848 research outputs found
Complexity of Non-Monotonic Logics
Over the past few decades, non-monotonic reasoning has developed to be one of
the most important topics in computational logic and artificial intelligence.
Different ways to introduce non-monotonic aspects to classical logic have been
considered, e.g., extension with default rules, extension with modal belief
operators, or modification of the semantics. In this survey we consider a
logical formalism from each of the above possibilities, namely Reiter's default
logic, Moore's autoepistemic logic and McCarthy's circumscription.
Additionally, we consider abduction, where one is not interested in inferences
from a given knowledge base but in computing possible explanations for an
observation with respect to a given knowledge base.
Complexity results for different reasoning tasks for propositional variants
of these logics have been studied already in the nineties. In recent years,
however, a renewed interest in complexity issues can be observed. One current
focal approach is to consider parameterized problems and identify reasonable
parameters that allow for FPT algorithms. In another approach, the emphasis
lies on identifying fragments, i.e., restriction of the logical language, that
allow more efficient algorithms for the most important reasoning tasks. In this
survey we focus on this second aspect. We describe complexity results for
fragments of logical languages obtained by either restricting the allowed set
of operators (e.g., forbidding negations one might consider only monotone
formulae) or by considering only formulae in conjunctive normal form but with
generalized clause types.
The algorithmic problems we consider are suitable variants of satisfiability
and implication in each of the logics, but also counting problems, where one is
not only interested in the existence of certain objects (e.g., models of a
formula) but asks for their number.Comment: To appear in Bulletin of the EATC
Determining Labour Shortages and the need for Labour Migration in Germany: Focus-Study by the German National Contact Point for the European Migration Network (EMN)
In der vorliegenden Studie werden die wichtigsten Aspekte und Grundannahmen des aktuellen Diskurses um Fachkräfteengpässe und künftige Fachkräftebedarfe in Deutschland rekonstruiert und zusammengefasst. Sie gibt zudem einen Überblick über die wichtigsten Variablen und Berechnungsgrundlagen zur Bestimmung von Fachkräfteengpässen und zur Identifizierung von Fachkräftebedarfen. Ein flächendeckender Fachkräftemangel ist in Deutschland derzeit nicht zu beobachten, wenngleich sich in einigen Berufen, etwa in der Gesundheits- und in der Pflegebranche, größere Engpässe abzeichnen. Dennoch lassen sich auch in anderen Berufen und Berufszweigen temporär oder regional begrenzt auftretende Fachkräfteengpässe messen, die sich als Momentaufnahme des Arbeitsmarktes entsprechend darstellen lassen. Da es keine "Königsvariable" zur Bestimmung von Fachkräfteengpässen gibt, gestaltet sich die methodische Herangehensweise zu deren Berechnung entsprechend schwierig. Erschwerend kommt hinzu, dass sich die Mobilität der Beschäftigten und die interne Durchlässigkeit der Betriebsstrukturen sowie die Ausrichtung der Stellenprofile als ausgesprochen dynamisch erweisen. Eine Fachkräfteengpassanalyse wird zweimal pro Jahr von der Bundesagentur für Arbeit erstellt. Diese verzichtet aufgrund der genannten methodischen Erfassungsprobleme darin jedoch stets auf eine Nennung zukünftiger Bedarfszahlen, wodurch zugleich eine Festlegung auf konkrete Zuwanderungskontingente vermieden werden kann. Die Migration in den deutschen Arbeitsmarkt im Allgemeinen und in identifizierte Engpass- oder Mangelberufe im Besonderen folgt daher dem Angebot-Nachfrage-Mechanismus.The study maps out important aspects and basic assumptions in relation to the debate about current skilled labour shortages and future demands for skilled labour in Germany. It provides an overview of the most important parameters and calculation bases used to determine and further observe skilled labour shortages and skilled labour supply. There are no signs of a nationwide shortage of labour or even of skilled labour in Germany. Currently, nationwide skilled labour bottlenecks can only be identified in the healthcare and nursing care professions. Notwithstanding the aforementioned, temporary and regional skilled labour bottlenecks certainly exist in other industries and can be recorded as a snapshot of the labour market. Since there is no "King's variable" available to determine skilled labour shortages, it is difficult to adopt a methodological approach for working out exact figures. This is rendered even more difficult by the fact that the mobility of employees, the internal permeability of corporate structures and the orientation of job profiles are extremely dynamic. The Federal Employment Agency (Bundesagentur für Arbeit, BA) is responsible for conducting the so-called "skilled labour shortage analysis" that is published twice a year. Due to the large number of parameters that need to be taken into account and the problem associated with recording actual shortages methodologically, the Federal Employment Agency never mentions a specific number of skilled workers who are likely to be required in future. Migration into the German labour market in general and into shortage occupations in particular adheres to the economic principle of supply and demand
Mobility Rules for Investors, Business Owners and other Business People in Germany: Focus-Study by the German National Contact Point for the European Migration Network (EMN)
Die nationale Studie der deutschen EMN-Kontaktstelle befasst sich mit den grundlegenden Mobilitätsbestimmungen für Investoren und Selbständige und den aufenthaltsrechtlichen Voraussetzungen für die Gründung bzw. Führung eines Unternehmens. In der vorliegenden Fokusstudie werden die organisatorischen und aufenthaltsrechtlichen Grundlagen erörtert, die es Investoren, Selbständigen und anderen Wirtschaftsvertretern aus Drittstaaten ermöglichen, in Deutschland zu investieren und/oder ein Unternehmen zu gründen. Die Studie zeigt, dass sich der Bereich der wirtschaftsbezogenen Mobilität als ausgesprochen dynamisch erweist. Dementsprechend schwierig ist die statistische Erfassung der Daten. So lassen sich zwar Aussagen über die Zahl der in Deutschland aufhältigen Drittstaatsangehörigen (nach § 21 AufenthG) treffen, die selbständig tätig sind. Über die Zahl der nach Deutschland eingereisten Investoren liegen jedoch keine statistischen Erkenntnisse vor. Dies liegt auch daran, dass dem umgangssprachlich so häufig verwendeten Begriff "Investor" keine eindeutige Definition zugrunde liegt. Die Grenzen zwischen Investoren und Selbständigen und ihren Tätigkeiten können zudem fließend sein. Jenseits der aufenthaltsrechtlichen Perspektive wird häufig nicht zwischen den beiden Gruppen unterschieden. Für Drittstaatsangehörige, die in Deutschland ein Unternehmen gründen und führen wollen, gelten - jenseits der aufenthaltsrechtlichen Fragen - dieselben Bedingungen wie für Deutsche und andere EU- oder EWR-Bürger. In den vergangenen Jahren hat es diesbezüglich eine Reihe von gesetzlichen Neuregelungen gegeben, wie etwa die Abschaffung der Mindestinvestitionssumme von 250.000 Euro im Jahr 2012. Zudem gab es Gesetzesänderungen im Bereich der abhängigen Erwerbstätigkeit, die nicht nur auf das Gründungsgeschehen einwirken, sondern auch mittel- und langfristig prognostizierten Engpässen bei Fachkräften entgegenwirken sollen. Die vorliegende Studie wurde von der beim Bundesamt für Migration und Flüchtlinge angesiedelten Nationalen Kontaktstelle des Europäischen Migrationsnetzwerks (EMN) als deutscher Beitrag für eine europaweit vergleichende Untersuchung erstellt und aus EU-Mitteln kofinanziert.Working Paper 61 deals with fundamental mobility rules for investors and self-employed people and with residence preconditions for the foundation respectively management of a company. Organizational and residence basic principles, which enable investors, self-employed people and other business agents from third countries to invest in Germany and/or to found a company, are being discussed in the current Focus Study. This study shows that the field of economic mobility proves to be highly dynamic. The statistical data collection is therefore difficult. Although, statements can be made about the number of self-employed third-country nationals staying in Germany (according to Section 21 of the German Residence Act), there are no statistical data about the number of investors that have moved to the country. This is also due to the fact that the term "investor", often used in colloquial speech, is not based on an exact definition. Furthermore, the borders between investors and self-employed, and their work can be blurred. In many cases no distinction is being made between these two groups when going beyond the perspective of the Residence law. Beyond the Residence law, the same provisions apply to third-country nationals who want to found and manage a company in Germany as to Germans and other EU or EEA citizen. There has been a set of new legal provisions about this topic in recent years, e. g. the elimination of a minimum investment of EUR 250.000 in 2012. Besides, there has been a legislative change in the field of paid employment, which has not only an impact on foundation activities but which should also counteract the forecasted medium- and long-term skilled-labor shortages. Working Paper 61 has been written by the National Contact Point of the European Migration Network (EMN), which has been established at the Federal Office for Migration and Refugees. It is the German contribution towards a pan-European comparative study on "Admitting third-country nationals for business purposes" and has been co-financed by EU funds
The Complexity of Reasoning for Fragments of Autoepistemic Logic
Autoepistemic logic extends propositional logic by the modal operator L. A
formula that is preceded by an L is said to be "believed". The logic was
introduced by Moore 1985 for modeling an ideally rational agent's behavior and
reasoning about his own beliefs. In this paper we analyze all Boolean fragments
of autoepistemic logic with respect to the computational complexity of the
three most common decision problems expansion existence, brave reasoning and
cautious reasoning. As a second contribution we classify the computational
complexity of counting the number of stable expansions of a given knowledge
base. To the best of our knowledge this is the first paper analyzing the
counting problem for autoepistemic logic
Simultaneous Representation of Proper and Unit Interval Graphs
In a confluence of combinatorics and geometry, simultaneous representations provide a way to realize combinatorial objects that share common structure. A standard case in the study of simultaneous representations is the sunflower case where all objects share the same common structure. While the recognition problem for general simultaneous interval graphs - the simultaneous version of arguably one of the most well-studied graph classes - is NP-complete, the complexity of the sunflower case for three or more simultaneous interval graphs is currently open. In this work we settle this question for proper interval graphs. We give an algorithm to recognize simultaneous proper interval graphs in linear time in the sunflower case where we allow any number of simultaneous graphs. Simultaneous unit interval graphs are much more "rigid" and therefore have less freedom in their representation. We show they can be recognized in time O(|V|*|E|) for any number of simultaneous graphs in the sunflower case where G=(V,E) is the union of the simultaneous graphs. We further show that both recognition problems are in general NP-complete if the number of simultaneous graphs is not fixed. The restriction to the sunflower case is in this sense necessary
Opportunities to change the residence title and the purpose of stay in Germany: Focus-Study by the German National Contact Point for the European Migration Network (EMN)
Jährlich wechseln Tausende Migranten ihren Aufenthaltstitel und -zweck, z. B. weil sie nach der Ausbildung in den Beruf wechseln, heiraten oder Asyl beantragen. Die neue EMN-Studie dokumentiert die Voraussetzungen, Konsequenzen und Ausschlusskriterien für den Spurwechsel. Die Studie geht der Frage nach, welche Wechsel zwischen Aufenthaltstiteln und -zwecken unter welchen Voraussetzungen erlaubt sind und mit welchen sozialen und aufenthaltsrechtlichen Konsequenzen diese Wechsel für die betreffenden Personen einhergehen.Every year thousands of immigrants change their residence title and purpose of stay, be it as they change from vocational training into employment, because they get married or due to an application for asylum. The new EMN study documents the various requirements, consequences and exclusion criteria for a status change. The study questions which change of residence title and purpose of stay is possible under which conditions and which social and legal changes come along with each change
Model Checking CTL is Almost Always Inherently Sequential
The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations—restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that in most applications, approaching CTL model checking by parallelism will not result in the desired speed up. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL +, and ECTL +
On complexity and efficiency of mutual information estimation on static and dynamic data
Mutual Information (MI) is an established measure for the dependence of two variables and is often used as a generalization of correlation measures. Existing methods to estimate MI focus on static data. However, dynamic data is ubiquitous as well, and MI estimates on it are useful for stream mining and advanced monitoring tasks. In dynamic data, small changes (e.g., insertion or deletion of a value) may often invalidate the previous estimate. In this article, we study how to efficiently adjust an existing MI estimate when such a change occurs. As a first step, we focus on the well-known nearest-neighbor based estimators for static data and derive a tight lower bound for their computational complexity, which is unknown so far. We then propose two dynamic data structures that can update existing estimates asymptotically faster than any approach that computes the estimates independently, i.e., from scratch. Next, we infer a lower bound for the computational complexity of such updates, irrespective of the data structure and the algorithm, and present an algorithm that is only a logarithmic factor slower than this bound. In absolute numbers, these solutions offer fast and accurate estimates of MI on dynamic data as well.</p
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