Hilbert's tenth problem
Term rewriting and all that
Journal of the ACM (JACM)
WMP '00 Proceedings of the Workshop on Multiset Processing: Multiset Processing, Mathematical, Computer Science, and Molecular Computing Points of View
Beyond Regularity: Equational Tree Automata for Associative and Commutative Theories
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Expressiveness of a Spatial Logic for Trees
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
The Mathematical Theory of Context-Free Languages
The Mathematical Theory of Context-Free Languages
XML schema, tree logic and sheaves automata
Applicable Algebra in Engineering, Communication and Computing
Theoretical Computer Science - Foundations of software science and computation structures
Alternating two-way AC-tree automata
Information and Computation
Journal of Computer and System Sciences
Recognizing boolean closed A-tree languages with membership conditional rewriting mechanism
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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Tree automata modulo associativity and commutativity axioms, called AC tree automata, accept trees by iterating the transition modulo equational reasoning. The class of languages accepted by monotoneAC tree automata is known to include the solution set of the inequality $x \times y \geqslant z$, which implies that the class properly includes the AC closure of regular tree languages. In the paper, we characterize more precisely the expressiveness of monotone AC tree automata, based on the observation that, in addition to polynomials, a class of exponential constraints (called monotone exponential Diophantine inequalities) can be expressed by monotone AC tree automata with a minimal signature. Moreover, we show that a class of arithmetic logic consisting of monotone exponential Diophantine inequalities is definable by monotone AC tree automata. The results presented in the paper are obtained by applying our novel tree automata technique, called linearly bounded projection.