Improved Algorithm of Global Model-Checking for Propositional μ-Calculus

2012 ◽  
Vol 263-266 ◽  
pp. 2314-2319
Author(s):  
Hua Jiang ◽  
Jian Qing Xi
Keyword(s):  
Model Checking ◽  
Time Complexity ◽  
Transition System ◽  
Global Model ◽  
Space Complexity ◽  
Partial Ordering ◽  
Improved Algorithm

Based on the research of the author when he was a Ph.D. student, he deeply studied the proposition of μ-Calculus, and used solving the partial ordering relation in formula μ-Calculus to solve formula μ-Calculus quickly. This paper improves and perfects the algorithm in reference [11]. The time complexity of the algorithm in this paper is O((2n+1)^(d/2+1)), its space complexity is O(dn), where n is the number of states in the transition system and d is the nesting depth of fixpoint operators in the formula of proposition μ-Calculus.

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 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.

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.

A New Algorithm for Euclidean Shortest Path of Visiting Segments in a Polygon

2014 ◽  
Vol 644-650 ◽  
pp. 1891-1894
Author(s):  
Li Juan Wang ◽  
An Sheng Deng ◽  
Bo Jiang ◽  
Qi Wei
Keyword(s):  
Test Data ◽  
Shortest Path ◽  
Time Complexity ◽  
Simple Polygon ◽  
Rubber Band ◽  
Crossing Over ◽  
Euclidean Shortest Path ◽  
Adjacent Segments ◽  
Improved Algorithm

Let s and t be two points on the boundary of a simple polygon, how to compute the Euclidean shortest path between s and t which visits a sequence of segments given in the simple polygon is the problem to be discussed, especially, the situation of the adjacent segments intersect is the focus of our study. In this paper, we first analyze the degeneration applying rubber-band algorithm to solve the problem. Then based on rubber-band algorithm, we present an improved algorithm which can solve the degeneration by the method of crossing over two segments to deal with intersection and in our algorithm the adjacent segments order can be changed when they intersect. Particularly, we have implemented the algorithm and have applied a large of test data to test it. The experiments demonstrate that our algorithm is correct and efficient, and it has the same time complexity as the rubber-band algorithm.

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 $9$.

MODEL CHECKING OF COMPONENT BASED SOFTWARE USING COMPOSITIONAL REDUCTIONS

2008 ◽  
Vol 18 (05) ◽  
pp. 683-712 ◽  
Author(s):  
MOHAMMAD IZADI ◽  
ALI MOVAGHAR
Keyword(s):  
Model Checking ◽  
Composition Operators ◽  
Linear Time ◽  
Operational Semantics ◽  
Computing System ◽  
Transition System ◽  
Compositional Model ◽  
Temporal Properties ◽  
Labeled Transition System ◽  
Constraint Automata

A component-based computing system consists of two main parts: a set of components and a coordination subsystem. Reo is an exogenous coordination language for compositional construction of the coordination subsystem. Constraint automaton has been defined as the operational semantics of Reo. The main goal of this paper is to prepare a model checking method for verifying linear time temporal properties of component-based systems whose coordinating subsystems are modeled by Reo and components are modeled by labeled transition systems. For this purpose, we introduce modified definitions of constraint automata and their composition operators by which, every constraint automaton can be considered as a labeled transition system and each labeled transition system can be translated into a constraint automaton. We show that failure-based equivalences CFFD and NDFD are congruences with respect to the composition operators of constraint automata. Also we present a method for compositional model checking of component-based systems using these equivalences for reducing the sizes of constraint automata models.

An Algorithm for Testing Isomorphism of Planer Graph Based on Distant Matrix

2012 ◽  
Vol 487 ◽  
pp. 317-321
Author(s):  
Yan Peng Wu ◽  
Shui Qiang Liu
Keyword(s):  
Graph Theory ◽  
Polynomial Time ◽  
Time Complexity ◽  
Graph Isomorphism ◽  
Distance Matrix ◽  
Space Complexity ◽  
The Subject ◽  
The Many

The testing for graph isomorphism is one of the many problems in the subject of graph theory. This thesis proposes an algorithm for testing isomorphism of planer graph of polynomial time via structuring characteristics of planer graph based on distance matrix. The algorithm, with a time complexity of O (n^4) and a space complexity of O (n^2), has a great application value.

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