scholarly journals The Computational Complexity of Structure-Based Causality

2017 ◽  
Vol 58 ◽  
pp. 431-451 ◽  
Author(s):  
Gadi Aleksandrowicz ◽  
Hana Chockler ◽  
Joseph Y. Halpern ◽  
Alexander Ivrii
Keyword(s):  
Computational Complexity ◽  
Complexity Classes ◽  
Final Version ◽  
New Family ◽  
Original Definition ◽  
Np Complete ◽  
Definition Of

Halpern and Pearl introduced a definition of actual causality; Eiter and Lukasiewicz showed that computing whether X = x is a cause of Y = y is NP-complete in binary models (where all variables can take on only two values) and Σ^P_2 -complete in general models. In the final version of their paper, Halpern and Pearl slightly modified the definition of actual cause, in order to deal with problems pointed out by Hopkins and Pearl. As we show, this modification has a nontrivial impact on the complexity of computing whether {X} = {x} is a cause of Y = y. To characterize the complexity, a new family D_k^P , k = 1, 2, 3, . . ., of complexity classes is introduced, which generalises the class DP introduced by Papadimitriou and Yannakakis (DP is just D_1^P). We show that the complexity of computing causality under the updated definition is D_2^P -complete. Chockler and Halpern extended the definition of causality by introducing notions of responsibility and blame, and characterized the complexity of determining the degree of responsibility and blame using the original definition of causality. Here, we completely characterize the complexity using the updated definition of causality. In contrast to the results on causality, we show that moving to the updated definition does not result in a difference in the complexity of computing responsibility and blame.

scholarly journals Low complexity algorithms in knot theory

2019 ◽  
Vol 29 (02) ◽  
pp. 245-262
Author(s):  
Olga Kharlampovich ◽  
Alina Vdovina
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Linear Time ◽  
Circuit Complexity ◽  
Equivalence Problem ◽  
Low Complexity ◽  
Combinatorial Structure ◽  
Complexity Classes ◽  
Np Complete ◽  
Almost All

Agol, Haas and Thurston showed that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. This shows that (unless P[Formula: see text]NP) the genus problem has high computational complexity even for knots in a 3-manifold. We initiate the study of classes of knots where the genus problem and even the equivalence problem have very low computational complexity. We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace[Formula: see text]. Alternating knots with some additional combinatorial structure will be referred to as standard. As expected, almost all alternating knots of a given genus are standard. We show that the genus problem for these knots belongs to [Formula: see text] circuit complexity class. We also show, that the equivalence problem for such knots with [Formula: see text] crossings has time complexity [Formula: see text] and is in Logspace[Formula: see text] and [Formula: see text] complexity classes.

scholarly journals Alternative space definitions for P systems with active membranes

2021 ◽  
Author(s):  
Artiom Alhazov ◽  
Alberto Leporati ◽  
Luca Manzoni ◽  
Giancarlo Mauri ◽  
Claudio Zandron
Keyword(s):  
Physical Space ◽  
Space Complexity ◽  
P Systems ◽  
Complexity Classes ◽  
Formal Definition ◽  
Single Object ◽  
Active Membranes ◽  
Original Definition ◽  
Definition Of ◽  
Alternative Space

AbstractThe first definition of space complexity for P systems was based on a hypothetical real implementation by means of biochemical materials, and thus it assumes that every single object or membrane requires some constant physical space. This is equivalent to using a unary encoding to represent multiplicities for each object and membrane. A different approach can also be considered, having in mind an implementation of P systems in silico; in this case, the multiplicity of each object in each membrane can be stored using binary numbers, thus reducing the amount of needed space. In this paper, we give a formal definition for this alternative space complexity measure, we define the corresponding complexity classes and we compare such classes both with standard space complexity classes and with complexity classes defined in the framework of P systems considering the original definition of space.

scholarly journals Logarithmic Space Verifiers on NP-complete

2019 ◽  
Author(s):  
Frank Vega
Keyword(s):  
Computer Science ◽  
Complexity Class ◽  
Complexity Classes ◽  
Input Tape ◽  
Open Problems ◽  
Logarithmic Space ◽  
Np Completeness ◽  
Np Complete ◽  
Definition Of ◽  
Np Problem

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have f ailed. NP is the complexity class of languages defined b y p olynomial t ime v erifiers M su ch th at wh en th e in put is an el ement of the language with its certificate, then M outputs a string which belongs to a single language in P. Another major complexity classes are L and NL. The certificate-based definition of NL is based on logarithmic space Turing machine with an additional special read-once input tape: This is called a logarithmic space verifier. NL is the complexity class of languages defined by logarithmic space verifiers M s uch t hat when t he i nput i s a n e lement o f t he l anguage with i ts c ertificate, th en M outputs 1. To attack the P versus NP problem, the NP-completeness is a useful concept. We demonstrate there is an NP-complete language defined by a logarithmic space verifier M such that when the input is an element of the language with its certificate, then M outputs a s tring which belongs to a single language in L. In this way, we obtain if L is not equal to NL, then P = NP. In addition, we show that L is not equal to NL. Hence, we prove the complexity class P is equal to NP.

scholarly journals A Virtual Class Calculus

2005 ◽  
Vol 34 (577) ◽  
Author(s):  
Erik Ernst ◽  
Klaus Ostermann ◽  
William Cook
Keyword(s):  
Programming Languages ◽  
Large Scale ◽  
Object Identity ◽  
New Family ◽  
Original Definition ◽  
Virtual Class ◽  
Virtual Classes ◽  
Program Composition ◽  
Definition Of ◽  
Open Question

Virtual classes are class-valued attributes of objects.<br />Like virtual methods, virtual classes are defined in<br />an object’s class and may be redefined within subclasses.<br />They resemble inner classes, which are also<br />defined within a class, but virtual classes are accessed<br />through object instances, not as static components<br />of a class. When used as types, virtual classes depend<br />upon object identity – each object instance introduces<br />a new family of virtual class types. Virtual classes support large-scale program composition techniques,<br />including higher-order hierarchies and family<br />polymorphism. The original definition of virtual<br />classes in Beta left open the question of static type<br />safety, since some type errors were not caught until<br />runtime. Later the languages Caesar and gbeta have<br />used a more strict static analysis in order to ensure<br />static type safety. However, the existence of a sound,<br />statically typed model for virtual classes has been a<br />long-standing open question. This technical report<br />presents a virtual class calculus, vc, that captures<br />the essence of virtual classes in these full-fledged programming languages. The key contributions of the<br />paper are a formalization of the dynamic and static<br />semantics of vc and a proof of the soundness of vc.<br />Categories: D.3.3 [Language Constructs and Features]:<br />Classes and objects, inheritance, polymorphism.<br />F.3.3 [Studies of Program Constructs]:<br />Object-oriented constructs, type structure. F.3.2<br />[Semantics of Programming Languages]: Operational<br />semantics.

Populism and Liberal Democracy

2019 ◽  
Author(s):  
Takis S. Pappas
Keyword(s):  
United States ◽  
Liberal Democracy ◽  
The United States ◽  
Comprehensive Theory ◽  
The People ◽  
Original Definition ◽  
Key Issues ◽  
Great Relevance ◽  
Definition Of

Based on an original definition of modern populism as “democratic illiberalism” and many years of meticulous research, Takis Pappas marshals extraordinary empirical evidence from Argentina, Greece, Peru, Italy, Venezuela, Ecuador, Hungary, the United States, Spain, and Brazil to develop a comprehensive theory about populism. He addresses all key issues in the debate about populism and answers significant questions of great relevance for today’s liberal democracy, including: • What is modern populism and how can it be differentiated from comparable phenomena like nativism and autocracy? • Where in Latin America has populism become most successful? Where in Europe did it emerge first? Why did its rise to power in the United States come so late? • Is Trump a populist and, if so, could he be compared best with Venezuela’s Chávez, France’s Le Pens, or Turkey’s Erdoğan? • Why has populism thrived in post-authoritarian Greece but not in Spain? And why in Argentina and not in Brazil? • Can populism ever succeed without a charismatic leader? If not, what does leadership tell us about how to challenge populism? • Who are “the people” who vote for populist parties, how are these “made” into a group, and what is in their minds? • Is there a “populist blueprint” that all populists use when in power? And what are the long-term consequences of populist rule? • What does the expansion, and possibly solidification, of populism mean for the very nature and future of contemporary democracy? Populism and Liberal Democracy will change the ways the reader understands populism and imagines the prospects of liberal democracy.

Logical Decision Problems and Complexity of Logic Programs

1987 ◽  
Vol 10 (1) ◽  
pp. 1-33
Author(s):  
Egon Börger ◽  
Ulrich Löwen
Keyword(s):  
Fixed Point ◽  
Computational Complexity ◽  
Decision Problem ◽  
Decision Problems ◽  
Complexity Classes ◽  
Logic Programs ◽  
Finite Structures ◽  
Syntactic Restrictions

We survey and give new results on logical characterizations of complexity classes in terms of the computational complexity of decision problems of various classes of logical formulas. There are two main approaches to obtain such results: The first approach yields logical descriptions of complexity classes by semantic restrictions (to e.g. finite structures) together with syntactic enrichment of logic by new expressive means (like e.g. fixed point operators). The second approach characterizes complexity classes by (the decision problem of) classes of formulas determined by purely syntactic restrictions on the formation of formulas.

scholarly journals Popular Matching in Roommates Setting Is NP-hard

2021 ◽  
Vol 13 (2) ◽  
pp. 1-20
Author(s):  
Sushmita Gupta ◽  
Pranabendu Misra ◽  
Saket Saurabh ◽  
Meirav Zehavi
Keyword(s):  
Computational Complexity ◽  
Np Hard ◽  
Np Complete ◽  
Open Question ◽  
Popular Matching

An input to the P OPULAR M ATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) where each vertex ranks its neighbors in strict order, known as its preference. In the P OPULAR M ATCHING problem the objective is to test whether there exists a matching M * such that there is no matching M where more vertices prefer their matched status in M (in terms of their preferences) over their matched status in M *. In this article, we settle the computational complexity of the P OPULAR M ATCHING problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.

scholarly journals Proportional lumpability and proportional bisimilarity

2021 ◽  
Author(s):  
Andrea Marin ◽  
Carla Piazza ◽  
Sabina Rossi
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Upper And Lower Bounds ◽  
General Definition ◽  
Performance Indices ◽  
State Aggregation ◽  
Structural Regularity ◽  
Original Definition ◽  
Aggregation Technique ◽  
Definition Of

AbstractIn this paper, we deal with the lumpability approach to cope with the state space explosion problem inherent to the computation of the stationary performance indices of large stochastic models. The lumpability method is based on a state aggregation technique and applies to Markov chains exhibiting some structural regularity. Moreover, it allows one to efficiently compute the exact values of the stationary performance indices when the model is actually lumpable. The notion of quasi-lumpability is based on the idea that a Markov chain can be altered by relatively small perturbations of the transition rates in such a way that the new resulting Markov chain is lumpable. In this case, only upper and lower bounds on the performance indices can be derived. Here, we introduce a novel notion of quasi-lumpability, named proportional lumpability, which extends the original definition of lumpability but, differently from the general definition of quasi-lumpability, it allows one to derive exact stationary performance indices for the original process. We then introduce the notion of proportional bisimilarity for the terms of the performance process algebra PEPA. Proportional bisimilarity induces a proportional lumpability on the underlying continuous-time Markov chains. Finally, we prove some compositionality results and show the applicability of our theory through examples.

scholarly journals Feynman diagrams and rooted maps

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 149-167 ◽  
Author(s):  
Andrea Prunotto ◽  
Wanda Maria Alberico ◽  
Piotr Czerski
Keyword(s):  
Single Particle ◽  
Feynman Diagram ◽  
Feynman Diagrams ◽  
Topological Properties ◽  
Many Body ◽  
Perturbative Order ◽  
Original Definition ◽  
Many Body Systems ◽  
Definition Of ◽  
Particle Propagator

Abstract The rooted maps theory, a branch of the theory of homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.

Systemic Lupus Erythematosus Disease Activity Index 2000 Responder Index-50 Enhances the Ability of SLE Responder Index to Identify Responders in Clinical Trials

2011 ◽  
Vol 38 (11) ◽  
pp. 2395-2399 ◽  
Author(s):  
ZAHI TOUMA ◽  
DAFNA D. GLADMAN ◽  
DOMINIQUE IBAÑEZ ◽  
SHAHRZAD TAGHAVI-ZADEH ◽  
MURRAY B. UROWITZ
Keyword(s):  
Systemic Lupus Erythematosus ◽  
Clinical Trials ◽  
Disease Activity ◽  
Lupus Erythematosus ◽  
Activity Index ◽  
Disease Activity Index ◽  
Systemic Lupus ◽  
Original Definition ◽  
Definition Of

Objective.To evaluate the performance of the Systemic Lupus Erythematosus (SLE) Responder Index (SRI) when the SLE Disease Activity Index 2000 (SLEDAI-2K) is substituted with SLEDAI-2K Responder Index-50 (SRI-50), a valid and reliable index of disease activity improvement. Also, to determine whether the SRI-50 will enhance the ability of SRI in detecting responders.Methods.Our study was conducted on patients who attended the Lupus Clinic from September 2009 to September 2010. SLEDAI-2K, SRI-50, the British Isles Lupus Assessment Group measure, and the Physician’s Global Assessment were determined initially and at followup. SRI was determined at the followup visit according to its original definition using the SLEDAI-2K score and by substituting SLEDAI-2K with SRI-50.Results.A total of 117 patients with SLEDAI-2K ≥ 4 at baseline were studied. Patients had 1 followup visit over a 3-month period. Twenty-nine percent of patients met the original definition of SRI and 35% of patients met the definition of SRI when SLEDAI-2K was substituted with SRI-50. The use of SRI-50 allowed determination of significant improvement in 7 additional patients. This improvement could not be discerned with the use of SLEDAI-2K as a component of SRI. At followup visits that showed improvement, SRI-50 scores decreased to a greater extent than SLEDAI-2K scores (p < 0.0001).Conclusion.SRI-50 enhances the ability of SRI to identify patients with clinically important improvement in disease activity. SRI-50 was superior to SLEDAI-2K in detecting partial clinical improvement, ≥ 50%, between visits. These properties of the SRI-50 enable it to be used as an independent outcome measure of improvement or as a component of SRI in clinical trials.

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