12,771 research outputs found
Constraint-Based Abstraction of a Model Checker for Infinite State Systems
Abstract. Abstract interpretation-based model checking provides an approach to verifying properties of infinite-state systems. In practice, most previous work on abstract model checking is either restricted to verifying universal properties, or develops special techniques for temporal logics such as modal transition sys-tems or other dual transition systems. By contrast we apply completely standard techniques for constructing abstract interpretations to the abstraction of a CTL semantic function, without restricting the kind of properties that can be verified. Furthermore we show that this leads directly to implementation of abstract model checking algorithms for abstract domains based on constraints, making use of an SMT solver.
Model Checking a Temporal Logic via Program Verification
openThe thesis explores the possibility of viewing Model Checking as an instance of program verification in order to allow for the reuse of the vast theory and toolset of Abstract Interpretation in the setting of Model Checking. Model Checking is a formal verification technique used to analyse the correctness of software systems, based on a representation of the system as a formal model, such as a finite-state machine or a transition system, and on a representation of the properties it must satisfy as temporal logic formulae. On the other hand, Abstract Interpretation is a program analysis method, based on the idea of extracting properties of programs by (over-)approximating their semantics over a so-called abstract domain, typically a complete lattice, whose elements represent program properties. The thesis focuses on ACTL, the universal fragment of the temporal logic CTL, which can describe properties of executions which are universally quantified. It shows how properties expressed in ACTL can be mapped into programs written in a suitable programming language, whose semantics consists of counterexamples to the validity of the formula. Then such a program is analysed by Abstract Interpretation over some abstract domain, exploiting the idea of local completeness as put forward in some recent work, combining lower- and under-approximations.The thesis explores the possibility of viewing Model Checking as an instance of program verification in order to allow for the reuse of the vast theory and toolset of Abstract Interpretation in the setting of Model Checking. Model Checking is a formal verification technique used to analyse the correctness of software systems, based on a representation of the system as a formal model, such as a finite-state machine or a transition system, and on a representation of the properties it must satisfy as temporal logic formulae. On the other hand, Abstract Interpretation is a program analysis method, based on the idea of extracting properties of programs by (over-)approximating their semantics over a so-called abstract domain, typically a complete lattice, whose elements represent program properties. The thesis focuses on ACTL, the universal fragment of the temporal logic CTL, which can describe properties of executions which are universally quantified. It shows how properties expressed in ACTL can be mapped into programs written in a suitable programming language, whose semantics consists of counterexamples to the validity of the formula. Then such a program is analysed by Abstract Interpretation over some abstract domain, exploiting the idea of local completeness as put forward in some recent work, combining lower- and under-approximations
Deciding Full Branching Time Logic by Program Transformation
We present a method based on logic program transformation, for verifying Computation Tree Logic (CTL*) properties of finite state reactive systems. The finite state systems and the CTL* properties we want to verify, are encoded as logic programs on infinite lists. Our verification method consists of two steps. In the first step we transform the logic program that encodes the given system and the given property, into a monadic ω -program, that is, a stratified program defining nullary or unary predicates on infinite lists. This transformation is performed by applying unfold/fold rules that preserve the perfect model of the initial program. In the second step we verify the property of interest by using a proof method for monadic ω-program
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
Layered Fixed Point Logic
We present a logic for the specification of static analysis problems that
goes beyond the logics traditionally used. Its most prominent feature is the
direct support for both inductive computations of behaviors as well as
co-inductive specifications of properties. Two main theoretical contributions
are a Moore Family result and a parametrized worst case time complexity result.
We show that the logic and the associated solver can be used for rapid
prototyping and illustrate a wide variety of applications within Static
Analysis, Constraint Satisfaction Problems and Model Checking. In all cases the
complexity result specializes to the worst case time complexity of the
classical methods
Computation Tree Logic with Deadlock Detection
We study the equivalence relation on states of labelled transition systems of
satisfying the same formulas in Computation Tree Logic without the next state
modality (CTL-X). This relation is obtained by De Nicola & Vaandrager by
translating labelled transition systems to Kripke structures, while lifting the
totality restriction on the latter. They characterised it as divergence
sensitive branching bisimulation equivalence.
We find that this equivalence fails to be a congruence for interleaving
parallel composition. The reason is that the proposed application of CTL-X to
non-total Kripke structures lacks the expressiveness to cope with deadlock
properties that are important in the context of parallel composition. We
propose an extension of CTL-X, or an alternative treatment of non-totality,
that fills this hiatus. The equivalence induced by our extension is
characterised as branching bisimulation equivalence with explicit divergence,
which is, moreover, shown to be the coarsest congruence contained in divergence
sensitive branching bisimulation equivalence
Satisfiability of CTL* with constraints
We show that satisfiability for CTL* with equality-, order-, and
modulo-constraints over Z is decidable. Previously, decidability was only known
for certain fragments of CTL*, e.g., the existential and positive fragments and
EF.Comment: To appear at Concur 201
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
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