Editing Rete algorithm (section)

=== Beta network ===
The "right" (''beta'') side of the graph chiefly performs joins between different WMEs. It is optional, and is only included if required. It consists of 2-input nodes where each node has a "left" and a "right" input. Each beta node sends its output to a ''beta memory''.

In descriptions of Rete, it is common to refer to token passing within the beta network. In this article, however, we will describe data propagation in terms of WME lists, rather than tokens, in recognition of different implementation options and the underlying purpose and use of tokens. As any one WME list passes through the beta network, new WMEs may be added to it, and the list may be stored in beta memories. A WME list in a beta memory represents a partial match for the conditions in a given production.

WME lists that reach the end of a branch of beta nodes represent a complete match for a single production, and are passed to terminal nodes. These nodes are sometimes called ''p-nodes'', where "p" stands for ''production''. Each terminal node represents a single production, and each WME list that arrives at a terminal node represents a complete set of matching WMEs for the conditions in that production. For each WME list it receives, a production node will "activate" a new production instance on the "agenda". Agendas are typically implemented as [[Priority queue|prioritised queues]].

Beta nodes typically perform joins between WME lists stored in beta memories and individual WMEs stored in alpha memories.   Each beta node is associated with two input memories.    An alpha memory holds WM and performs "right" activations on the beta node each time it stores a new WME.    A beta memory holds WME lists and performs "left" activations on the beta node each time it stores a new WME list.  When a join node is right-activated, it compares one or more attributes of the newly stored WME from its input alpha memory against given attributes of specific WMEs in each WME list contained in the input beta memory.   When a join node is left-activated it traverses a single newly stored WME list in the beta memory, retrieving specific attribute values of given WMEs.   It compares these values with attribute values of each WME in the alpha memory.

Each beta node outputs WME lists that are either stored in a beta memory or sent directly to a terminal node.   WME lists are stored in beta memories whenever the engine will perform additional left activations on subsequent beta nodes.

Logically, a beta node at the head of a branch of beta nodes is a special case because it takes no input from any beta memory higher in the network.  Different engines handle this issue in different ways. Some engines use specialised adapter nodes to connect alpha memories to the left input of beta nodes. Other engines allow beta nodes to take input directly from two alpha memories, treating one as a "left" input and the other as a "right" input.   In both cases, "head" beta nodes take their input from two alpha memories.

In order to eliminate node redundancies, any one alpha or beta memory may be used to perform activations on multiple beta nodes.   As well as join nodes, the beta network may contain additional node types, some of which are described below.   If a Rete contains no beta network, alpha nodes feed tokens, each containing a single WME, directly to p-nodes.   In this case, there may be no need to store WMEs in alpha memories.