Combining Equational Tree Automata Over AC and ACI Theories

Hendrix, Joe; Ohsaki, Hitoshi

Permalink

https://hdl.handle.net/2142/11428 Copy

Description

Title

Combining Equational Tree Automata Over AC and ACI Theories

Author(s)

• Hendrix, Joe
• Ohsaki, Hitoshi

Issue Date

2008-02

Keyword(s)

computer science

Abstract

In this paper, we study combining equational tree automata in two different senses: (1) whether decidability results about equational tree automata over disjoint theories imply similar decidability results in the combined theory; (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 E contains a single ACI symbol and arbitrary free symbols, is emptiness decidable for a Boolean combination of regular E-tree languages?

Type of Resource

text

Permalink

http://hdl.handle.net/2142/11428

Copyright and License Information

You are granted permission for the non-commercial reproduction, distribution, display, and performance of this technical report in any format, BUT this permission is only for a period of 45 (forty-five) days from the most recent time that you verified that this technical report is still available from the University of Illinois at Urbana-Champaign Computer Science Department under terms that include this permission. All other rights are reserved by the author(s).

Owning Collections