# Polynomial-Time Many-One reductions for Petri nets

• Catherine Dufourd
• Alain Finkel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1346)

## Abstract

We apply to Petri net theory the technique of polynomialtime many-one reductions. We study boundedness, reachability, deadlock, liveness problems and some of their variations. We derive three main results. Firstly, we highlight the power of expression of reachability which can polynomially give evidence of unboundedness. Secondly, we prove that reachability and deadlock are polynomially-time equivalent; this improves the known recursive reduction and it complements the result of Cheng and al. [4]. Moreover, we show the polynomial equivalence of liveness and t-liveness. Hence, we regroup the problems in three main classes: boundedness, reachability and liveness. Finally, we give an upper bound on the boundedness for post self-modified nets: $$2^{O(size(N)^2 *\log size(N))}$$. This improves a decidability result of Valk [18].

## Key words

Petri net theory Complexity Theory Program Verification Equivalences

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