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The paper determines the number of states in two-way deterministic finite automata (2DFA) over a one-letter alphabet sufficient and in the worst case necessary to represent the results of basic language-theoretic operations on 2DFAs with a certain number of states. It is proved that (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^(^1^+^o^(^1^)^)^n^l^n^n is the maximum value of lcm(p"1,...,p"k) for @?p"i=