Reachability Analyses in Petri Nets by Groebner Bases

Tadashi Matsumoto; Maki Takata; Seiichiro Moro

doi:10.11499/sicep.2002.0.179.0

SICE Annual Conference 2002

DOI https://doi.org/10.11499/sicep.2002.0.179.0

会議情報

主催: The Society of Instrument and Control Engineers

共催: IEEE/Industiral Electronic Society, IEEE/Robotics and Automation Society, IEEE/Control System Society

Reachability Analyses in Petri Nets by Groebner Bases

Tadashi Matsumoto, Maki Takata, Seiichiro Moro

著者情報

キーワード: Integer programming, Groebner basis, Buchberger algorithm, Algebraic geometry,, Petri net reachability problems, Symbolic computation systems

会議録・要旨集フリー

p. 179

詳細

抄録

Finding an non-negative integer solution x∈Z^n×1₊ for Ax=b (A∈Z^m×n, b∈Z^m×1) in Petri nets is NP-complete. Being NP-complete, even algorithms with theoretically bad worst case and with average complexity can be useful for a special class of problems, hence deserve investigation. Then a Groebner basis approach to integer programming problems was proposed in 1991 and some symbolic computation systems became to have useful tools for ideals, varieties, and algorithms for algebraic geometry. In this paper, two kinds of examples are given to show how Groebner basis approach is applied to reachability problems in Petri nets.

責任著者(Corresponding author)

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