MemD Category (Categories for the Working Software Defect Researcher, Part 1)

I started applying category theory (as an alternative to traditional set-theoretic approach of memory bits) to memory dump analysis, debugging and software trace analysis in parallel to my studies of that branch of mathematics and reading the book Memory Evolutive Systems. In addition to complex systems modelled in the latter book I apply evolutive systems approach to computer memory. Here is a picture illustrating MemD category of memory dumps (snapshots) as category objects and category arrows as different ways in arriving at the same memory picture:

 

This category definitely applies to software traces as well if we consider every individual trace message or statement as a minidump. We currently consider software trace category MemT as a subcategory of MemD.

Configuration category of a computer memory dump represents its memory internals at an instant t (ideal memory dumps) or at a time interval T: components and links, pointers, wait chains, causal relations, data flows, … .

Pointers and their links are also objects and arrows to form a category, called MemP(tr). The following picture illustrates it with the last pointer shown as a dereference fixpoint:

The perception field of a pointer is a category of all links to its memory location:

However, the operating field of a pointer is its link to a memory location it is pointing to.

- Dmitry Vostokov @ DumpAnalysis.org -

3 Responses to “MemD Category (Categories for the Working Software Defect Researcher, Part 1)”

  1. Crash Dump Analysis » Blog Archive » Operating Closure of Memory (Categories for the Working Software Defect Researcher, Part 2) Says:

    […] part 1 we defined MemP category and the operating field of a pointer as its link to a memory location […]

  2. Crash Dump Analysis » Blog Archive » Collective Pointer (Categories for the Working Software Defect Researcher, Part 3) Says:

    […] example is when we split the perception field of a pointer into disjoint collective pointers (the perception field is already the collective […]

  3. Crash Dump Analysis » Blog Archive » On God and Miracles Says:

    […] that Memory Region B doesn’t have pointers that point outside of it. In other words, all operating fields of Region B pointers are in Region B. However, Region A can have pointers pointing to […]

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