Handbook of formal languages, vol. 3
Journal of the ACM (JACM)
A Method for Automatic Cryptographic Protocol Verification
IPDPS '00 Proceedings of the 15 IPDPS 2000 Workshops on Parallel and Distributed Processing
Reasoning about The Past with Two-Way Automata
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
A Good Class of Tree Automata and Application to Inductive Theorem Proving
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Decidability and Closure Properties of Equational Tree Languages
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Counting and equality constraints for multitree automata
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Theoretical Computer Science - Foundations of software science and computation structures
A survey of algebraic properties used in cryptographic protocols
Journal of Computer Security
Alternating two-way AC-tree automata
Information and Computation
Languages Modulo Normalization
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Combining Equational Tree Automata over AC and ACI Theories
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Flat and One-Variable Clauses for Single Blind Copying Protocols: The XOR Case
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
On the completeness of context-sensitive order-sorted specifications
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
On the complexity of equational horn clauses
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Automata and logics for unranked and unordered trees
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Alternation in equational tree automata modulo XOR
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
YAPA: A Generic Tool for Computing Intruder Knowledge
ACM Transactions on Computational Logic (TOCL)
| Hi-index | 0.00 |
We study two-way tree automata modulo equational theories. We deal with the theories of Abelian groups (ACUM), idempotent commutative monoids (ACUI), and the theory of exclusive-or (ACUX), as well as some variants including the theory of commutative monoids (ACU). We show that the one-way automata for all these theories are closed under union and intersection, and emptiness is decidable. For two-way automata the situation is more complex. In all these theories except ACUI, we show that two-way automata can be effectively reduced to one-way automata, provided some care is taken in the definition of the so-called push clauses. (The ACUI case is open.) In particular, the two-way automata modulo these theories are closed under union and intersection, and emptiness is decidable. We also note that alternating variants have undecidable emptiness problem for most theories, contrarily to the non-equational case where alternation is essentially harmless.