Compression vs Queryability - A Case Study

International audienceSome compromise on compression is known to be necessary, if the relative positions of the information stored by semi-structured documents are to remain accessible under queries. With this in view, we compare, on an example, the `query-friendliness' of XML documents, when compressed into straightline tree grammars which are either regular or context-free. The queries considered are in a limited fragment of XPath, corresponding to a type of patterns; each such query defines naturally a non-deterministic, bottom-up `query automaton' that runs just as well on a tree as on its compressed dag

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

Distributed Transition Systems with Tags for Privacy Analysis

We present a logical framework that formally models how a given private information P stored on a given database D, can get captured progressively, by an agent/adversary querying the database repeatedly.Named DLTTS (Distributed Labeled Tagged Transition System), the frame-work borrows ideas from several domains: Probabilistic Automata of Segala, Probabilistic Concurrent Systems, and Probabilistic labelled transition systems. To every node on a DLTTS is attached a tag that represents the 'current' knowledge of the adversary, acquired from the responses of the answering mechanism of the DBMS to his/her queries, at the nodes traversed earlier, along any given run; this knowledge is completed at the same node, with further relational deductions, possibly in combination with 'public' information from other databases given in advance. A 'blackbox' mechanism is also part of a DLTTS, and it is meant as an oracle; its role is to tell if the private information has been deduced by the adversary at the current node, and if so terminate the run. An additional special feature is that the blackbox also gives information on how 'close',or how 'far', the knowledge of the adversary is, from the private information P , at the current node. A metric is defined for that purpose, on the set of all 'type compatible' tuples from the given database, the data themselves being typed with the headers of the base. Despite the transition systems flavor of our framework, this metric is not 'behavioral' in the sense presented in some other works. It is exclusively database oriented,and allows to define new notions of adjacency and of -indistinguishabilty between databases, more generally than those usually based on the Hamming metric (and a restricted notion of adjacency). Examples are given all along to illustrate how our framework works. Keywords:Database, Privacy, Transition System, Probability, Distribution

Unification modulo Lists with Reverse as Solving Simple Sets of Word Equations

Decision procedures for various list theories have been investigated in the literature with applications to automated verification. Here we show that the unifiability problem for some list theories with a reverse operator is NP-complete. We also give a unifiability algorithm for the case where the theories are extended with a length operator on lists

Unification modulo Lists with Reverse as Solving Simple Sets of Word Equations

Decision procedures for various list theories have been investigated in the literature with applications to automated verification. Here we show that the unifiability problem for some list theories with a reverse operator is NP-complete. We also give a unifiability algorithm for the case where the theories are extended with a length operator on lists

Information Flow Analysis Via Equational Reasoning

In this work, a process algebra is designed around an ACUID equational theory extended with prefixes symbolizing actions, and by making parallel synchronous composition distributive over non-deterministic choice; such a synchronous composition is commutative and non-associative. Bisimulation between processes is then interpretable as congruence over such an equational theory. It is shown that information flow analysis is strictly finer when based on bisimulation on the synchronous algebra, than when it is based on trace or weak bisimulation equivalence

A Synchronous Bisimulation Based Approach For Information Flow Analysis

A process algebra is defined where parallel composition is structured around synchronous communication. Its essential difference with CCS is the hypothesis that internal actions must be observable for the clock; consequently, in our formalism (strong) bisimulation will be the basis for information flow analysis, instead of equivalences based on trace or weak bisimulation. Bisimulation reduce

An application of automated equational reasoning to many-valued logic

In this paper we present the theorem prover SBR3 for equational logic and itsapplication in the many-valued logic of Lukasiewicz. We give a new equational axiomatization of many-valued logic and we prove by SBR3 that it is equivalent to the classical equational presentation of such logic given by Wajsberg. We feel that our equational axiomatization of Wajsberg algebras is better suited for automated reasoning than the classical one. Indeed, it has allowed us to obtain a fast mechanical proof of the so called "fifth Lukasiewicz conjecture'', which is regarded as a challenge problem for theorem provers