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Questions tagged [tree-automata]

Tree automata work on finite or infinite trees. They generalize word automata (Finite, Buchi, Rabin, Streett, Muller, etc.).

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Can all regular tree types be expressed as $\mu$ types?

In "Types and Programming Languages", Pierce gives a translation from recursive types ($\mu$ types) to types expressed as regular trees: possibly infinite trees, but with finitely many distinct subtrees. I'm wondering, is the converse true? Can…
Joey Eremondi
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Proving the (Non-)Emptiness condition for Rabin tree automata given by Pnueli and Rosner

At section 8 of the paper On the Synthesis of a Reactive Module, the authors state the following theorem: Proposition 2 (Non-Emptiness Condition) Let $A = (Q, \delta, Q_0, \Omega)$ be a tree automaton with $\Omega = \{(L_i, U_i) | 1 \leq i \leq…
xpicox
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Can Nondet Rabin Tree automaton be determinized?

In other words, are they equally powerful? (for word automata the answer is "yes"; this question is about tree automata). (i am talking about tree automata that work on $in$finite trees)
Ayrat
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State-of-the-art for Set Constraints?

I've recently stumbled across the field of Set constraints for program analysis, that is, solving equations of the form $exp_1 \subseteq exp_2$, where (depending on the particular variant of the problem), $exp_i$ is a term involving $\cup, \cap,…
Joey Eremondi
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How do tree automata work?

I've started with tree automata. The definition is (Leaf-to-root) Tree automaton $\mathcal M$ over (nonempty, finite) alphabet $\Sigma$ is quintuple $\mathcal M=(K,\Sigma,\delta,S,F)$ and bound $f$ (the fan-in bound), where $K$ is finite set of…
byk7
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Extending minimal top-down tree automata

I'm trying to find an algorithm to update minimal top-down tree automata/hypergraphs. Regular tree grammars can be seen as definitions for recursive data structures: List -> cons(Bool, List) | nil() Bool -> true() | false() By minimal I mean that…
Taren
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Algorithm to determine if a top-down non deterministic tree automaton accepts some tree?

Given a non-deterministic top-down tree automaton, is there an algorithm that can determine if there exists any tree that is accepted by this automaton? if so, what is the most efficient algorithm known? Thanks.
BOB123
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Construction of a Deterministic Tree Automaton (DTA)

Let $L \subseteq \Sigma^*$ be a regular language. Let $\Sigma' = \Sigma_0 \cup \Sigma_2$ where $\Sigma_0 =\Sigma$ and $\Sigma_2=\{*\}$. We define $T_L=\{t \in t_{\Sigma'} \mid \text{The leafs from t are from a word in $L$}\}$ as a tree language. The…
Marc
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Resources on Tree Automata Regular Expressions

Is there a text that goes through some explicit examples of converting tree automata to tree regular expressions? I'm working through Comon's "Tree Automata Techniques and Applications", and I'm trying to work out some examples of regular…
TomKern
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