He is the author of a number of classic results on synthesis, reliability, and classification of control systems (Russian: Управляющие системы), the term used in the USSR and Russia for a generalization of finite-state automata, Boolean circuits and multi-valued logic circuits.

Yablonsky and his students were ones of the first in the world to raise the issues of potentially inherent unavoidability of the brute force search for some problems, the precursor of the P = NP problem, though Gödel's letter to von Neumann, dated 20 March 1956 and discovered in 1988, may have preceded them.

[1] In Russia, a group led by Yablonsky had the idea that combinatorial problems are hard in proportion to the amount of brute-force search required to find a solution.

In particular, they noticed that for many problems they could not find a useful way to organize the space of potential solutions so as to avoid brute force search.

[3] In August 1942, after completing his first year at Moscow State University's Faculty of Mechanics and Mathematics, Yablonsky, then 17, went to serve in the Soviet Army, fighting in the second world war as a member of the tank brigade 242.

Over the period of the 1950s and 1960s, together with Alexey Lyapunov, Yablonsky organized the seminar on cybernetics, showing his support to the new field of mathematics that had been a subject of a significant controversy fueled by Soviet ideologists.

In 1966 Yablonsky (together with Yuri Zhuravlyov and Oleg Lupanov) was awarded Lenin Prize for their work on the theory of control systems (in the discrete-mathematical sense, as explained above).

Yablonsky played an active role in the creation of the Faculty of Computational Mathematics and Cybernetics at Moscow State University in 1970.