Operational State Complexity of Deterministic Unranked Tree Automata

We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic tree automata are obtained. For tree concatenation we establish a tight upper bound that is of a different order than the known state complexity of concatenation of regular string languages. We show that (n+1) ( (m+1)2^n-2^(n-1) )-1 vertical states are sufficient, and necessary in the worst case, to recognize the concatenation of tree languages recognized by (strongly or weakly) deterministic automata with, respectively, m and n vertical states.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Transformations Between Different Types of Unranked Bottom-Up Tree Automata

We consider the representational state complexity of unranked tree automata. The bottom-up computation of an unranked tree automaton may be either deterministic or nondeterministic, and further variants arise depending on whether the horizontal string languages defining the transitions are represented by a DFA or an NFA. Also, we consider for unranked tree automata the alternative syntactic definition of determinism introduced by Cristau et al. (FCT'05, Lect. Notes Comput. Sci. 3623, pp. 68-79). We establish upper and lower bounds for the state complexity of conversions between different types of unranked tree automata.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Lower bounds for the size of deterministic unranked tree automata

AbstractTree automata operating on unranked trees use regular languages, called horizontal languages, to define the transitions of the vertical states that define the bottom-up computation of the automaton. It is well known that the deterministic tree automaton with smallest total number of states, that is, number of vertical states and number of states used to define the horizontal languages, is not unique and it is hard to establish lower bounds for the total number of states. By relying on existing bounds for the size of unambiguous finite automata, we give a lower bound for the size blow-up of determinizing a nondeterministic unranked tree automaton. The lower bound improves the earlier known lower bound that was based on an ad hoc construction