23,610 research outputs found
Model Checking Well-Behaved Fragments of HS: The (Almost) Final Picture
Model checking is one of the most powerful and widespread
tools for system verification with applications in many areas
of computer science and artificial intelligence. The large majority
of model checkers deal with properties expressed in
point-based temporal logics, such as LTL and CTL. However,
there exist relevant properties of systems which are inherently
interval-based. Model checking algorithms for interval
temporal logics (ITLs) have recently been proposed to check
interval properties of computations. As the model checking
problem for full Halpern and Shoham\u2019s ITL (HS for short)
turns out to be decidable, but computationally heavy, research
has focused on its well-behaved fragments. In this paper, we
provide an almost final picture of the computational complexity
of model checking for HS fragments with modalities for
(a subset of) Allen\u2019s relations meets, met by, starts, and end
Formal Proofs for Nonlinear Optimization
We present a formally verified global optimization framework. Given a
semialgebraic or transcendental function and a compact semialgebraic domain
, we use the nonlinear maxplus template approximation algorithm to provide a
certified lower bound of over . This method allows to bound in a modular
way some of the constituents of by suprema of quadratic forms with a well
chosen curvature. Thus, we reduce the initial goal to a hierarchy of
semialgebraic optimization problems, solved by sums of squares relaxations. Our
implementation tool interleaves semialgebraic approximations with sums of
squares witnesses to form certificates. It is interfaced with Coq and thus
benefits from the trusted arithmetic available inside the proof assistant. This
feature is used to produce, from the certificates, both valid underestimators
and lower bounds for each approximated constituent. The application range for
such a tool is widespread; for instance Hales' proof of Kepler's conjecture
yields thousands of multivariate transcendental inequalities. We illustrate the
performance of our formal framework on some of these inequalities as well as on
examples from the global optimization literature.Comment: 24 pages, 2 figures, 3 table
Complexity of ITL model checking: some well-behaved fragments of the interval logic HS
Model checking has been successfully used in many computer science fields,
including artificial intelligence, theoretical computer science, and databases.
Most of the proposed solutions make use of classical, point-based temporal
logics, while little work has been done in the interval temporal logic setting.
Recently, a non-elementary model checking algorithm for Halpern and Shoham's
modal logic of time intervals HS over finite Kripke structures (under the
homogeneity assumption) and an EXPSPACE model checking procedure for two
meaningful fragments of it have been proposed. In this paper, we show that more
efficient model checking procedures can be developed for some expressive enough
fragments of HS
MTL-Model Checking of One-Clock Parametric Timed Automata is Undecidable
Parametric timed automata extend timed automata (Alur and Dill, 1991) in that
they allow the specification of parametric bounds on the clock values. Since
their introduction in 1993 by Alur, Henzinger, and Vardi, it is known that the
emptiness problem for parametric timed automata with one clock is decidable,
whereas it is undecidable if the automaton uses three or more parametric
clocks. The problem is open for parametric timed automata with two parametric
clocks. Metric temporal logic, MTL for short, is a widely used specification
language for real-time systems. MTL-model checking of timed automata is
decidable, no matter how many clocks are used in the timed automaton. In this
paper, we prove that MTL-model checking for parametric timed automata is
undecidable, even if the automaton uses only one clock and one parameter and is
deterministic.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
Which Fragments of the Interval Temporal Logic HS are Tractable in Model Checking?
Since the 80s, model checking (MC) has been applied to the automatic verification of hardware/software systems. Point-based temporal logics, such as LTL, CTL, CTLâ, and the like, are commonly used in MC as the specification language; however, there are some inherently interval-based properties of computations, e.g., temporal aggregations and durations, that cannot be properly dealt with by these logics, as they model a state-by-state evolution of systems. Recently, an MC framework for the verification of interval-based properties of computations, based on Halpern and Shoham's interval temporal logic (HS, for short) and its fragments, has been proposed and systematically investigated. In this paper, we focus on the boundaries that separate tractable and intractable HS fragments in MC. We first prove that MC for the logic BE of Allen's relations started-by and finished-by is provably intractable, being EXPSPACE-hard. Such a lower bound immediately propagates to full HS. Then, in contrast, we show that other noteworthy HS fragments, i.e., the logic AAâŸBB⟠(resp., AAâŸEEâŸ) of Allen's relations meets, met-by, starts (resp., finishes), and started-by (resp., finished-by), are well-behaved, and turn out to have the same complexity as LTL (PSPACE-complete). Halfway are the fragments AAâŸBBâŸE⟠and AAâŸEBâŸEâŸ, whose EXPSPACE membership and PSPACE hardness are already known. Here, we give an original proof of EXPSPACE membership, that substantially simplifies the complexity of the constructions previously used for such a result. Contraction techniquesâsuitably tailored to each HS fragmentâare at the heart of our results, enabling us to prove a pair of remarkable small-model propertie
Constraint-based reachability
Iterative imperative programs can be considered as infinite-state systems
computing over possibly unbounded domains. Studying reachability in these
systems is challenging as it requires to deal with an infinite number of states
with standard backward or forward exploration strategies. An approach that we
call Constraint-based reachability, is proposed to address reachability
problems by exploring program states using a constraint model of the whole
program. The keypoint of the approach is to interpret imperative constructions
such as conditionals, loops, array and memory manipulations with the
fundamental notion of constraint over a computational domain. By combining
constraint filtering and abstraction techniques, Constraint-based reachability
is able to solve reachability problems which are usually outside the scope of
backward or forward exploration strategies. This paper proposes an
interpretation of classical filtering consistencies used in Constraint
Programming as abstract domain computations, and shows how this approach can be
used to produce a constraint solver that efficiently generates solutions for
reachability problems that are unsolvable by other approaches.Comment: In Proceedings Infinity 2012, arXiv:1302.310
- âŠ