1. In a speech recognition apparatus wherein speech units are each characterized by a sequence of template patterns, and having means for processing a speech input signal for repetitively deriving therefrom, at a frame repetition rate, a plurality of speech recognition acoustic parameters, and means responsive to said acoustic parameters for generating likelihood costs between said acoustic parameters and said speech template patterns, and for processing said likelihood costs for determining the speech units in said speech input signal, a method of template matching and cost processing for recognizing the correspondence of said speech input signal and said template patterns, said method comprising the steps of characterizing the allowable possible sequences of speech units as a grammer graph structure having a beginning node, an ending node and a plurality of intermediate nodes, all said nodes being connected by grammar arcs to at least one other node, initializing each said node with a high cumulative likelihood cost designating a bad score, generating likelihood costs representing the similarity of said acoustic parameters and selected ones of said template patterns, associating with each said node, at each frame time, a cumulative score corresponding to an accumulated template likelihood score in reaching said node, and generating a recognition decision when said cumulative score associated with the ending node is better than the cumulative score associated with any other node, storing a source representation of said grammar graph in a changeable memory of said responsive means, replacing said memory data with a representation of a second grammar graph, and generating a speech recognition decision based upon the second grammar graph, whereby said grammar source representing is software interchangeable and can be edited.