17,912 research outputs found
Timed Multiparty Session Types
We propose a typing theory, based on multiparty session types, for modular verification of real-time choreographic interactions. To model real-time implementations, we introduce a simple calculus with delays and a decidable static proof system. The proof system ensures type safety and time-error freedom, namely processes respect the prescribed timing and causalities between interactions. A decidable condition on timed global types guarantees time-progress for validated processes with delays, and gives a sound and complete characterisation of a new class of CTAs with general topologies that enjoys progress and liveness
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
Iterative forcing and hyperimmunity in reverse mathematics
The separation between two theorems in reverse mathematics is usually done by
constructing a Turing ideal satisfying a theorem P and avoiding the solutions
to a fixed instance of a theorem Q. Lerman, Solomon and Towsner introduced a
forcing technique for iterating a computable non-reducibility in order to
separate theorems over omega-models. In this paper, we present a modularized
version of their framework in terms of preservation of hyperimmunity and show
that it is powerful enough to obtain the same separations results as Wang did
with his notion of preservation of definitions.Comment: 15 page
Linear Time Logics - A Coalgebraic Perspective
We describe a general approach to deriving linear time logics for a wide
variety of state-based, quantitative systems, by modelling the latter as
coalgebras whose type incorporates both branching behaviour and linear
behaviour. Concretely, we define logics whose syntax is determined by the
choice of linear behaviour and whose domain of truth values is determined by
the choice of branching, and we provide two equivalent semantics for them: a
step-wise semantics amenable to automata-based verification, and a path-based
semantics akin to those of standard linear time logics. We also provide a
semantic characterisation of the associated notion of logical equivalence, and
relate it to previously-defined maximal trace semantics for such systems.
Instances of our logics support reasoning about the possibility, likelihood or
minimal cost of exhibiting a given linear time property. We conclude with a
generalisation of the logics, dual in spirit to logics with discounting, which
increases their practical appeal in the context of resource-aware computation
by incorporating a notion of offsetting.Comment: Major revision of previous version: Sections 4 and 5 generalise the
results in the previous version, with new proofs; Section 6 contains new
result
Indexed Labels for Loop Iteration Dependent Costs
We present an extension to the labelling approach, a technique for lifting
resource consumption information from compiled to source code. This approach,
which is at the core of the annotating compiler from a large fragment of C to
8051 assembly of the CerCo project, looses preciseness when differences arise
as to the cost of the same portion of code, whether due to code transformation
such as loop optimisations or advanced architecture features (e.g. cache). We
propose to address this weakness by formally indexing cost labels with the
iterations of the containing loops they occur in. These indexes can be
transformed during the compilation, and when lifted back to source code they
produce dependent costs.
The proposed changes have been implemented in CerCo's untrusted prototype
compiler from a large fragment of C to 8051 assembly.Comment: In Proceedings QAPL 2013, arXiv:1306.241
Decidability Results for the Boundedness Problem
We prove decidability of the boundedness problem for monadic least
fixed-point recursion based on positive monadic second-order (MSO) formulae
over trees. Given an MSO-formula phi(X,x) that is positive in X, it is
decidable whether the fixed-point recursion based on phi is spurious over the
class of all trees in the sense that there is some uniform finite bound for the
number of iterations phi takes to reach its least fixed point, uniformly across
all trees. We also identify the exact complexity of this problem. The proof
uses automata-theoretic techniques. This key result extends, by means of
model-theoretic interpretations, to show decidability of the boundedness
problem for MSO and guarded second-order logic (GSO) over the classes of
structures of fixed finite tree-width. Further model-theoretic transfer
arguments allow us to derive major known decidability results for boundedness
for fragments of first-order logic as well as new ones
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