3,104 research outputs found
Attacking Group Protocols by Refuting Incorrect Inductive Conjectures
Automated tools for finding attacks on flawed security protocols often fail to deal adequately with group protocols. This is because the abstractions made to improve performance on fixed 2 or 3 party protocols either preclude the modelling of group protocols all together, or permit modelling only in a fixed scenario, which can prevent attacks from being discovered. This paper describes Coral, a tool for finding counterexamples to incorrect inductive conjectures, which we have used to model protocols for both group key agreement and group key management, without any restrictions on the scenario. We will show how we used Coral to discover 6 previously unknown attacks on 3 group protocols
Nominal Abstraction
Recursive relational specifications are commonly used to describe the
computational structure of formal systems. Recent research in proof theory has
identified two features that facilitate direct, logic-based reasoning about
such descriptions: the interpretation of atomic judgments through recursive
definitions and an encoding of binding constructs via generic judgments.
However, logics encompassing these two features do not currently allow for the
definition of relations that embody dynamic aspects related to binding, a
capability needed in many reasoning tasks. We propose a new relation between
terms called nominal abstraction as a means for overcoming this deficiency. We
incorporate nominal abstraction into a rich logic also including definitions,
generic quantification, induction, and co-induction that we then prove to be
consistent. We present examples to show that this logic can provide elegant
treatments of binding contexts that appear in many proofs, such as those
establishing properties of typing calculi and of arbitrarily cascading
substitutions that play a role in reducibility arguments.Comment: To appear in the Journal of Information and Computatio
The Complexity of Rooted Phylogeny Problems
Several computational problems in phylogenetic reconstruction can be
formulated as restrictions of the following general problem: given a formula in
conjunctive normal form where the literals are rooted triples, is there a
rooted binary tree that satisfies the formula? If the formulas do not contain
disjunctions, the problem becomes the famous rooted triple consistency problem,
which can be solved in polynomial time by an algorithm of Aho, Sagiv,
Szymanski, and Ullman. If the clauses in the formulas are restricted to
disjunctions of negated triples, Ng, Steel, and Wormald showed that the problem
remains NP-complete. We systematically study the computational complexity of
the problem for all such restrictions of the clauses in the input formula. For
certain restricted disjunctions of triples we present an algorithm that has
sub-quadratic running time and is asymptotically as fast as the fastest known
algorithm for the rooted triple consistency problem. We also show that any
restriction of the general rooted phylogeny problem that does not fall into our
tractable class is NP-complete, using known results about the complexity of
Boolean constraint satisfaction problems. Finally, we present a pebble game
argument that shows that the rooted triple consistency problem (and also all
generalizations studied in this paper) cannot be solved by Datalog
Transformations of Logic Programs on Infinite Lists
We consider an extension of logic programs, called \omega-programs, that can
be used to define predicates over infinite lists. \omega-programs allow us to
specify properties of the infinite behavior of reactive systems and, in
general, properties of infinite sequences of events. The semantics of
\omega-programs is an extension of the perfect model semantics. We present
variants of the familiar unfold/fold rules which can be used for transforming
\omega-programs. We show that these new rules are correct, that is, their
application preserves the perfect model semantics. Then we outline a general
methodology based on program transformation for verifying properties of
\omega-programs. We demonstrate the power of our transformation-based
verification methodology by proving some properties of Buechi automata and
\omega-regular languages.Comment: 37 pages, including the appendix with proofs. This is an extended
version of a paper published in Theory and Practice of Logic Programming, see
belo
E-Generalization Using Grammars
We extend the notion of anti-unification to cover equational theories and
present a method based on regular tree grammars to compute a finite
representation of E-generalization sets. We present a framework to combine
Inductive Logic Programming and E-generalization that includes an extension of
Plotkin's lgg theorem to the equational case. We demonstrate the potential
power of E-generalization by three example applications: computation of
suggestions for auxiliary lemmas in equational inductive proofs, computation of
construction laws for given term sequences, and learning of screen editor
command sequences.Comment: 49 pages, 16 figures, author address given in header is meanwhile
outdated, full version of an article in the "Artificial Intelligence
Journal", appeared as technical report in 2003. An open-source C
implementation and some examples are found at the Ancillary file
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