2DFA to 1DFA - Converting two way deterministic finite automata to one way deterministic finite automata
Kozen presents a constructive proof of the equivalence of 1dfa and 2dfa in a chapter of his book titled "Automata and Computability". If I recall correctly,  it is a standard argument and the algrothim follows clearly from the proof. The chapter can be found at the following link.  https://link.springer.com/chapter/10.1007/978-1-4612-1844-9_22