работе показано, что эта задача является NP-полной, а также предложен эффективный алгоритм решения задачи для случая сильно связного автомата.

Braid groups of type ADE, Garside monoids, and the categorified root lattice

We study Artin-Tits braid groups $\mathbb{B}_W$ of type ADE via the action of $\mathbb{B}_W$ on the homotopy category $\mathcal{K}$ of graded projective zigzag modules (which categorifies the action of the Weyl group $W$ on the root lattice). Following Brav-Thomas, we define a metric on $\mathbb{B}_W$ induced by the canonical $t$-structure on $\mathcal{K}$, and prove that this metric on $\mathbb{B}_W$ agrees with the word-length metric in the canonical generators of the standard positive monoid $\mathbb{B}_W^+$ of the braid group. We also define, for each choice of a Coxeter element $c$ in $W$, a baric structure on $\mathcal{K}$. We use these baric structures to define metrics on the braid group, and we identify these metrics with the word-length metrics in the Birman-Ko-Lee/Bessis dual generators of the associated dual positive monoid $\mathbb{B}_{W.c}^\vee$. As consequences, we give new proofs that the standard and dual positive monoids inject into the group, give linear-algebraic solutions to the membership problem in the standard and dual positive monoids, and provide new proofs of the faithfulness of the action of $\mathbb{B}_W$ on $\mathcal{K}$. Finally, we use the compatibility of the baric and $t$-structures on $\mathcal{K}$ to prove a conjecture of Digne and Gobet regarding the canonical word-length of the dual simple generators of ADE braid groups.

A generic algorithm for the membership problem in the semigroups of integer matrices

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algorithm on typical (almost all) inputs and ignores the rest of inputs. In this paper we prove generic decidability of the membership problem and the mortality problem for semigroups of integer matrices of arbitrary order.

A Short Contribution to the Theory of Regular Chains

This paper contains short contributions to the theory of regular chains which follow a recent JSC paper by the same authors. These contributions apply to both the nondifferential and the differential context. They deal with the computation of normal forms and with the membership problem to ideals defined by regular chains.

On the Membership Problem of Permutation Grammars — A Direct Proof of NP-Completeness

One of the most essential classes of problems related to formal languages is the membership problem (also called word problem), i.e., to decide whether a given input word belongs to the language specified, e.g., by a generative grammar. For context-free languages the problem is solved efficiently by various well-known parsing algorithms. However, there are several important languages that are not context-free. The membership problem of the context-sensitive language class is PSPACE-complete, thus, it is believed that it is generally not solvable in an efficient way. There are various language classes between the above mentioned two classes having membership problems with various complexity. One of these classes, the class of permutation languages, is generated by permutation grammars, i.e., context-free grammars extended with permutation rules, where a permutation rule allows to interchange the position of two consecutive nonterminals in the sentential form. In this paper, the membership problem for permutation languages is studied. A proof is presented to show that this problem is NP-complete.