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Orbits, half-frozen tokens and the liveness of weighted circuits.

Chrzastowski-Wachtel, Piotr; Raczunas, Marek

In: Desel, J.: Structures in Concurrency Theory, Proceedings of the International Workshop on Structures in Concurrency Theory (STRICT), Berlin, 11-13 May 1995, pages 116-128. 1995.

Abstract: The paper deals with the problem of liveness of weighted.conservative circuits. The weight of a marking gives us an important information about its liveness. Some weights correspond only to live markings, some only to dead ones and some to both. The simultaneous presence of live and dead markings with the same weight is associated with the presence of several equivalence classes generated by the solutions of the state equation. We call such classes orbits. It is impossible to reach from a given marking a state belonging to a different orbit and this creates an opportunity of coexistence of a dead and a live marking with the same weight. Different orbits are also associated with the presence of a kind of frozen tokens, which we call half-frozen. A discussion of problems associated with determining liveness for weighted circuits follows and an arithmetical condition to determine whether a given marking is live is presented.

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