## Geometrical Debugging (Part 1)

Most of (if not all) debugging is arithmetical. Here I would like to introduce a new kind of debugging and troubleshooting approach that interprets observables as objects in their own spaces, for example, the possible space of various GUI forms. These spaces are not necessarily rational-valued spaces of simulation output or discreet arithmetic spaces of memory locations and values.

This geometrical approach applies modeling and systems theory to debugging and troubleshooting by treating them as mappings (or functions in the case of one-to-one or many-to-one mappings) from the space of all possible software environment states (SE) to the space(s) of observables. Here we have a family of mappings to different spaces:

f_{i}: SE → SO_{i}

Some observables can be found fixed like the list of components and the number of mappings can be reduced (i < j):

f_{j}: SE_{a,b,c,d,…} → SO_{j}

In every system and its environment we have something fixed as parameters (a, b, c, d, …) and this could be the list of components as high level ”genotype” or it could be just specific code (low-level “genotype”), specific data or hardware specification. The whole family of mappings become parametrized. If we want, we can reduce mappings even more to treat them as many-valued (one-to-many or many-to-many) if several observables belong to the same kind of space.

Let me illustrate this by an analogy with modeling of a natural system. The system to be modeled is a falling ball together with its environment (Earth). The system obviously has some internal structure (abstract space of states, E) but we don’t know it. Fortunately, we can observe some measurable values like the ball position at any time (Q). So we have these mappings for balls with different masses:

f_{m}: E → Q

We also find that for any individual ball its mass doesn’t change so we abstract it as a parameter:

f: E_{m} → Q

The same modeling approach can be applied to a software system be it an application or a service running inside an operating system or a software system itself running inside a hardware. The case of pure software system abstracted from hardware is simple. In such a case SE space theoretically could be the space of abstract memory dumps. Practically we deal with the space of observables (universal memory dumps) that approximate SE and spaces of software “phenotypes”, observable behaviour, like distorted GUI, for example, or measured values of memory and CPU consumption or disk I/O throughput.

- Dmitry Vostokov @ DumpAnalysis.org -