594 research outputs found
On relating CTL to Datalog
CTL is the dominant temporal specification language in practice mainly due to
the fact that it admits model checking in linear time. Logic programming and
the database query language Datalog are often used as an implementation
platform for logic languages. In this paper we present the exact relation
between CTL and Datalog and moreover we build on this relation and known
efficient algorithms for CTL to obtain efficient algorithms for fragments of
stratified Datalog. The contributions of this paper are: a) We embed CTL into
STD which is a proper fragment of stratified Datalog. Moreover we show that STD
expresses exactly CTL -- we prove that by embedding STD into CTL. Both
embeddings are linear. b) CTL can also be embedded to fragments of Datalog
without negation. We define a fragment of Datalog with the successor build-in
predicate that we call TDS and we embed CTL into TDS in linear time. We build
on the above relations to answer open problems of stratified Datalog. We prove
that query evaluation is linear and that containment and satisfiability
problems are both decidable. The results presented in this paper are the first
for fragments of stratified Datalog that are more general than those containing
only unary EDBs.Comment: 34 pages, 1 figure (file .eps
Flow Logic
Flow networks have attracted a lot of research in computer science. Indeed,
many questions in numerous application areas can be reduced to questions about
flow networks. Many of these applications would benefit from a framework in
which one can formally reason about properties of flow networks that go beyond
their maximal flow. We introduce Flow Logics: modal logics that treat flow
functions as explicit first-order objects and enable the specification of rich
properties of flow networks. The syntax of our logic BFL* (Branching Flow
Logic) is similar to the syntax of the temporal logic CTL*, except that atomic
assertions may be flow propositions, like or , for
, which refer to the value of the flow in a vertex, and
that first-order quantification can be applied both to paths and to flow
functions. We present an exhaustive study of the theoretical and practical
aspects of BFL*, as well as extensions and fragments of it. Our extensions
include flow quantifications that range over non-integral flow functions or
over maximal flow functions, path quantification that ranges over paths along
which non-zero flow travels, past operators, and first-order quantification of
flow values. We focus on the model-checking problem and show that it is
PSPACE-complete, as it is for CTL*. Handling of flow quantifiers, however,
increases the complexity in terms of the network to , even
for the LFL and BFL fragments, which are the flow-counterparts of LTL and CTL.
We are still able to point to a useful fragment of BFL* for which the
model-checking problem can be solved in polynomial time. Finally, we introduce
and study the query-checking problem for BFL*, where under-specified BFL*
formulas are used for network exploration
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
Quantified CTL: Expressiveness and Complexity
While it was defined long ago, the extension of CTL with quantification over
atomic propositions has never been studied extensively. Considering two
different semantics (depending whether propositional quantification refers to
the Kripke structure or to its unwinding tree), we study its expressiveness
(showing in particular that QCTL coincides with Monadic Second-Order Logic for
both semantics) and characterise the complexity of its model-checking and
satisfiability problems, depending on the number of nested propositional
quantifiers (showing that the structure semantics populates the polynomial
hierarchy while the tree semantics populates the exponential hierarchy)
Numerical Integration and Dynamic Discretization in Heuristic Search Planning over Hybrid Domains
In this paper we look into the problem of planning over hybrid domains, where
change can be both discrete and instantaneous, or continuous over time. In
addition, it is required that each state on the trajectory induced by the
execution of plans complies with a given set of global constraints. We approach
the computation of plans for such domains as the problem of searching over a
deterministic state model. In this model, some of the successor states are
obtained by solving numerically the so-called initial value problem over a set
of ordinary differential equations (ODE) given by the current plan prefix.
These equations hold over time intervals whose duration is determined
dynamically, according to whether zero crossing events take place for a set of
invariant conditions. The resulting planner, FS+, incorporates these features
together with effective heuristic guidance. FS+ does not impose any of the
syntactic restrictions on process effects often found on the existing
literature on Hybrid Planning. A key concept of our approach is that a clear
separation is struck between planning and simulation time steps. The former is
the time allowed to observe the evolution of a given dynamical system before
committing to a future course of action, whilst the later is part of the model
of the environment. FS+ is shown to be a robust planner over a diverse set of
hybrid domains, taken from the existing literature on hybrid planning and
systems.Comment: 17 page
A Supervisory Control Algorithm Based on Property-Directed Reachability
We present an algorithm for synthesising a controller (supervisor) for a
discrete event system (DES) based on the property-directed reachability (PDR)
model checking algorithm. The discrete event systems framework is useful in
both software, automation and manufacturing, as problems from those domains can
be modelled as discrete supervisory control problems. As a formal framework,
DES is also similar to domains for which the field of formal methods for
computer science has developed techniques and tools. In this paper, we attempt
to marry the two by adapting PDR to the problem of controller synthesis. The
resulting algorithm takes as input a transition system with forbidden states
and uncontrollable transitions, and synthesises a safe and
minimally-restrictive controller, correct-by-design. We also present an
implementation along with experimental results, showing that the algorithm has
potential as a part of the solution to the greater effort of formal supervisory
controller synthesis and verification.Comment: 16 pages; presented at Haifa Verification Conference 2017, the final
publication is available at Springer via
https://doi.org/10.1007/978-3-319-70389-3_
Dual Forgetting Operators in the Context of Weakest Sufficient and Strongest Necessary Conditions
Forgetting is an important concept in knowledge representation and automated
reasoning with widespread applications across a number of disciplines. A
standard forgetting operator, characterized in [Lin and Reiter'94] in terms of
model-theoretic semantics and primarily focusing on the propositional case,
opened up a new research subarea. In this paper, a new operator called weak
forgetting, dual to standard forgetting, is introduced and both together are
shown to offer a new more uniform perspective on forgetting operators in
general. Both the weak and standard forgetting operators are characterized in
terms of entailment and inference, rather than a model theoretic semantics.
This naturally leads to a useful algorithmic perspective based on quantifier
elimination and the use of Ackermman's Lemma and its fixpoint generalization.
The strong formal relationship between standard forgetting and strongest
necessary conditions and weak forgetting and weakest sufficient conditions is
also characterized quite naturally through the entailment-based, inferential
perspective used. The framework used to characterize the dual forgetting
operators is also generalized to the first-order case and includes useful
algorithms for computing first-order forgetting operators in special cases.
Practical examples are also included to show the importance of both weak and
standard forgetting in modeling and representation
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