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.

scholarly journals Space and time complexity for infinite time Turing machines

2020 ◽  
Vol 30 (6) ◽  
pp. 1239-1255
Author(s):  
Merlin Carl
Keyword(s):  
Time Complexity ◽  
Space Complexity ◽  
Complexity Classes ◽  
Turing Machines ◽  
Infinite Time ◽  
Space And Time ◽  
Open Questions ◽  
Separation Results ◽  
Ordinal Computability

Abstract We consider notions of space by Winter [21, 22]. We answer several open questions about these notions, among them whether low space complexity implies low time complexity (it does not) and whether one of the equalities P=PSPACE, P$_{+}=$PSPACE$_{+}$ and P$_{++}=$PSPACE$_{++}$ holds for ITTMs (all three are false). We also show various separation results between space complexity classes for ITTMs. This considerably expands our earlier observations on the topic in Section 7.2.2 of Carl (2019, Ordinal Computability: An Introduction to Infinitary Machines), which appear here as Lemma $6$ up to Corollary $9$.

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 Efficient Nonrecursive Bit-Parallel Karatsuba Multiplier for a Special Class of Trinomials

VLSI Design ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yin Li ◽  
Yu Zhang ◽  
Xiaoli Guo
Keyword(s):  
Time Delay ◽  
Special Class ◽  
Time Complexity ◽  
Space Complexity ◽  
Polynomial Basis ◽  
Gate Delay ◽  
Complexity Bound ◽  
Parallel Multiplier ◽  
Highly Efficient ◽  
First Time

Recently, we present a novel Mastrovito form of nonrecursive Karatsuba multiplier for all trinomials. Specifically, we found that related Mastrovito matrix is very simple for equally spaced trinomial (EST) combined with classic Karatsuba algorithm (KA), which leads to a highly efficient Karatsuba multiplier. In this paper, we consider a new special class of irreducible trinomial, namely, xm+xm/3+1. Based on a three-term KA and shifted polynomial basis (SPB), a novel bit-parallel multiplier is derived with better space and time complexity. As a main contribution, the proposed multiplier costs about 2/3 circuit gates of the fastest multipliers, while its time delay matches our former result. To the best of our knowledge, this is the first time that the space complexity bound is reached without increasing the gate delay.

scholarly journals Impact of Membrane Computing and P Systems in ISI WoS. Celebrating the 65th Birthday of Gheorghe Păun

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Ioan DZITAC
Keyword(s):  
Computer Science ◽  
Membrane Computing ◽  
Research Area ◽  
P Systems ◽  
65Th Birthday ◽  
Membrane Systems ◽  
Journal Paper ◽  
Technical Report ◽  
The Impact

Membrane Computing is a branch of Computer Science initiated by<br />Gheorghe Păun in 1998, in a technical report of Turku Centre for Computer Science<br />published as a journal paper ("Computing with Membranes" in Journal of Computer<br />and System Sciences) in 2000. Membrane systems, as Gheorghe Păun called the<br />models he has introduced, are known nowadays as "P Systems" (with the letter P<br />coming from the initial of the name of this research area "father").<br />This note is an overview of the impact in ISI WoS of Gheorghe Păun’s works, focused<br />on Membrane Computing and P Systems field, on the occasion of his 65th birthday<br />anniversary.

scholarly journals Cryptanalytic Performance Appraisal of Improved CCH2 Proxy Multisignature Scheme

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Raman Kumar ◽  
Nonika Singla
Keyword(s):  
Elliptic Curve ◽  
Performance Appraisal ◽  
Time Complexity ◽  
Space Complexity ◽  
Elliptic Curve Cryptosystem ◽  
Forgery Attack ◽  
Signature Schemes ◽  
Computational Overhead ◽  
Threshold Schemes

Many of the signature schemes are proposed in which thetout ofnthreshold schemes are deployed, but they still lack the property of security. In this paper, we have discussed implementation of improved CCH1 and improved CCH2 proxy multisignature scheme based on elliptic curve cryptosystem. We have represented time complexity, space complexity, and computational overhead of improved CCH1 and CCH2 proxy multisignature schemes. We have presented cryptanalysis of improved CCH2 proxy multisignature scheme and showed that improved CCH2 scheme suffered from various attacks, that is, forgery attack and framing attack.

Asynchronous P Systems

2014 ◽  
pp. 90-108
Author(s):  
Tudor Bălănescu ◽  
Radu Nicolescu ◽  
Huiling Wu
Keyword(s):  
Distributed Algorithms ◽  
Complexity Measure ◽  
P Systems ◽  
Breadth First Search ◽  
New Approach ◽  
Depth First Search ◽  
Empirical Results ◽  
A Performance

In this paper, the authors propose a new approach to fully asynchronous P systems, and a matching complexity measure, both inspired from the field of distributed algorithms. The authors validate the proposed approach by implementing several well-known distributed depth-first search (DFS) and breadth-first search (BFS) algorithms. Empirical results show that the proposed P algorithms have shorter descriptions and achieve a performance comparable to the corresponding distributed algorithms.

An Efficient Algorithm for Automating Classification of Chemical Reactions into Classes in Ugi’s Reaction Scheme

2013 ◽  
pp. 285-296
Author(s):  
Sanjay Ram ◽  
Somnath Pal
Keyword(s):  
Chemical Reactions ◽  
Efficient Algorithm ◽  
Time Complexity ◽  
Symmetric Matrix ◽  
Reaction Scheme ◽  
Space Complexity ◽  
Average Case ◽  
Model Driven ◽  
Reaction Matrix

There are two approaches for classification of chemical reactions: Model-Driven and Data-Driven. In this paper, the authors develop an efficient algorithm based on a model-driven approach developed by Ugi and co-workers for classification of chemical reactions. The authors’ algorithm takes reaction matrix of a chemical reaction as input and generates its appropriate class as output. Reaction matrices being symmetric, matrix implementation of Ugi’s scheme using upper/lower tri-angular matrix is of O(n2) in terms of space complexity. Time complexity of similar matrix implementation is O(n4), both in worst case as well as in average case. The proposed algorithm uses two fixed size look-up tables in a novel way and requires constant space complexity. Time complexity both in worst and average cases of the algorithm is linear.

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