On the equivalence problem for regular Thue systems

AbstractA decision procedure is presented for the equivalence problem for regular almost-confluent Thue systems. On the other hand, the equivalence problem for regular preperfect systems is shown to be undecidable

On the Complexity of the Tiden-Arnborg Algorithm for Unification modulo One-Sided Distributivity

We prove that the Tiden and Arnborg algorithm for equational unification modulo one-sided distributivity is not polynomial time bounded as previously thought. A set of counterexamples is developed that demonstrates that the algorithm goes through exponentially many steps.Comment: In Proceedings UNIF 2010, arXiv:1012.455

Unification of Concept Terms in Description Logics: Revised Version

Unification of concept terms is a new kind of inference problem for Description Logics, which extends the equivalence problem by allowing to replace certain concept names by concept terms before testing for equivalence. We show that this inference problem is of interest for applications, and present first decidability and complexity results for a small concept description language.This revised version of LTCS-Report 97-02 provides a stronger complexity result in Section 6. An abridged version will appear in Proc. ECAI'98

Unfication of Concept Terms in Description Logics

Unification of concept terms is a new kind of inference problem for Description Logics, which extends the equivalence problem by allowing to replace certain concept names by concept terms before testing for equivalence. We show that this inference problem is of interest for applications, and present first decidability and complexity results for a small concept description language

Unification modulo a 2-sorted Equational theory for Cipher-Decipher Block Chaining

We investigate unification problems related to the Cipher Block Chaining (CBC) mode of encryption. We first model chaining in terms of a simple, convergent, rewrite system over a signature with two disjoint sorts: list and element. By interpreting a particular symbol of this signature suitably, the rewrite system can model several practical situations of interest. An inference procedure is presented for deciding the unification problem modulo this rewrite system. The procedure is modular in the following sense: any given problem is handled by a system of `list-inferences', and the set of equations thus derived between the element-terms of the problem is then handed over to any (`black-box') procedure which is complete for solving these element-equations. An example of application of this unification procedure is given, as attack detection on a Needham-Schroeder like protocol, employing the CBC encryption mode based on the associative-commutative (AC) operator XOR. The 2-sorted convergent rewrite system is then extended into one that fully captures a block chaining encryption-decryption mode at an abstract level, using no AC-symbols; and unification modulo this extended system is also shown to be decidable.Comment: 26 page

How Useful are Dag Automata?

25 pagesRapport de Recherche (LIFO)Tree automata are widely used in various contexts; and their emptiness problem is known to be decidable in polynomial time. Dag automata -- with or without labels -- are natural extensions of tree automata, which can also be used for solving problems. Our purpose in this work is to show that algebraically they behave quite differently: the class of dag automata is not closed under complementation, dag automata are not determinizable, their membership problem turns out to be NP-complete, and universality is undecidable; and proving emptiness is NP-complete even for deterministic labeled dag automata