Memory Dump - A Mathematical Definition

This is the first post in Science of Memory Dump Analysis category where I apply philosophy, systems theory, mathematics, physics and computer science ideas. It was inspired after reading Life Itself book written by Robert Rosen where computers are depicted as direct sums of states. As shown in that book, in the case of machines, their synthetic models (direct sums) are equivalent to analytic models (direct product of observables). Taking every single bit as an observable having its values in Z2 set {0, 1} we can make a definition of an ideal memory dump as a direct product or a direct sum of bits saved instantaneously at the given time:

i si = i si

Of course, we can also consider bytes having 8 bits as observables having their values from Z256 set, etc.

In our case we can simply rewrite direct sum or product as the list of bits, bytes, words or double words, etc:

(…, si-1, si, si+1, …, sj-1, sj, sj+1, …)

According to Rosen we include hardware states (registers, for example) and partition memory into input, output states for particular computation and other states.

Saving a memory dump takes certain amount of time. Suppose that it takes 3 discrete time events (ticks). During the first tick we save memory up to (…, si-1, si) and that memory has some relationship to sj state. During the second tick sj state changes its value and during the 3rd tick we copy the rest of the memory (si+1, …, sj-1, sj, sj+1, …). Now we see that the final memory dump is inconsistent:

(…, si-1, si, si+1, …, sj-1, sj, sj+1, …)

I explained this earlier in plain words in Inconsistent Dump pattern. Therefore we might consider a real memory dump as a direct sum of disjoint memory areas Mt taken during some time interval (t0, …, tn)

M = t Mt where Mt = k stk or simply

M = t k stk

- Dmitry Vostokov @ -

8 Responses to “Memory Dump - A Mathematical Definition”

  1. Crash Dump Analysis » Blog Archive » Memoretics Says:

    […] Memoretics studies computer memory snapshots and their evolution in […]

  2. Crash Dump Analysis » Blog Archive » Memiotics: a definition Says:

    […] of computer memory snapshots (memory dumps) is the domain of memoretics. Computer memory semiotics (memiotics) is the branch […]

  3. Crash Dump Analysis » Blog Archive » Universal Memory Dump: A Definition Says:

    […] (0×7D9) - The Year of Debugging Applying  a mathematical definition of a memory dump to natural systems we can introduce: Universal Memory Dump: A snapshot of observables describing […]

  4. Crash Dump Analysis » Blog Archive » Geometrical Debugging (Part 1) Says:

    […] 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 […]

  5. Crash Dump Analysis » Blog Archive » Software Trace - A Mathematical Definition Says:

    […] where every tsi is a sequence of bits, bytes or other discrete units (see the definition of a memory dump): […]

  6. Crash Dump Analysis » Blog Archive » The Meaning of DATA Says:

    […] was suddenly enlightened by the unification of software traces with memory dumps and it came to me that DATA is simply Dump Analysis + Trace Analysis. It is commutative with TADA, […]

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