Checking geometric programs or verification of geometric structures

Abstract

A program checker verifies that a particular program execution is correct.

Certifying algorithms

“…We use a proof checker for the formal system S to verify that w 2 is a proof for statement (7). We use an interpreter for the programming language L to verify that w 3 is the run of P on input x and that y = P(x).…”

“…14 shows, i.e., the non-smoothness of simplicial surfaces complicates matters. The following theorem is the proper formulation for the polyhedral case: We refer the reader to [7] for a proof of this result. Fig.…”

“…The papers [76] and [7] describe methods for certifying convexity of polyhedra and convex hulls (see Section 9.1) and various types of planar subdivisions, such as triangulations, Delaunay triangulations, and convex subdivisions. Another application of local to global principles for certification of convexity can be found in [100].…”

“…The term "certifying algorithm" was first used in [6]. Before that Mehlhorn and Näher used the term Program Checking or Result Checking, see [7][8][9]. We give a detailed account of extant work in Section 4.…”

Construction Sequences and Certifying 3-connectivity

“…The concept of certifying algorithms, which give a small and easy-to-verify certificate of correctness along with their output, was initiated by Blum and Kannan [3] and developed further by Mehlhorn et al [8][9][10]. While being important for program verification, certifying algorithms often provide new insights into a problem, which can lead to new techniques.…”