 With Benda and his wife Kamila's decision during the Soviet-led invasion of August 1968 not to flee the country, he remained at Charles University.Benda completed his doctorate in theoretical cybernetics in 1975, published works on philosophy and mathematics, and then worked as a computer programmer.Benda was active in the dissident movement against the Czechoslovak Socialist Republic, and in 1977 became a signatory to Charter 77.