Abstract
A specification of systems based on message passing paradigm is proposed. To this end, an algebraic structure called a semiring of formal polynomials with restricted idempotency of multiplication is taken and fix-point equations specifying (parallel) systems are constructed. Their solution provides an "implementation" of the system, in particular, a Petri net of various kind. Moreover, it determines a global information on capability of sending or receiving a message by objects from a local information on their readiness to do this.
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