39,042 research outputs found
Generalized Strong Preservation by Abstract Interpretation
Standard abstract model checking relies on abstract Kripke structures which
approximate concrete models by gluing together indistinguishable states, namely
by a partition of the concrete state space. Strong preservation for a
specification language L encodes the equivalence of concrete and abstract model
checking of formulas in L. We show how abstract interpretation can be used to
design abstract models that are more general than abstract Kripke structures.
Accordingly, strong preservation is generalized to abstract
interpretation-based models and precisely related to the concept of
completeness in abstract interpretation. The problem of minimally refining an
abstract model in order to make it strongly preserving for some language L can
be formulated as a minimal domain refinement in abstract interpretation in
order to get completeness w.r.t. the logical/temporal operators of L. It turns
out that this refined strongly preserving abstract model always exists and can
be characterized as a greatest fixed point. As a consequence, some well-known
behavioural equivalences, like bisimulation, simulation and stuttering, and
their corresponding partition refinement algorithms can be elegantly
characterized in abstract interpretation as completeness properties and
refinements
Generalizing the Paige-Tarjan Algorithm by Abstract Interpretation
The Paige and Tarjan algorithm (PT) for computing the coarsest refinement of
a state partition which is a bisimulation on some Kripke structure is well
known. It is also well known in model checking that bisimulation is equivalent
to strong preservation of CTL, or, equivalently, of Hennessy-Milner logic.
Drawing on these observations, we analyze the basic steps of the PT algorithm
from an abstract interpretation perspective, which allows us to reason on
strong preservation in the context of generic inductively defined (temporal)
languages and of possibly non-partitioning abstract models specified by
abstract interpretation. This leads us to design a generalized Paige-Tarjan
algorithm, called GPT, for computing the minimal refinement of an abstract
interpretation-based model that strongly preserves some given language. It
turns out that PT is a straight instance of GPT on the domain of state
partitions for the case of strong preservation of Hennessy-Milner logic. We
provide a number of examples showing that GPT is of general use. We first show
how a well-known efficient algorithm for computing stuttering equivalence can
be viewed as a simple instance of GPT. We then instantiate GPT in order to
design a new efficient algorithm for computing simulation equivalence that is
competitive with the best available algorithms. Finally, we show how GPT allows
to compute new strongly preserving abstract models by providing an efficient
algorithm that computes the coarsest refinement of a given partition that
strongly preserves the language generated by the reachability operator.Comment: Keywords: Abstract interpretation, abstract model checking, strong
preservation, Paige-Tarjan algorithm, refinement algorith
Coalgebraic completeness-via-canonicity for distributive substructural logics
We prove strong completeness of a range of substructural logics with respect
to a natural poset-based relational semantics using a coalgebraic version of
completeness-via-canonicity. By formalizing the problem in the language of
coalgebraic logics, we develop a modular theory which covers a wide variety of
different logics under a single framework, and lends itself to further
extensions. Moreover, we believe that the coalgebraic framework provides a
systematic and principled way to study the relationship between resource models
on the semantics side, and substructural logics on the syntactic side.Comment: 36 page
Preserving Preservation
We present preservation theorems for countable support iteration of nep
forcing notions satisfying ``old reals are not Lebesgue null'' and ``old reals
are not meager''. (Nep is a generalization of Suslin proper.) We also give some
results for general Suslin ccc ideals
Dualized Simple Type Theory
We propose a new bi-intuitionistic type theory called Dualized Type Theory
(DTT). It is a simple type theory with perfect intuitionistic duality, and
corresponds to a single-sided polarized sequent calculus. We prove DTT strongly
normalizing, and prove type preservation. DTT is based on a new propositional
bi-intuitionistic logic called Dualized Intuitionistic Logic (DIL) that builds
on Pinto and Uustalu's logic L. DIL is a simplification of L by removing
several admissible inference rules while maintaining consistency and
completeness. Furthermore, DIL is defined using a dualized syntax by labeling
formulas and logical connectives with polarities thus reducing the number of
inference rules needed to define the logic. We give a direct proof of
consistency, but prove completeness by reduction to L.Comment: 47 pages, 10 figure
The PER model of abstract non-interference
Abstract. In this paper, we study the relationship between two models of secure information flow: the PER model (which uses equivalence relations) and the abstract non-interference model (which uses upper closure operators). We embed the lattice of equivalence relations into the lattice of closures, re-interpreting abstract non-interference over the lattice of equivalence relations. For narrow abstract non-interference, we show non-interference it is strictly less general. The relational presentation of abstract non-interference leads to a simplified construction of the most concrete harmless attacker. Moreover, the PER model of abstract noninterference allows us to derive unconstrained attacker models, which do not necessarily either observe all public information or ignore all private information. Finally, we show how abstract domain completeness can be used for enforcing the PER model of abstract non-interference
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