I study some problems concerning pseudo-freeness of families of computational universal algebras. Several types of decidability for classes of algebraic systems in polynomial time using an oracle that performs basic operations and predicates were studied. I obtained some results concerning both decidability and undecidability in polynomial time for some finitely based varieties of universal algebras. A number of problems from the Kourovka Notebook was solved. Most part of the Cand. Sci. thesis was concerned with algorithmic problems for groups presented by finitely many generators and identical relations as well as for finitely based varieties of groups.
Main publications:
M. Anokhin, “A certain family of subgroups of $\mathbb Z_n^\star$ is weakly pseudo-free under the general integer factoring intractability assumption”, Groups Complex. Cryptol., 10:2 (2018), 99–110
M. Anokhin, “Pseudo-free families of finite computational elementary abelian $p$-groups”, Groups Complex. Cryptol., 9:1 (2017), 1–18
M. Anokhin, “Constructing a pseudo-free family of finite computational groups under the general integer factoring intractability assumption”, Groups Complex. Cryptol., 5:1 (2013), 53 –74
M. I. Anokhin, “Decidability of classes of algebraic systems in polynomial time”, Sb. Math., 193:2 (2002), 157–186
M. I. Anokhin, “Embedding lattices in lattices of varieties of groups”, Izv. Math., 63:4 (1999), 649–665
ISTINA
