Relating Word and Tree Automata - Logic in Computer Science, 1996. LICS '96. Proceedings., Eleventh Annual IEEE Symposium on

I n the automata-theoretic approach to verification, we translate specifications to automata. Complexity considerations motivate the distinction between different types of automata. Already in the 60's) it was known that deterministic Biichi word automata are less expressive than nondeterministic Biichi word automata. The proof is easy and can be stated in a few lines. I n the late 60's) Rabin proved that Buchi tree automata are less expressive than Rabin tree automata. This proof is much harder. I n this work we relate the expressiveness gap between deterministic and nondeterministic Buchi word automata and the expressiveness gap between Buchi and Rabin tree automata. W e consider tree automata that recognize derived languages. For a word language L, the derived language of L , denoted LA, is the set of all trees all of whose paths are in L. Since often we want to specify that all the computations of the program satisfy some property, the interest an derived languages is clear. Our main result shows that L is recognizable b y a nondeterministic Buchi word automaton but not b y a deterministic Biichi word automaton iff L A is recognizable b y a Rabin tree automaton and not by a Biichi tree automaton. Our result provides a simple explanation to the *Address: 600 Mountain Avenue, Murray Hill, NJ 07974, U S A . Email: okaresearch. att . com +Address: School of Mathematics, Tel Aviv 69978, Israel. Email: saf rammath. tau. ac . il $Address: Department of Computer Science, Houston, TX 77005-1892, U.S.A. Email: vardiacs .rice.edu URL: http://www.cs.rice.edu/"vardi expressiveness gap between Biichi and Rabin tree automata. Since the gap between deterministic and nondeterministic Biichi word automata is well understood, our result also provides a characterization of derived languages that can be recognized by Biichi tree automata. Finally, it also provides an exponential determinization of Biichi tree automata that recognize derived languages.