Trace Analysis Patterns (Part 252)
Monday, August 4th, 2025We can view traces and logs as abstract polynomials that consists of abstract monomials. For example, if we have trace messages A,B,C, and D, the trace ABCACACACCD represents a single monomial. The multiplication operation in monomials represents message concatenation. But we can also split the trace as an abstract sum of several monomials, for example, ABC + AC + AC + AC + CD, or ABC + 3*AC + CD. The addition operation is a concatenation of traces even if concatenated traces consist of just one message. Note the distinction here between concatenation of messages and traces. By Trace Polynomial we mean a canonical abstract polynomial representation where we divide the trace by monomial when the next message in the message stream is already contained in the previous monomial, for example, ABC + 2AC + AC^2D.
Both addition and multiplication are non-commutative, and no distributivity between them. Mathematically speaking, we have the so-called a non‑distributive bi‑semigroup, or, in a category-theoretic sense, such abstract polynomials are objects in a free 2‑semigroupal category without interchange.
- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -