P/Tペトリネットの状態方程式の非負整数解の代数的構造に関する基礎的考察

概要

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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.
2009-08-01