Finitary Deduction Systems

Cryptographic protocols are the cornerstone of security in distributed systems. The formal analysis of their properties is accordingly one of the focus points of the security community, and is usually split among two groups. In the first group, one focuses on trace-based security properties such as confidentiality and authentication, and provides decision procedures for the existence of attacks for an on-line attackers. In the second group, one focuses on equivalence properties such as privacy and guessing attacks, and provides decision procedures for the existence of attacks for an offline attacker. In all cases the attacker is modeled by a deduction system in which his possible actions are expressed. We present in this paper a notion of finitary deduction systems that aims at relating both approaches. We prove that for such deduction systems, deciding equivalence properties for on-line attackers can be reduced to deciding reachability properties in the same setting.Comment: 30 pages. Work begun while in the CASSIS Project, INRIA Nancy Grand Es

Compiling and securing cryptographic protocols

Protocol narrations are widely used in security as semi-formal notations to specify conversations between roles. We define a translation from a protocol narration to the sequences of operations to be performed by each role. Unlike previous works, we reduce this compilation process to well-known decision problems in formal protocol analysis. This allows one to define a natural notion of prudent translation and to reuse many known results from the literature in order to cover more crypto-primitives. In particular this work is the first one to show how to compile protocols parameterised by the properties of the available operations.Comment: A short version was submitted to IP

Unification and Matching on Compressed Terms

Term unification plays an important role in many areas of computer science, especially in those related to logic. The universal mechanism of grammar-based compression for terms, in particular the so-called Singleton Tree Grammars (STG), have recently drawn considerable attention. Using STGs, terms of exponential size and height can be represented in linear space. Furthermore, the term representation by directed acyclic graphs (dags) can be efficiently simulated. The present paper is the result of an investigation on term unification and matching when the terms given as input are represented using different compression mechanisms for terms such as dags and Singleton Tree Grammars. We describe a polynomial time algorithm for context matching with dags, when the number of different context variables is fixed for the problem. For the same problem, NP-completeness is obtained when the terms are represented using the more general formalism of Singleton Tree Grammars. For first-order unification and matching polynomial time algorithms are presented, each of them improving previous results for those problems.Comment: This paper is posted at the Computing Research Repository (CoRR) as part of the process of submission to the journal ACM Transactions on Computational Logic (TOCL)

Productive Corecursion in Logic Programming

Logic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the existing state-of-the-art algorithms can only semi-decide coinductive soundness of queries in logic programming for regular formulae. Another, less famous, but equally fundamental and important undecidable property is productivity. If a derivation is infinite and coinductively sound, we may ask whether the computed answer it determines actually computes an infinite formula. If it does, the infinite computation is productive. This intuition was first expressed under the name of computations at infinity in the 80s. In modern days of the Internet and stream processing, its importance lies in connection to infinite data structure processing. Recently, an algorithm was presented that semi-decides a weaker property -- of productivity of logic programs. A logic program is productive if it can give rise to productive derivations. In this paper we strengthen these recent results. We propose a method that semi-decides productivity of individual derivations for regular formulae. Thus we at last give an algorithmic counterpart to the notion of productivity of derivations in logic programming. This is the first algorithmic solution to the problem since it was raised more than 30 years ago. We also present an implementation of this algorithm.Comment: Paper presented at the 33nd International Conference on Logic Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017 16 pages, LaTeX, no figure

Language, logic and ontology: uncovering the structure of commonsense knowledge

The purpose of this paper is twofold: (i) we argue that the structure of commonsense knowledge must be discovered, rather than invented; and (ii) we argue that natural language, which is the best known theory of our (shared) commonsense knowledge, should itself be used as a guide to discovering the structure of commonsense knowledge. In addition to suggesting a systematic method to the discovery of the structure of commonsense knowledge, the method we propose seems to also provide an explanation for a number of phenomena in natural language, such as metaphor, intensionality, and the semantics of nominal compounds. Admittedly, our ultimate goal is quite ambitious, and it is no less than the systematic ‘discovery’ of a well-typed ontology of commonsense knowledge, and the subsequent formulation of the longawaited goal of a meaning algebra