Hyperedge Replacement Grammars Sample Clauses

Hyperedge Replacement Grammars. The verification method for pointer-manipulating programs based on hyperedge replacement grammars (HRGs) introduced in [110, 65, 81] aims at abstracting the (possibly) infinite state space arising during the analysis of heap-manipulating programs into a finite one. It employs an intuitive graph-based model of heap structures where vertices can be interpreted as heap objects while labeled edges (i.e., pairs of vertices) visualize selector references between the objects. Additionally, a mapping of program variables to vertices is required to link the program to the heap. Thus pointer-manipulating operations correspond to graph transformations. For the purpose of obtaining a finite state space, hyperedge replacement grammars (HRGs) [51] are utilized to shrink and expand parts of the heap. The production rules of the HRGs reflect the data structures that occur in the program, such as lists, trees, lists of trees, etc. The key idea is to employ hyperedges to represent abstract parts of a heap, e.g., a singly-linked list of arbitrary length. Thus, heap representations are partially concrete and partially abstract. To guarantee soundness of the abstraction approach, additional requirements are to be fulfilled by the HRGs. We are able to list these requirements and show that there exist transformation procedures that output suitable HRGs only [81]. The basic approach has been adapted towards Java programs and implemented in the abstraction framework Juggrnaut [64] featuring e.g. object types, null pointers, method stacks and local as well as static variables. The tool has been successfully applied to various case studies including the Xxxxxxxxx variant [91] of the Deutsch-Xxxxxx-Xxxxx algorithm [117], which is considered a benchmark for pointer program analysis [93, 22].
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