Reachability Analysis of Procedural Programs with Affine Integer Arithmetic

2006 ◽  
pp. 281-282 ◽  
Author(s):  
Michael Luttenberger
Keyword(s):  
Reachability Analysis ◽  
Integer Arithmetic

Symbolic Reachability Analysis of Hybrid Systems

2009 ◽  
Vol 19 (12) ◽  
pp. 3111-3121 ◽  
Author(s):  
Hai-Bin ZHANG ◽  
Zhen-Hua DUAN
Keyword(s):  
Hybrid Systems ◽  
Reachability Analysis

Reachability analysis of nonlinear hybrid systems based on polyhedron inclusion

2013 ◽  
Vol 33 (5) ◽  
pp. 1289-1293
Author(s):  
Jin ZOU ◽  
Wang LIN ◽  
Yong LUO ◽  
Zhenbing ZENG
Keyword(s):  
Hybrid Systems ◽  
Reachability Analysis ◽  
Nonlinear Hybrid

An Ada package for multi-precision integer arithmetic

1993 ◽  
Vol 19 (2) ◽  
pp. 17-24 ◽  
Author(s):  
D. G. Knight
Keyword(s):  
Integer Arithmetic

scholarly journals Computing the Exact Number of Similarity Classes in the Longest Edge Bisection of Tetrahedra

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1447
Author(s):  
Jose P. Suárez ◽  
Agustín Trujillo ◽  
Tania Moreno
Keyword(s):  
Data Structure ◽  
Stability Condition ◽  
Open Problem ◽  
Integer Arithmetic ◽  
Exact Number ◽  
Similarity Class ◽  
The Stability ◽  
High Level ◽  
The Cost

Showing whether the longest-edge (LE) bisection of tetrahedra meshes degenerates the stability condition or not is still an open problem. Some reasons, in part, are due to the cost for achieving the computation of similarity classes of millions of tetrahedra. We prove the existence of tetrahedra where the LE bisection introduces, at most, 37 similarity classes. This family of new tetrahedra was roughly pointed out by Adler in 1983. However, as far as we know, there has been no evidence confirming its existence. We also introduce a new data structure and algorithm for computing the number of similarity tetrahedral classes based on integer arithmetic, storing only the square of edges. The algorithm lets us perform compact and efficient high-level similarity class computations with a cost that is only dependent on the number of similarity classes.

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