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Work in Progress- ↪️ ↩️
Finite State Automata for Directed Acyclic Graphs
Analogously to regular string and tree languages, regular directed graph (DAG) languages had been defined in literature. Although called regular, those DAG-languages are way more powerful and, consequently, standard problems have a higher complexity than in the string case. Top-down as well as bottom-up deterministic DAG languages are subclasses of the regular DAG languages. We refine this hierarchy by providing a weaker subclass of the deterministic DAG languages. Obviously, this weaker class exhibits beneficial algorithmic properties.
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For a DAG-automaton recognizing a language in this new DAG language class, a classical finite state automaton (FSA) can be constructed whose states enumerate the dangling edges throughout an appropriate run of the DAG-automaton. An edge is called dangling if not yet all of its vertices have been read in the run. This means that an FSA can be used for deciding membership of such DAGs.
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The motivation behind this is the transfer of results about regular string languages to graphs. Furthermore, we provide a characterization of the class via the DAG-automaton's rules.
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