Results 1  10
of
29
Verification of the MillerRabin Probabilistic Primality Test
, 2003
"... Using the HOL theorem prover, we apply our formalization of probability theory to specify and verify the MillerRabin probabilistic primality test. The version of the test commonly found in algorithm textbooks implicitly accepts probabilistic termination, but our own verified implementation satisfie ..."
Abstract

Cited by 18 (3 self)
 Add to MetaCart
Using the HOL theorem prover, we apply our formalization of probability theory to specify and verify the MillerRabin probabilistic primality test. The version of the test commonly found in algorithm textbooks implicitly accepts probabilistic termination, but our own verified implementation
Accelerating the Distributed Multiplication Protocol with Applications to the Distributed MillerRabin Primality Test
"... Summary. In the light of information security it is highly desirable to avoid a “single point of failure ” because this would be an attractive target for attackers. Cryptographic protocols for distributed computations are important techniques in pursuing this goal. An essential module in this conte ..."
Abstract
 Add to MetaCart
classical interpolation formula. The distributed version of the famous probabilistic primality test of Miller and Rabin is built of several modules, which depend on distributed multiplications. Applications of the new method to these modules is studied and its importance for distributed signatures
The Rabin Miller Probabilistic Primality Test: Some Results on the Number of NonWitnesses to Compositeness
"... This paper introduces the reader to the RabinMiller probabilistic primality test, the concept of nonwitnesses to compositeness, and the problem of determining the number of nonwitnesses to compositeness. Given in this paper are two conjectures: one on determining the number of nonwitnesses to co ..."
Abstract
 Add to MetaCart
This paper introduces the reader to the RabinMiller probabilistic primality test, the concept of nonwitnesses to compositeness, and the problem of determining the number of nonwitnesses to compositeness. Given in this paper are two conjectures: one on determining the number of non
Fast primality testing for integers that fit . . .
"... For large integers, the most efficient primality tests are probabilistic. However, for integers with a small fixed number of bits the best tests in practice are deterministic. Currently the best known tests of this type involve 3 rounds of the MillerRabin test for 32bit integers and 7 rounds for 6 ..."
Abstract
 Add to MetaCart
For large integers, the most efficient primality tests are probabilistic. However, for integers with a small fixed number of bits the best tests in practice are deterministic. Currently the best known tests of this type involve 3 rounds of the MillerRabin test for 32bit integers and 7 rounds
Formal Verification of Probabilistic Algorithms
, 2002
"... This thesis shows how probabilistic algorithms can be formally verified using a mechanical theorem prover. We begin with an extensive foundational development of probability, creating a higherorder logic formalization of mathematical measure theory. This allows the definition of the probability spac ..."
Abstract

Cited by 53 (3 self)
 Add to MetaCart
probabilistic programs: sampling algorithms for four probability distributions; some optimal procedures for generating dice rolls from coin flips; the symmetric simple random walk. In addition, we verify the MillerRabin primality test, a wellknown and commercially used probabilistic algorithm. Our fundamental
Probabilistic Hoarelike Logics in Comparison
"... Abstract. Probabilistic algorithms are recognized for their simplicity and speed. A canonical example is the MillerRabin primality test algorithm. It is simple and achieves high accuracy with a small amount of computation. In this paper, we present two verification exercises of this algorithm usin ..."
Abstract
 Add to MetaCart
Abstract. Probabilistic algorithms are recognized for their simplicity and speed. A canonical example is the MillerRabin primality test algorithm. It is simple and achieves high accuracy with a small amount of computation. In this paper, we present two verification exercises of this algorithm
A Note on Monte Carlo Primality Tests and Algorithmic Information Theory
, 1978
"... Solovay and Strassen, and Miller and Rabin have discovered fast algorithms for testing primality which use coinflipping and whose conclusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random or patternles ..."
Abstract
 Add to MetaCart
Solovay and Strassen, and Miller and Rabin have discovered fast algorithms for testing primality which use coinflipping and whose conclusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random
Almost All Primes Can be Quickly Certified
"... This paper presents a new probabilistic primality test. Upon termination the test outputs "composite" or "prime", along with a short proof of correctness, which can be verified in deterministic polynomial time. The test is different from the tests of Miller [M], SolovayStrassen ..."
Abstract

Cited by 87 (4 self)
 Add to MetaCart
This paper presents a new probabilistic primality test. Upon termination the test outputs "composite" or "prime", along with a short proof of correctness, which can be verified in deterministic polynomial time. The test is different from the tests of Miller [M], Solovay
Polynomial Time Algorithms for Testing Probabilistic Bisimulation and Simulation
 Proc. CAV'96, LNCS 1102
, 1996
"... . Various models and equivalence relations or preorders for probabilistic processes are proposed in the literature. This paper deals with a model based on labelled transition systems extended to the probabalistic setting and gives an O(n 2 \Delta m) algorithm for testing probabilistic bisimula ..."
Abstract

Cited by 22 (5 self)
 Add to MetaCart
. Various models and equivalence relations or preorders for probabilistic processes are proposed in the literature. This paper deals with a model based on labelled transition systems extended to the probabalistic setting and gives an O(n 2 \Delta m) algorithm for testing probabilistic
LTL path checking is efficiently parallelizable
 Proc. 36th Int. Conf. Autom. Lang. Program., Part II, Rhodes (Susanne Albers, Alberto MarchettiSpaccamela, Yossi Matias, Sotiris E. Nikoletseas and Wolfgang Thomas, eds.), LNCS 5556, 235– 246, 2009. Leslie Lamport. ‘Sometime’ is sometimes ‘not never’, Pr
"... Abstract. We present an AC 1 (logDCFL) algorithm for checking LTL formulas over finite paths, thus establishing that the problem can be efficiently parallelized. Our construction provides a foundation for the parallelization of various applications in monitoring, testing, and verification. Linearti ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
online, during the execution of the system, or offline, for example based on an error report. Similarly, path checking occurs in testing [2] and in several static verification techniques, notably in MonteCarlobased probabilistic verification, where large numbers of randomly generated sample paths
Results 1  10
of
29