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 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 Introducing a Space Complexity Measure for P Systems

2009 ◽  
Vol 4 (3) ◽  
pp. 301 ◽  
Author(s):  
Antonio E. Porreca ◽  
Alberto Leporati ◽  
Giancarlo Mauri ◽  
Claudio Zandron
Keyword(s):  
Time Complexity ◽  
Membrane Computing ◽  
Complexity Measure ◽  
Space Complexity ◽  
P Systems ◽  
Complexity Classes ◽  
Mutual Relations ◽  
Initial Results

We define space complexity classes in the framework of membrane computing, giving some initial results about their mutual relations and their connection with time complexity classes, and identifying some potentially interesting problems which require further research.

A survey on space complexity of P systems with active membranes

2018 ◽  
Vol 10 (3) ◽  
pp. 221-229 ◽  
Author(s):  
Alberto Leporati ◽  
Luca Manzoni ◽  
Giancarlo Mauri ◽  
Antonio E. Porreca ◽  
Claudio Zandron
Keyword(s):  
Space Complexity ◽  
P Systems ◽  
Active Membranes

scholarly journals Space complexity equivalence of P systems with active membranes and Turing machines

2014 ◽  
Vol 529 ◽  
pp. 69-81 ◽  
Author(s):  
Artiom Alhazov ◽  
Alberto Leporati ◽  
Giancarlo Mauri ◽  
Antonio E. Porreca ◽  
Claudio Zandron
Keyword(s):  
Space Complexity ◽  
P Systems ◽  
Turing Machines ◽  
Active Membranes

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.

scholarly journals Students’ Understanding on Formal Definition of Limit

2021 ◽  
Vol 1752 (1) ◽  
pp. 012082
Author(s):  
Nurdin ◽  
S F Assagaf ◽  
F Arwadi
Keyword(s):  
Formal Definition ◽  
Definition Of

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.

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