Study on Deterministic and Probabilistic Computation of Primality Test

2019 ◽  
Author(s):  
Jyotshna Rajput ◽  
Abhishek Bajpai
Keyword(s):  
Probabilistic Computation ◽  
Primality Test

Bounded Model Checking for Probabilistic Computation Tree Logic

2012 ◽  
Vol 23 (7) ◽  
pp. 1656-1668 ◽  
Author(s):  
Cong-Hua ZHOU ◽  
Zhi-Feng LIU ◽  
Chang-Da WANG
Keyword(s):  
Model Checking ◽  
Bounded Model Checking ◽  
Probabilistic Computation ◽  
Computation Tree Logic ◽  
Computation Tree

scholarly journals Cover Picture: Optochemical Control of DNA‐Switching Circuits for Logic and Probabilistic Computation (Angew. Chem. Int. Ed. 7/2021)

2021 ◽  
Vol 60 (7) ◽  
pp. 3313-3313
Author(s):  
Xiewei Xiong ◽  
Mingshu Xiao ◽  
Wei Lai ◽  
Li Li ◽  
Chunhai Fan ◽  
...  
Keyword(s):  
Probabilistic Computation ◽  
Switching Circuits

scholarly journals A primality test for $Kp^n+1$ numbers

2014 ◽  
Vol 84 (291) ◽  
pp. 505-512 ◽  
Author(s):  
José María Grau ◽  
Antonio M. Oller-Marcén ◽  
Daniel Sadornil
Keyword(s):  
Primality Test

scholarly journals COMPARISON STUDY OF FERMAT, SOLOVAY-STRASSEN AND MILLER-RABIN PRIMALITY TEST USING MATHEMATICA 6.0

2012 ◽  
Vol 3 (1) ◽  
pp. 1-10
Author(s):  
Ega Gradini
Keyword(s):  
Quantitative Comparison ◽  
Comparison Study ◽  
Source Codes ◽  
Powerful Test ◽  
Euler’S Theorem ◽  
Primality Test ◽  
Miller Test ◽  
Mathematica Software ◽  
The Given

This paper presents three primality tests; Fermat test, Solovay-Strassen test, and Rabin-Miller test. Mathematica software is used to carry out the primality tests. The application of Fermat’s Litle Theorem as well as Euler’s Theorem on the tests was also discussed and this leads to the concept of pseudoprime. This paper is also discussed some results on pseudoprimes with certain range and do quantitative comparison. Those primality tests need to be evaluated in terms of its ability to compute as well as correctness in determining primality of given numbers. The answer to this is to create a source codes for those tests and evaluate them by using Mathematica 6.0. Those are Miller-Rabin test, Solovay-Strassen test, Fermat test and Lucas-Lehmer test. Each test was coded using an algorithm derived from number theoretic theorems and coded using the Mathematica version 6.0. Miller-Rabin test, SolovayStrassen test, and Fermat test are probabilistic tests since they cannot certainly identify the given number is prime, sometimes they fail. Using Mathematica 6.0, comparison study of primality test has been made and given the Miller- Rabin test as the most powerful test than other.

On multitype branching processes in a random environment

1981 ◽  
Vol 13 (3) ◽  
pp. 464-497 ◽  
Author(s):  
David Tanny
Keyword(s):  
Random Environment ◽  
Stability Condition ◽  
Branching Processes ◽  
Classification Theorem ◽  
Regularity Conditions ◽  
Exponential Rate ◽  
Probabilistic Computation ◽  
Multitype Branching Processes ◽  
The Stability ◽  
Functional Iteration

This paper is concerned with the growth of multitype branching processes in a random environment (mbpre). It is shown that, under suitable regularity conditions, the process either explodes of becomes extinct. A classification theorem is given delineating the cases of explosion or extinction. Furthermore, it is shown that the process grows at an exponential rate on its set of non-extinction provided the process is stable. Criteria is given for non-certain extinction of the mbpre to occur, and an example shows that the stability condition cannot be removed. The method of proof used, in general, is direct probabilistic computation rather than the classical functional iteration techniques. Growth theorems are first proved for increasing mbpre and subsequently transferred to general mbpre using the associated mbpre and the reduced mbpre.

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