Multiple congruence relations, first-order theories on terms, and the frames of the applied pi-calculus

Authors:
Florent Jacquemard;Étienne Lozes;Ralf Treinen;Jules Villard
Affiliations:
LSV, ENS Cachan, CNRS UMR 8643 and INRIA, France;LSV, ENS Cachan, CNRS UMR 8643 and INRIA, France;PPS, Université Paris Diderot, CNRS UMR 7126, France;LSV, ENS Cachan, CNRS UMR 8643 and INRIA, France
Venue:
TOSCA'11 Proceedings of the 2011 international conference on Theory of Security and Applications
Year:
2011

Citing 18
Cited 0

Equational problems anddisunification

Journal of Symbolic Computation
Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems

Information and Computation
A new method for undecidability proofs of first order theories

Journal of Symbolic Computation
Equational formulae with membership constraints

Information and Computation
Syntacticness, cycle-syntacticness, and shallow theories

Information and Computation
Logic with equality: partisan corroboration and shifted pairing

Information and Computation
Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems: Abstract Properties and Applications to Term Rewriting Systems

Journal of the ACM (JACM)
Mobile values, new names, and secure communication

POPL '01 Proceedings of the 28th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The first-order theory of subtyping constraints

POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Satisfiability of Systems of Ordinal Notations with the Subterm Property is Decidable

ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Undecidability of the exists*forall* Part of the Theory of Ground Term Algebra Modulo an AC Symbol

RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Encompassment Properties and Automata with Constraints

RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Automatic Structures

LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Structural Subtyping of Non-Recursive Types is Decidable

LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Deciding knowledge in security protocols under equational theories

Theoretical Computer Science - Automated reasoning for security protocol analysis
A Logical Characterisation of Static Equivalence

Electronic Notes in Theoretical Computer Science (ENTCS)
A Spatial Equational Logic for the Applied Π-Calculus

CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Termination of rewriting with right-flat rules

RTA'07 Proceedings of the 18th international conference on Term rewriting and applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate the problem of deciding first-order theories of finite trees with several distinguished congruence relations, each of them given by some equational axioms. We give an automata-based solution for the case where the different equational axiom systems are linear and variable-disjoint (this includes the case where all axioms are ground), and where the logic does not permit to express tree relations x =f (y ,z ). We show that the problem is undecidable when these restrictions are relaxed. As motivation and application, we show how to translate the model-checking problem of $\mathcal{A}\pi \mathcal{L}$ , a spatial equational logic for the applied pi-calculus, to the validity of first-order formulas in term algebras with multiple congruence relations.