A pioneer in the theory of quantum computing and organizing activities in the field, Gruska graduated in mathematics from Commenius University in Bratislava and received a Ph.D. in Computer Science from the Slovak Academy of Sciences in 1965. For most of his career, Gruska has been affiliated with institutes of the Slovak Academy of Sciences.
His research interests have been concentrated in the fields of descriptional complexity (he is one of the founders of the area), parallel automata, and the foundations of computing. His teaching involvement has ranged from high schools (in 1977, he developed a special curriculum and wrote basic textbooks) to teaching at several universities, at home and abroad, to the education of ten Ph.D. students.
Gruska also finished a basic textbook, Foundations of Computing, with a novel, much broader approach than usual, published by International Thomson Computer Press.