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The paper determines the number of states in a two-way deterministic finite automaton (2DFA) over a one-letter alphabet sufficient and in the worst case necessary to represent the results of the following operations: (i) intersection of an m-state 2DFA and an n-state 2DFA requires between m + n and m + n + 1 states; (ii) union of an m-state 2DFA and an n-state 2DFA, between m+ n and 2m+ n + 4 states; (iii) Kleene star of an n-state 2DFA, (g(n) + O(n))2 states, where g(n) = e√nln n(1+o(1)) is the maximum value of lcm(p1, . . . , pk) for Σ Pi ≤ n known as Landau's function; (iv) k-th power of an n-state 2DFA, between (k - 1)g(n) - k and k(g(n) + n) states; (v) concatenation of an m-state and an n-state 2DFAs, e(1+o(1)) √(m+n) ln(m+n) states.