Bottom-Up Tree Automata with Term Constraints

We introduce bottom-up tree automata with equality and disequality term constraints. These constraints are more expressive than the equality and disequality constraints between brothers introduced by Bogaert and Tison in 1992. Our new class of automata is still closed under Boolean operations. Moreover, we show that for tree automata with term constraints not only membership but also emptiness is decidable. This contrasts with the undecidability of emptiness for automata with arbitrary equality constraints between subterms identified by paths as shown in 1981 by Mongy.

[1]  Max Dauchet,et al.  Encompassment Properties and Automata with Constraints , 1993, RTA.

[2]  Christof Löding,et al.  On Nondeterministic Unranked Tree Automata with Sibling Constraints , 2009, FSTTCS.

[3]  Florent Jacquemard,et al.  Ground Reducibility and Automata with Disequality Constraints , 1994, STACS.

[4]  Guillem Godoy,et al.  The Emptiness Problem for Tree Automata with Global Constraints , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[5]  Hubert Comon,et al.  Tree automata techniques and applications , 1997 .

[6]  Jean-Marc Talbot,et al.  Tree Automata with Global Constraints , 2008, Int. J. Found. Comput. Sci..

[7]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[8]  Carme Àlvarez,et al.  The HOM problem is decidable , 2010, STOC '10.

[9]  Florent Jacquemard,et al.  Ground reducibility is EXPTIME-complete , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[10]  Florent Jacquemard,et al.  Pumping, Cleaning and Symbolic Constraints Solving , 1994, ICALP.

[11]  Sophie Tison,et al.  Equality and Disequality Constraints on Direct Subterms in Tree Automata , 1992, STACS.

[12]  Thom W. Frühwirth,et al.  Logic programs as types for logic programs , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.