On the Complexity of the Tiden-Arnborg Algorithm for Unification modulo One-Sided Distributivity
نویسندگان
چکیده
Equational unification is central to automated deduction and its applications in areas such as symbolic protocol analysis. In particular, the unification problem for the theory AC (“Associativity-Commutativity”) and its extensions ACI (“AC plus Idempotence”) and ACUI (“ACI with Unit element”) have been studied in great detail in the past. Distributivity (of one binary operator over another) has received less attention comparatively. Some significant results have been obtained such as Schmidt-Schauss’ breakthrough decidability result [7] for unification modulo the theory of two-sided distributivity
منابع مشابه
On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry
An algorithm for unification modulo one-sided distributivity is an early result by Tidén and Arnborg. More recently this theory has been of interest in cryptographic protocol analysis due to the fact that many cryptographic operators satisfy this property. Unfortunately the algorithm presented in the paper, although correct, has recently been shown not to be polynomial time bounded as claimed. ...
متن کاملAn Algorithm for Distributive Unification
We consider unification of terms under the equational theory of two-sided distributivity D with the axioms x*(y+z) = x*y + x*z and (x+y)*z = x*z + y*z. The main result of this paper is that Dunification is decidable by giving a non-deterministic transformation algorithm. The generated unification are: an AC1-problem with linear constant restrictions and a second-order unification problem that c...
متن کاملSolving *-Problems Modulo Distributivity by a Reduction to AC1-Unification
(Received) We show that uniication modulo both-sided distributivity of the symbol on + can be reduced to AC1-uniication for all uniication problems which do not involve the + operator. Moreover, in this case, we can describe \almost all" solutions in a nite way, although there are in general innnitely many minimal solutions for such problems.
متن کاملUnification Modulo ACU I Plus Homomorphisms/Distributivity
E-unification problems are central in automated deduction. In this paper, we consider theories that are extensions of the well-known ACI or ACUI , obtained by adding finitely many homomorphism symbols, or a symbol ‘∗’ that distributes over the ACUIsymbol denoted ‘+’. We first show that when we adjoin a set of commuting homomorphisms to ACUI , unification is undecidable. We then consider the ACU...
متن کاملSmaran: A Congruence-Closure Based System for Equational Computations
p. 1 Redundancy Criteria for Constrained Completion p. 2 Bi-rewriting, a Term Rewriting Technique for Monotonic Order Relations p. 17 A Case Study of Completion Modulo Distributivity and Abelian Groups p. 32 A Semantic Approach to Order-Sorted Rewriting p. 47 Distributing Equational Theorem Proving p. 62 On the Correctness of a Distributed Memory Grobner Basis Algorithm p. 77 Improving Transfor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010