Network algebra with demonic relation operators

Relations with demonic operators are used in studies related to predicate transformer semantics of nondeterministic programs, to model the connection wires in synchronous dataaow networks, or in process algebra setting to model the communication between agents and their envirnoments. The aim of this paper is to provide equational axiomatisations for various classes of nite relations with demonic (including looping) operators. We present axiomatisations for three types of demonic calculi: i.e. calculi for relations with forward demonic {, backward demonic { or two-way demonic operators. The algebraic structures involved are basic network algebras (a certain class of symmetric strict monoidal categories enriched with a looping operation { feedback) with appropriate ramiication and identiication constants.