scholarly journals AMulet 2.0 for Verifying Multiplier Circuits

2021 ◽  
pp. 357-364
Author(s):  
Daniela Kaufmann ◽  
Armin Biere
Keyword(s):  
Computer Algebra ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Reduction Algorithm ◽  
Elimination Theory ◽  
Verification Tool ◽  
Polynomial Reduction ◽  
Fully Automatic ◽  
Automatic Tool ◽  
The Given

AbstractAMulet 2.0 is a fully automatic tool for the verification of integer multipliers using computer algebra. Our tool models multiplier circuits given as and-inverter graphs as a set of polynomials and applies preprocessing techniques based on elimination theory of Gröbner bases. Finally it uses a polynomial reduction algorithm to verify the correctness of the given circuit. AMulet 2.0 is a re-factorization and improved re-implementation of our previous multiplier verification tool AMulet 1.0.

scholarly journals Distributive laws between the operads Lie and Com

2020 ◽  
Vol 30 (08) ◽  
pp. 1565-1576
Author(s):  
Murray Bremner ◽  
Vladimir Dotsenko
Keyword(s):  
Lie Algebras ◽  
Computer Algebra ◽  
Gröbner Bases ◽  
Classification Problem ◽  
Grobner Bases ◽  
Polynomial Rings ◽  
Associative Algebras ◽  
Distributive Law ◽  
Free Modules

Using methods of computer algebra, especially, Gröbner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads: we show that the only nontrivial (possibly inhomogeneous) distributive law between the operad of Lie algebras and the operad of commutative associative algebras is given by the Livernet–Loday formula deforming the Poisson operad into the associative operad.

Determining of Level Sets for a Fuzzy Surface Using Gröbner Basis

2015 ◽  
Vol 4 (2) ◽  
pp. 1-14
Author(s):  
Hamed Farahani ◽  
Sajjad Rahmany ◽  
Abdolali Basiri
Keyword(s):  
Level Sets ◽  
Gröbner Basis ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Grobner Basis ◽  
Statistical Nature ◽  
Numerical Examples ◽  
Incomplete Datasets ◽  
The Given

In this paper, a manner to determine the level sets of a fuzzy surface using the benefits of Gröbner basis is presented. Fuzzy surfaces are constructed from incomplete datasets or from data that contain uncertainty which has not statistical nature. The authors firstly define the concept of level sets for the fuzzy surfaces. Then, employing Gröbner bases benefits a criterion is proposed for when the level sets of the fuzzy surface are nonempty sets. Moreover, a new algorithm is designed to determine the level sets. The big advantage of the proposed method lies in the fact that it attains all members of the level sets of the fuzzy surface at a time. Finally, some applied numerical examples are illustrated to demonstrate the proficiency of the given approach.

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