1. A speech recognition apparatus comprising: a storage medium for storing tree structured dictionary data that contains a plurality of words as nodes in a tree structure; a backward speech comparison unit for comparing a backward speech resulting from reproducing an input speech in chronologically backward order with a backward acoustic model corresponding to a speech of reversely reproducing a word string sequence toward a root of the tree structure, wherein a comparison is performed in reverse order of the sequence; a forward speech comparison unit for comparing the input speech with a forward acoustic model corresponding to a speech resulting from reproducing a leaf node word of the tree structure in chronologically forward order; a detection unit for detecting a beginning and an end of receiving the input speech, wherein the forward speech comparison unit starts comparing received part of the input speech with the forward acoustic model immediately when the detection unit detects a beginning of receiving the input speech before detecting an end of receiving the input speech; and an output unit for outputting a word or a word string highly likely matching the input speech based on a comparison result each from the backward speech comparison unit and the forward speech comparison unit.