Algebraic modelling of an ad hoc network for mobile computing

We develop an algebraic model of an ad hoc network (Johnson, 1994) for mobile computing. The ad hoc network´s structure and functionality is based (in our approach) on a pathset algebra. A pathset is the set of all paths in the network having specific source(s) and destination(s). The pathsets´ set refers to a multi-digraph that constitutes the physical infrastructure of an ad hoc network. The applications, actions, and/or services (referred further under the general term services) are organized as multi-agent systems. The formal model of every multi-agent system is based on a modal algebra. An additional function (or special operation) couples the two algebras specifying thus the interface of their interoperability. This operation is analogous to the scalar multiplication of a vector space on a field