42,382 research outputs found
Checking Interval Properties of Computations
Model checking is a powerful method widely explored in formal verification.
Given a model of a system, e.g., a Kripke structure, and a formula specifying
its expected behaviour, one can verify whether the system meets the behaviour
by checking the formula against the model.
Classically, system behaviour is expressed by a formula of a temporal logic,
such as LTL and the like. These logics are "point-wise" interpreted, as they
describe how the system evolves state-by-state. However, there are relevant
properties, such as those constraining the temporal relations between pairs of
temporally extended events or involving temporal aggregations, which are
inherently "interval-based", and thus asking for an interval temporal logic.
In this paper, we give a formalization of the model checking problem in an
interval logic setting. First, we provide an interpretation of formulas of
Halpern and Shoham's interval temporal logic HS over finite Kripke structures,
which allows one to check interval properties of computations. Then, we prove
that the model checking problem for HS against finite Kripke structures is
decidable by a suitable small model theorem, and we provide a lower bound to
its computational complexity.Comment: In Journal: Acta Informatica, Springer Berlin Heidelber, 201
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
Power of Quantum Computation with Few Clean Qubits
This paper investigates the power of polynomial-time quantum computation in
which only a very limited number of qubits are initially clean in the |0>
state, and all the remaining qubits are initially in the totally mixed state.
No initializations of qubits are allowed during the computation, nor
intermediate measurements. The main results of this paper are unexpectedly
strong error-reducible properties of such quantum computations. It is proved
that any problem solvable by a polynomial-time quantum computation with
one-sided bounded error that uses logarithmically many clean qubits can also be
solvable with exponentially small one-sided error using just two clean qubits,
and with polynomially small one-sided error using just one clean qubit. It is
further proved in the case of two-sided bounded error that any problem solvable
by such a computation with a constant gap between completeness and soundness
using logarithmically many clean qubits can also be solvable with exponentially
small two-sided error using just two clean qubits. If only one clean qubit is
available, the problem is again still solvable with exponentially small error
in one of the completeness and soundness and polynomially small error in the
other. As an immediate consequence of the above result for the two-sided-error
case, it follows that the TRACE ESTIMATION problem defined with fixed constant
threshold parameters is complete for the classes of problems solvable by
polynomial-time quantum computations with completeness 2/3 and soundness 1/3
using logarithmically many clean qubits and just one clean qubit. The
techniques used for proving the error-reduction results may be of independent
interest in themselves, and one of the technical tools can also be used to show
the hardness of weak classical simulations of one-clean-qubit computations
(i.e., DQC1 computations).Comment: 44 pages + cover page; the results in Section 8 are overlapping with
the main results in arXiv:1409.677
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
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