def dfa_word_acceptance(dfa: dict, word: list) ->bool:
    """ Checks if a given **word** is accepted by a DFA,
    returning True/false.

    The word w is accepted by a DFA if DFA has an accepting run
    on w. Since A is deterministic,
    :math:`w ∈ L(A)` if and only if :math:`ρ(s_0 , w) ∈ F` .

    :param dict dfa: input DFA;
    :param list word: list of actions ∈ dfa['alphabet'].
    :return: *(bool)*, True if the word is accepted, False in the
             other case.
    """
    current_state = dfa['initial_state']
    for action in word:
        if (current_state, action) in dfa['transitions']:
            current_state = dfa['transitions'][current_state, action]
        else:
            return False
    if current_state in dfa['accepting_states']:
        return True
    else:
        return False
