134 research outputs found
Complexity of Decision Problems for Mixed and Modal Specifications
International audienceWe present a new algorithm for solving Simple Stochastic Games (SSGs). This algorithm is based on an exhaustive search of a special kind of positional optimal strategies, the f-strategies. The running time is , where and are respectively the number of vertices, random vertices and edges, and the maximum bit-length of a transition probability. Our algorithm improves existing algorithms for solving SSGs in three aspects. First, our algorithm performs well on SSGs with few random vertices, second it does not rely on linear or quadratic programming, third it applies to all SSGs, not only stopping SSGs
Weighted Modal Transition Systems
Specification theories as a tool in model-driven development processes of
component-based software systems have recently attracted a considerable
attention. Current specification theories are however qualitative in nature,
and therefore fragile in the sense that the inevitable approximation of systems
by models, combined with the fundamental unpredictability of hardware
platforms, makes it difficult to transfer conclusions about the behavior, based
on models, to the actual system. Hence this approach is arguably unsuited for
modern software systems. We propose here the first specification theory which
allows to capture quantitative aspects during the refinement and implementation
process, thus leveraging the problems of the qualitative setting.
Our proposed quantitative specification framework uses weighted modal
transition systems as a formal model of specifications. These are labeled
transition systems with the additional feature that they can model optional
behavior which may or may not be implemented by the system. Satisfaction and
refinement is lifted from the well-known qualitative to our quantitative
setting, by introducing a notion of distances between weighted modal transition
systems. We show that quantitative versions of parallel composition as well as
quotient (the dual to parallel composition) inherit the properties from the
Boolean setting.Comment: Submitted to Formal Methods in System Desig
Decision Problems for Partial Specifications: Empirical and Worst-Case Complexities
Partial specifications allow approximate models of systems such as Kripke structures, or labeled
transition systems to be created. Using the abstraction possible with these models, an avoidance
of the state-space explosion problem is possible, whilst still retaining a structure that can
have properties checked over it. A single partial specification abstracts a set of systems, whether
Kripke, labeled transition systems, or systems with both atomic propositions and named transitions.
This thesis deals in part with problems arising from a desire to efficiently evaluate
sentences of the modal ÎĽ-calculus over a partial specification.
Partial specifications also allow a single system to be modeled by a number of partial specifications,
which abstract away different parts of the system. Alternatively, a number of partial
specifications may represent different requirements on a system. The thesis also addresses the
question of whether a set of partial specifications is consistent, that is to say, whether a single
system exists that is abstracted by each member of the set. The effect of nominals, special
atomic propositions true on only one state in a system, is also considered on the problem of the
consistency of many partial specifications. The thesis also addresses the question of whether
the systems a partial specification abstracts are all abstracted by a second partial specification,
the problem of inclusion.
The thesis demonstrates how commonly used “specification patterns” – useful properties specified
in the modal ÎĽ-calculus, can be efficiently evaluated over partial specifications, and gives
upper and lower complexity bounds on the problems related to sets of partial specifications
On Refinements of Boolean and Parametric Modal Transition Systems
We consider the extensions of modal transition systems (MTS), namely Boolean
MTS and parametric MTS and we investigate the refinement problems over both
classes. Firstly, we reduce the problem of modal refinement over both classes
to a problem solvable by a QBF solver and provide experimental results showing
our technique scales well. Secondly, we extend the algorithm for thorough
refinement of MTS providing better complexity then via reductions to previously
studied problems. Finally, we investigate the relationship between modal and
thorough refinement on the two classes and show how the thorough refinement can
be approximated by the modal refinement
Refinement checking on parametric modal transition systems
Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently known extensions are incapable of expressing some practically needed aspects in the refinement process like exclusive, conditional and persistent choices. We introduce a new model called parametric modal transition systems (PMTS) together with a general modal refinement notion that overcomes many of the limitations. We investigate the computational complexity of modal and thorough refinement checking on PMTS and its subclasses and provide a direct encoding of the modal refinement problem into quantified Boolean formulae, allowing us to employ state-of-the-art QBF solvers for modal refinement checking. The experiments we report on show that the feasibility of refinement checking is more influenced by the degree of nondeterminism rather than by the syntactic restrictions on the types of formulae allowed in the description of the PMTS
Refinement for Transition Systems with Responses
Motivated by the response pattern for property specifications and
applications within flexible workflow management systems, we report upon an
initial study of modal and mixed transition systems in which the must
transitions are interpreted as must eventually, and in which implementations
can contain may behaviors that are resolved at run-time. We propose Transition
Systems with Responses (TSRs) as a suitable model for this study. We prove that
TSRs correspond to a restricted class of mixed transition systems, which we
refer to as the action-deterministic mixed transition systems. We show that
TSRs allow for a natural definition of deadlocked and accepting states. We then
transfer the standard definition of refinement for mixed transition systems to
TSRs and prove that refinement does not preserve deadlock freedom. This leads
to the proposal of safe refinements, which are those that preserve deadlock
freedom. We exemplify the use of TSRs and (safe) refinements on a small
medication workflow.Comment: In Proceedings FIT 2012, arXiv:1207.348
Modal Transition Systems: Composition and LTL Model Checking
Modal transition systems (MTS) is a~well established formalism used for specification and for abstract interpretation. We consider its disjunctive extension (DMTS) and we provide algorithms showing that refinement problems for DMTS are not harder than in the case of MTS. There are two main results in the paper. Firstly, we identify an error in a~previous attempt at LTL model checking of MTS and provide algorithms for LTL model checking of MTS and DMTS. Moreover, we show how to apply this result to compositional verification and circumvent the general incompleteness of the MTS composition. Secondly, we give a~solution to the common implementation and conjunctive composition problems lowering the complexity from EXPTIME to PTIME
Responsibility and verification: Importance value in temporal logics
We aim at measuring the influence of the nondeterministic choices of a part
of a system on its ability to satisfy a specification. For this purpose, we
apply the concept of Shapley values to verification as a means to evaluate how
important a part of a system is. The importance of a component is measured by
giving its control to an adversary, alone or along with other components, and
testing whether the system can still fulfill the specification. We study this
idea in the framework of model-checking with various classical types of
linear-time specification, and propose several ways to transpose it to
branching ones. We also provide tight complexity bounds in almost every case.Comment: 22 pages, 12 figure
Labelled transition systems as a Stone space
A fully abstract and universal domain model for modal transition systems and
refinement is shown to be a maximal-points space model for the bisimulation
quotient of labelled transition systems over a finite set of events. In this
domain model we prove that this quotient is a Stone space whose compact,
zero-dimensional, and ultra-metrizable Hausdorff topology measures the degree
of bisimilarity such that image-finite labelled transition systems are dense.
Using this compactness we show that the set of labelled transition systems that
refine a modal transition system, its ''set of implementations'', is compact
and derive a compactness theorem for Hennessy-Milner logic on such
implementation sets. These results extend to systems that also have partially
specified state propositions, unify existing denotational, operational, and
metric semantics on partial processes, render robust consistency measures for
modal transition systems, and yield an abstract interpretation of compact sets
of labelled transition systems as Scott-closed sets of modal transition
systems.Comment: Changes since v2: Metadata updat
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