112,143 research outputs found
A Team Based Variant of CTL
We introduce two variants of computation tree logic CTL based on team
semantics: an asynchronous one and a synchronous one. For both variants we
investigate the computational complexity of the satisfiability as well as the
model checking problem. The satisfiability problem is shown to be
EXPTIME-complete. Here it does not matter which of the two semantics are
considered. For model checking we prove a PSPACE-completeness for the
synchronous case, and show P-completeness for the asynchronous case.
Furthermore we prove several interesting fundamental properties of both
semantics.Comment: TIME 2015 conference version, modified title and motiviatio
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
Expressiveness and Completeness in Abstraction
We study two notions of expressiveness, which have appeared in abstraction
theory for model checking, and find them incomparable in general. In
particular, we show that according to the most widely used notion, the class of
Kripke Modal Transition Systems is strictly less expressive than the class of
Generalised Kripke Modal Transition Systems (a generalised variant of Kripke
Modal Transition Systems equipped with hypertransitions). Furthermore, we
investigate the ability of an abstraction framework to prove a formula with a
finite abstract model, a property known as completeness. We address the issue
of completeness from a general perspective: the way it depends on certain
abstraction parameters, as well as its relationship with expressiveness.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
The Complexity of Model Checking Higher-Order Fixpoint Logic
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed
\lambda-calculus and the modal \lambda-calculus. This makes it a highly
expressive temporal logic that is capable of expressing various interesting
correctness properties of programs that are not expressible in the modal
\lambda-calculus.
This paper provides complexity results for its model checking problem. In
particular we consider those fragments of HFL built by using only types of
bounded order k and arity m. We establish k-fold exponential time completeness
for model checking each such fragment. For the upper bound we use fixpoint
elimination to obtain reachability games that are singly-exponential in the
size of the formula and k-fold exponential in the size of the underlying
transition system. These games can be solved in deterministic linear time. As a
simple consequence, we obtain an exponential time upper bound on the expression
complexity of each such fragment.
The lower bound is established by a reduction from the word problem for
alternating (k-1)-fold exponential space bounded Turing Machines. Since there
are fixed machines of that type whose word problems are already hard with
respect to k-fold exponential time, we obtain, as a corollary, k-fold
exponential time completeness for the data complexity of our fragments of HFL,
provided m exceeds 3. This also yields a hierarchy result in expressive power.Comment: 33 pages, 2 figures, to be published in Logical Methods in Computer
Scienc
A First-Order Complete Temporal Logic for Structured Context-Free Languages
The problem of model checking procedural programs has fostered much research
towards the definition of temporal logics for reasoning on context-free
structures. The most notable of such results are temporal logics on Nested
Words, such as CaRet and NWTL. Recently, the logic OPTL was introduced, based
on the class of Operator Precedence Languages (OPLs), more powerful than Nested
Words. We define the new OPL-based logic POTL and prove its FO-completeness.
POTL improves on NWTL by enabling the formulation of requirements involving
pre/post-conditions, stack inspection, and others in the presence of
exception-like constructs. It improves on OPTL too, which instead we show not
to be FO-complete; it also allows to express more easily stack inspection and
function-local properties. In a companion paper we report a model checking
procedure for POTL and experimental results based on a prototype tool developed
therefor. For completeness a short summary of this complementary result is
provided in this paper too.Comment: Partially supersedes arXiv:1910.0932
Approximating attractors of Boolean networks by iterative CTL model checking
This paper introduces the notion of approximating asynchronous attractors of
Boolean networks by minimal trap spaces. We define three criteria for
determining the quality of an approximation: “faithfulness” which requires
that the oscillating variables of all attractors in a trap space correspond to
their dimensions, “univocality” which requires that there is a unique
attractor in each trap space, and “completeness” which requires that there are
no attractors outside of a given set of trap spaces. Each is a reachability
property for which we give equivalent model checking queries. Whereas
faithfulness and univocality can be decided by model checking the
corresponding subnetworks, the naive query for completeness must be evaluated
on the full state space. Our main result is an alternative approach which is
based on the iterative refinement of an initially poor approximation. The
algorithm detects so-called autonomous sets in the interaction graph,
variables that contain all their regulators, and considers their intersection
and extension in order to perform model checking on the smallest possible
state spaces. A benchmark, in which we apply the algorithm to 18 published
Boolean networks, is given. In each case, the minimal trap spaces are
faithful, univocal, and complete, which suggests that they are in general good
approximations for the asymptotics of Boolean networks
Gentzen-type axiomatization for PAL
AbstractThe aim of propositional algorithmic logic (PAL) is to investigate the properties of simple nondeterministic while-program schemes on propositional level. We present finite, cut-free, Gentzen-type axiomatization of PAL. As a corollary from completeness theorem, we obtain the small-model theorem and algorithm for checking the validity of PAL formulas
AI-enabled Automation for Completeness Checking of Privacy Policies
Technological advances in information sharing have raised concerns about data
protection. Privacy policies contain privacy-related requirements about how the
personal data of individuals will be handled by an organization or a software
system (e.g., a web service or an app). In Europe, privacy policies are subject
to compliance with the General Data Protection Regulation (GDPR). A
prerequisite for GDPR compliance checking is to verify whether the content of a
privacy policy is complete according to the provisions of GDPR. Incomplete
privacy policies might result in large fines on violating organization as well
as incomplete privacy-related software specifications. Manual completeness
checking is both time-consuming and error-prone. In this paper, we propose
AI-based automation for the completeness checking of privacy policies. Through
systematic qualitative methods, we first build two artifacts to characterize
the privacy-related provisions of GDPR, namely a conceptual model and a set of
completeness criteria. Then, we develop an automated solution on top of these
artifacts by leveraging a combination of natural language processing and
supervised machine learning. Specifically, we identify the GDPR-relevant
information content in privacy policies and subsequently check them against the
completeness criteria. To evaluate our approach, we collected 234 real privacy
policies from the fund industry. Over a set of 48 unseen privacy policies, our
approach detected 300 of the total of 334 violations of some completeness
criteria correctly, while producing 23 false positives. The approach thus has a
precision of 92.9% and recall of 89.8%. Compared to a baseline that applies
keyword search only, our approach results in an improvement of 24.5% in
precision and 38% in recall
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