Enhancing automatic speech recognition for mathematical applications via incremental parsing

Automatic speech recognition and automatic speech understanding systems have, over recent years, improved to the extent that they are used in many practical applications ranging from dictation systems to voice control of household devices (through systems such as Alexa and Amazon Echo) and dialogue systems for telephone shopping and customer services for utility companies. However, advancements in speech input systems for mathematical applications have tended to lag behind those for more general or commercial situations.
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\nOur system TalkMaths, which has been under development for several years, is an exception to this, and allows spoken dictation and editing of mathematical text (in standard mathematical notation) using relatively natural spoken language commands. However, up to now, correcting a mistake in a spoken form of a mathematical expression has required a complete re-parse of the spoken input, which is time consuming and potentially frustrating to the user.
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\nIn this paper, we discuss ways of improving on this situation using incremental approaches to parsing. These were first devised to make the parsing and compilation of computer program code more efficient, by only re-parsing those parts of the program code which had actually changed, and merging the parse trees of the unchanged and modified parts of the code. We adapt this methodology to allow editing of spoken forms of mathematical expressions, and their associated parse trees, and describe and discuss initial experiments to compare the performance of these novel methods with those of more conventional approaches.