Verifying Sierpinski and Riesel Numbers in ACL2
نویسندگان
چکیده
Sierpiński and Riesel numbers are not easy to find. To disqualify an odd positive integer as a Sierpiński number or a Riesel number, one need only locate a prime in the appropriate infinite list. With four exceptions, k = 47,103,143,197, all of the first 100 odd positive integers, 1 ≤ k ≤ 199, are disqualified as Sierpiński numbers by finding at least one prime in the first eight elements of the infinite list [3]:
منابع مشابه
Mechanically Verifying Real-valued Algorithms in Acl2
ACL2 is a theorem prover over a total, rst-order, mostly quantiier-free logic, supporting deened and constrained functions, equality and congruence rewriting, induction, and other reasoning techniques. Based on the Boyer-Moore theorem prover, ACL2 manages to retain much of the avor of its predecessor, while providing a large number of enhancements, one of which is the direct support of rational...
متن کاملFormally Verifying an Algorithm Based on Interval Arithmetic for Checking Transversality
In this paper we use ACL2 to formally verify the correctness of an algorithm used in the analysis of dynamical systems. The algorithm uses interval arithmetic to check that a given vector field is transverse (non-tangential) to an edge (line segment). Instead of operating on numbers, interval operations operate on intervals, and they are guaranteed to return an over-approximation of the actual ...
متن کاملLinear and Nonlinear Arithmetic in ACL2
As of version 2.7, the ACL2 theorem prover has been extended to automatically verify sets of polynomial inequalities that include nonlinear relationships. In this paper we describe our mechanization of linear and nonlinear arithmetic in ACL2. The nonlinear arithmetic procedure operates in cooperation with the pre-existing ACL2 linear arithmetic decision procedure. It extends what can be automat...
متن کاملTowards the Verification of The AKS Primality Test in ACL2
In this paper we present a recursive implementation of the Agrawal, Kayal and Saxena primality testing algorithm, which is the first unconditional deterministic polynomial time primality testing algorithm. Since the algorithm’s proof of correctness makes use of informal notation and omits many key steps, we present the progress made toward using ACL2 to verify the algorithm’s correctness. In pa...
متن کاملContinuity and Differentiability in ACL2
This case study shows how ACL2 can be used to reason about the real and complex numbers, using non-standard analysis. It describes some modifications to ACL2 that include the irrational real and complex numbers in ACL2’s numeric system. It then shows how the modified ACL2 can prove classic theorems of analysis, such as the intermediate-value and mean-value theorems.
متن کامل