Basic Considerations on Algebraic Structure in Nonnegative Integer Solutions for State Equation of a P/T Petri Net

P/T Petri nets and their extended models have been widely used for modelings, analyses, and verifications for discrete-event dynamic systems in various field. It is one of features that P/T Petri nets are analyzed by state equation. Generators for nonnegative integer homogeneous solutions(i.e., T-invariants) have been deeply studied, but minimal solutions for nonnegative integer inhomogeneous solutions have not been discussed in detail. While the augmented system Ax = 0m×1(A := [A,-b]) of state equation Ax = b has the well-known generators, then we can derive particular solutions of Ax = b from elementaly nonnegative rational T-invariants for Ax = 0m×1. In this paper, fundamental and algebraic properties of T-invariants and particular solutions for both Ax = 0m×1 and Ax = b ≠ 0m×1 are discussed