2,440 research outputs found
Lengths May Break Privacy â Or How to Check for Equivalences with Length
Security protocols have been successfully analyzed using symbolic models, where messages are represented by terms and protocols by processes. Privacy properties like anonymity or untraceability are typically expressed as equivalence between processes. While some decision procedures have been proposed for automatically deciding process equivalence, all existing approaches abstract away the information an attacker may get when observing the length of messages.
In this paper, we study process equivalence with length tests. We first show that, in the static case, almost all existing decidability results (for static equivalence) can be extended to cope with length tests.
In the active case, we prove decidability of trace equivalence with length tests, for a bounded number of sessions and for standard primitives. Our result relies on a previous decidability result from Cheval et al (without length tests). Our procedure has been implemented and we have discovered a new flaw against privacy in the biometric passport protocol
The First-Order Theory of Sets with Cardinality Constraints is Decidable
We show that the decidability of the first-order theory of the language that
combines Boolean algebras of sets of uninterpreted elements with Presburger
arithmetic operations. We thereby disprove a recent conjecture that this theory
is undecidable. Our language allows relating the cardinalities of sets to the
values of integer variables, and can distinguish finite and infinite sets. We
use quantifier elimination to show the decidability and obtain an elementary
upper bound on the complexity.
Precise program analyses can use our decidability result to verify
representation invariants of data structures that use an integer field to
represent the number of stored elements.Comment: 18 page
Fluid Model Checking
In this paper we investigate a potential use of fluid approximation
techniques in the context of stochastic model checking of CSL formulae. We
focus on properties describing the behaviour of a single agent in a (large)
population of agents, exploiting a limit result known also as fast simulation.
In particular, we will approximate the behaviour of a single agent with a
time-inhomogeneous CTMC which depends on the environment and on the other
agents only through the solution of the fluid differential equation. We will
prove the asymptotic correctness of our approach in terms of satisfiability of
CSL formulae and of reachability probabilities. We will also present a
procedure to model check time-inhomogeneous CTMC against CSL formulae
Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility
Word equations are a crucial element in the theoretical foundation of
constraint solving over strings, which have received a lot of attention in
recent years. A word equation relates two words over string variables and
constants. Its solution amounts to a function mapping variables to constant
strings that equate the left and right hand sides of the equation. While the
problem of solving word equations is decidable, the decidability of the problem
of solving a word equation with a length constraint (i.e., a constraint
relating the lengths of words in the word equation) has remained a
long-standing open problem. In this paper, we focus on the subclass of
quadratic word equations, i.e., in which each variable occurs at most twice. We
first show that the length abstractions of solutions to quadratic word
equations are in general not Presburger-definable. We then describe a class of
counter systems with Presburger transition relations which capture the length
abstraction of a quadratic word equation with regular constraints. We provide
an encoding of the effect of a simple loop of the counter systems in the theory
of existential Presburger Arithmetic with divisibility (PAD). Since PAD is
decidable, we get a decision procedure for quadratic words equations with
length constraints for which the associated counter system is \emph{flat}
(i.e., all nodes belong to at most one cycle). We show a decidability result
(in fact, also an NP algorithm with a PAD oracle) for a recently proposed
NP-complete fragment of word equations called regular-oriented word equations,
together with length constraints. Decidability holds when the constraints are
additionally extended with regular constraints with a 1-weak control structure.Comment: 18 page
Decidable Reasoning in Terminological Knowledge Representation Systems
Terminological knowledge representation systems (TKRSs) are tools for
designing and using knowledge bases that make use of terminological languages
(or concept languages). We analyze from a theoretical point of view a TKRS
whose capabilities go beyond the ones of presently available TKRSs. The new
features studied, often required in practical applications, can be summarized
in three main points. First, we consider a highly expressive terminological
language, called ALCNR, including general complements of concepts, number
restrictions and role conjunction. Second, we allow to express inclusion
statements between general concepts, and terminological cycles as a particular
case. Third, we prove the decidability of a number of desirable TKRS-deduction
services (like satisfiability, subsumption and instance checking) through a
sound, complete and terminating calculus for reasoning in ALCNR-knowledge
bases. Our calculus extends the general technique of constraint systems. As a
byproduct of the proof, we get also the result that inclusion statements in
ALCNR can be simulated by terminological cycles, if descriptive semantics is
adopted.Comment: See http://www.jair.org/ for any accompanying file
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