Rewrite Systems

Dershowitz, Nachum

doi:10.1016/b978-0-444-88074-1.50011-1

Cited by 750 publications

(483 citation statements)

References 134 publications

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“…For full definitions refer to [11,18]. Throughout this paper, V will denote a countably infinite set of variables and Σ denotes a set of function symbols, each with a fixed associated arity.…”

Section: Preliminariesmentioning

confidence: 99%

Narrowing approximations as an optimization for equational logic programs

Alpuente

Falaschi

Ramis

et al. 1993

Lecture Notes in Computer Science

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Solving equations in equational theories is a relevant programming paradigm which integrates logic and equational programming into one unified framework. Efficient methods based on narrowing strategies to solve systems of equations have been devised. In this paper, we formulate a narrowing-based equation solving calculus which makes use of a top-down abstract interpretation strategy to control the branching of the search tree. We define a refined, but still complete, equation solving procedure which allows us to reduce the branching factor. Our main idea consists of building an abstract narrower for equational theories and executing the set of equations to be solved in the approximated narrower. We prove that the set of answers computed by the abstract narrower has the property that each concrete solution of the set of equations is an instance of one of the substitutions in the answer set. Thus we define a strategy which computes such a set and uses the substitutions in it for cutting down the search space of the program without losing completeness. We also report on experimental results which demonstrate that our optimization can result in significant speed-ups in program execution.

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Section: Preliminariesmentioning

confidence: 99%

Narrowing approximations as an optimization for equational logic programs

Alpuente

Falaschi

Ramis

et al. 1993

Lecture Notes in Computer Science

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“…It has been shown (see [13]) that by applying the unfailing completion procedure [14] to a set of equations H we can derive a (possibly infinite) set of equations O such that:…”

Section: Terms and Subtermsmentioning

confidence: 99%

“…We shall introduce the notion of ordered rewriting [13], which is a useful technique that has been utilized (e.g. [3]) for proving the correctness of combination of unification algorithms.…”

Section: Terms and Subtermsmentioning

confidence: 99%

Combining Intruder Theories

Chevalier

Rusinowitch

2005

Automata, Languages and Programming

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Abstract. Most of the decision procedures for symbolic analysis of protocols are limited to a fixed set of algebraic operators associated with a fixed intruder theory. Examples of such sets of operators comprise XOR, multiplication/exponentiation, abstract encryption/decryption. In this paper we give an algorithm for combining decision procedures for arbitrary intruder theories with disjoint sets of operators, provided that solvability of ordered intruder constraints, a slight generalization of intruder constraints, can be decided in each theory. This is the case for most of the intruder theories for which a decision procedure has been given. In particular our result allows us to decide trace-based security properties of protocols that employ any combination of the above mentioned operators with a bounded number of sessions.

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“…We will essentially use strict orderings, and hence, the word ordering for them too. We will also make use of order-preserving operations on relations, namely multiset and lexicographic extensions, see [15].…”

Section: Higher-order Reduction Orderingsmentioning

confidence: 99%