We discuss two dichotomic views on crossing dependencies. This kind of phenomena is relevant both for natural language and biology as has been extensively argued. On one hand, we discuss an approach that looks for formalisms more powerful than context free grammars to capture the phenomena as a word recognition problem. On the other hand, we present an approach that deals with the same kind of problem, using finite state technology, but instead of treating the problem as a word recognition problem, it is solved using an automata construction approach. Unrestricted crossing dependencies are exemplified using the well known problem of propositional satisfiability.