Krohn–Rhodes-like decomposition conjecture for Krom programs

A propositional Krom logic program is a finite set of propositional rules of the form $a\leftarrow b$, possibly together with facts, and sequential composition is the program operation described in the paper. A program is aperiodic or a permutation program according to the corresponding algebraic decomposition notions.

Krohn–Rhodes-like decomposition conjecture. Every propositional Krom logic program can be sequentially decomposed into aperiodic and permutation programs.

This is proposed as an analogue of the Krohn–Rhodes decomposition in the algebra of Krom logic programs. The statement is presented as a computationally motivated conjecture, and no proof or counterexample is supplied; its status therefore remains open.