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 a first acoustic model identifier series based on a first type of feature, the first 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; a recognition data registration unit; and a transmitter configured to transmit the sound data outputted by the sound input unit to the second speech recognition device and the acoustic model identifier series generation apparatus, the second speech recognition device comprises: a first receiver configured to receive the sound data transmitted from the first speech recognition device; a second recognition dictionary configured to store recognition data formed of a combination of information on a character string, and a second acoustic model identifier series based on a second type of feature corresponding to the information on the character string, the second type of feature being 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 the sound data transmitted from the first speech recognition device, 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 the recognition data registration unit of the first speech recognition device, the acoustic model identifier series generation apparatus comprises: a second receiver configured to receive the sound data transmitted from the first speech recognition device; and an acoustic model identifier series generation unit configured to extract the first type of feature from the piece of the sound data transmitted from the first speech recognition device, and to generate the first acoustic model identifier series based on the first type of feature corresponding to the piece of the sound data, and to transmit the first acoustic model identifier series to the recognition data registration unit of the first recognition device, the recognition data registration unit of the first speech recognition device: receives the first acoustic model identifier series generated by the acoustic model identifier series generation unit and the information on the character string corresponding to the piece of sound data generated by the second speech recognition device; and forms a new recognition data of a combination of the received first acoustic model identifier series and the received information on the character string, and registers the new recognition data in the first recognition dictionary, wherein the second recognition dictionary is different from the first recognition dictionary in at least one of a system of an acoustic model identifier, a structure of parameters of an acoustic model, and the number of phonemes corresponding to one acoustic model, wherein the acoustic model of the first speech recognition device and the acoustic model of the second recognition device are not compatible with each other such that the first speech recognition device and the second recognition device are configured to extract different features, respectively, from identical sound data.