Official software site. Intro manual identifies both creators: www.fon.hum.uva.nl/praat/manual/Intro.html . Analysis, synthesis, annotation and scripting are separate capabilities.
Paul Boersma, manual pages dated 13 July 2005 and 21 April 2014 respectively. Section 1 states the source-filter hypothesis; part 2 constructs a formant filter and combines it with a separately created glottal source. Theory citation: www.fon.hum.uva.nl/praat/manual/Fant__1960_.html