Loosely Coupled Context-Free Devices

We present a model for distributed systems, where each node consists of two kinds of contextfree devices: grammars generate sequences of messages due to their context-free production set, which are send over the network; pushdown automata accept or reject incoming network messages with respect to their recognition rules. Assuming that the network is a broadcast medium, i.e a local area network, it can easily be shown that the shu e language of all communicating nodes seen by a network monitor is a context-sensitive language. In this paper, we investigate the family of coupled languages: a subfamily of the contextsensitive languages, which contains all context-free languages and is closed under intersection. We show how so-called coupled grammars generate and coupled automata accept words of coupled languages; the coupled automaton consists of loosely coupled pushdown automata. The trick is to restrict a given word to the input alphabet of each pushdown automaton: when all automata accept these restrictions the word belongs to their coupled language. If all pushdown automata use the same input alphabet, so-called normal-form languages are accepted, which are closed under most algebraic operations except the union.