1. A speech recognition system comprising: a first speech recognition device; a second speech recognition device; and an acoustic model identifier series generation apparatus, wherein the first speech recognition device comprises: a sound input unit configured to obtain sound and to output sound data of the obtained sound; a first recognition dictionary configured to store recognition data formed of a combination of information on a character string, and an acoustic model identifier series based on a first type of feature, the acoustic model identifier series corresponding to the information on the character string; a first speech recognition processing unit configured to extract the first type of feature from a piece of the sound data outputted by the sound input unit, and to perform a speech recognition process on the piece of sound data using the first type of feature and the first recognition dictionary; and a recognition data registration unit, the second speech recognition device comprises: a second recognition dictionary configured to store recognition data formed of a combination of information on a character string, and an acoustic model identifier series based on a second type of feature corresponding to the information on the character string and different from the first type of feature; and a second speech recognition processing unit configured to extract the second type of feature from the piece of sound data, and to perform a speech recognition process on the piece of sound data using the second type of feature and the second recognition dictionary, and to transmit information on a character string corresponding to the piece of sound data to an outside, the acoustic model identifier series generation apparatus comprises an acoustic model identifier series generation unit configured to extract the first type of feature from the piece of sound data, and to generate an acoustic model identifier series based on the first type of feature corresponding to the piece of sound data, and to transmit the acoustic model identifier series, the recognition data registration unit of the first speech recognition device: receives the acoustic model identifier series based on the first type of feature corresponding to the piece of sound data transmitted by the acoustic model identifier series generation unit, and the information on the character string corresponding to the piece of sound data transmitted by the second speech recognition processing unit; and registers, in the first recognition dictionary, the recognition data be stored in the first recognition dictionary, the recognition data being formed of a combination of the received acoustic model identifier series based on the first type of features and the information on the character string.