In this paper, we study combining equational tree automata in two different senses: (1) whether decidability results about equational tree automata over disjoint theories ε1 and ε2 imply similar decidability results in the combined theory ε1 ∪ ε2; (2) checking emptiness of a language obtained from the Boolean combination of regular equational tree languages. We present a negative result for the first problem. Specifically, we show that the intersection-emptiness problem for tree automata over a theory containing at least one AC symbol, one ACI symbol, and 4 constants is undecidable despite being decidable if either the AC or ACI symbol is removed. Our result shows that decidability of intersection-emptiness is a non-modular property even for the union of disjoint theories. Our second contribution is to show a decidability result which implies the decidability of two open problems: (1) If idempotence is treated as a rule f(x,x) →x rather than an equation f(x,x)=x, is it decidable whether an AC tree automata accepts an idempotent normal form? (2) If ε contains a single ACI symbol and arbitrary free symbols, is emptiness decidable for a Boolean combination of regular ε-tree languages? © 2008 Springer-Verlag.
CITATION STYLE
Hendrix, J., & Ohsaki, H. (2008). Combining equational tree automata over AC and ACI theories. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5117 LNCS, pp. 142–156). https://doi.org/10.1007/978-3-540-70590-1_10
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