Currently, the majority of investigations of linguistic manifestations of neurodegenerative disorders such as Alzheimer's disease are conducted based on manual linguistic analysis. Grammatical complexity is one of the language use characteristics sensitive to the effects of Alzheimer's disease and is difficult to operationalize and measure using manual approaches. In the current study, we demonstrate the application of computational linguistic methods to automate the analysis of grammatical complexity. We implemented the Computerized Linguistic Analysis System (CLAS) based on the Stanford syntactic parser (Klein and Manning, Pattern Recognition, 38(9), 1407-1419, 2005) for longitudinal analysis of changes in syntactic complexity in language affected by neurodegenerative disorders. We manually validated CLAS scoring and used it to analyze writings of Iris Murdoch, a renowned Irish author diagnosed with Alzheimer's disease. We found clear patterns of decline in grammatical complexity consistent with previous analyses of Murdoch's writing conducted by Garrard, Maloney, Hodges, and Patterson (Brain, 128(250-260, 2005). CLAS is a fully automated system that may be used to derive objective and reproducible measures of syntactic complexity in language production and can be particularly useful in longitudinal studies with large volumes of language samples.