6 research outputs found
Language Emptiness of Continuous-Time Parametric Timed Automata
Parametric timed automata extend the standard timed automata with the
possibility to use parameters in the clock guards. In general, if the
parameters are real-valued, the problem of language emptiness of such automata
is undecidable even for various restricted subclasses. We thus focus on the
case where parameters are assumed to be integer-valued, while the time still
remains continuous. On the one hand, we show that the problem remains
undecidable for parametric timed automata with three clocks and one parameter.
On the other hand, for the case with arbitrary many clocks where only one of
these clocks is compared with (an arbitrary number of) parameters, we show that
the parametric language emptiness is decidable. The undecidability result
tightens the bounds of a previous result which assumed six parameters, while
the decidability result extends the existing approaches that deal with
discrete-time semantics only. To the best of our knowledge, this is the first
positive result in the case of continuous-time and unbounded integer
parameters, except for the rather simple case of single-clock automata
Dense Integer-Complete Synthesis for Bounded Parametric Timed Automata
Ensuring the correctness of critical real-time systems, involving concurrent
behaviors and timing requirements, is crucial. Timed automata extend
finite-state automata with clocks, compared in guards and invariants with
integer constants. Parametric timed automata (PTAs) extend timed automata with
timing parameters. Parameter synthesis aims at computing dense sets of
valuations for the timing parameters, guaranteeing a good behavior. However, in
most cases, the emptiness problem for reachability (i.e., whether the emptiness
of the parameter valuations set for which some location is reachable) is
undecidable for PTAs and, as a consequence, synthesis procedures do not
terminate in general, even for bounded parameters. In this paper, we introduce
a parametric extrapolation, that allows us to derive an underapproximation in
the form of linear constraints containing not only all the integer points
ensuring reachability, but also all the (non-necessarily integer) convex
combinations of these integer points, for general PTAs with a bounded parameter
domain. We also propose two further algorithms synthesizing parameter
valuations guaranteeing unavoidability, and preservation of the untimed
behavior w.r.t. a reference parameter valuation, respectively. Our algorithms
terminate and can output constraints arbitrarily close to the complete result.
We demonstrate their applicability and efficiency using the tool Rom\'eo on two
classical benchmarks.Comment: This is an extended version of the paper by the same authors
published in the proceedings of the 9th International Workshop on
Reachability Problems (RP 2015
Reachability and liveness in parametric timed automata
We study timed systems in which some timing features are unknown parameters.
Parametric timed automata (PTAs) are a classical formalism for such systems but
for which most interesting problems are undecidable. Notably, the parametric
reachability emptiness problem, i.e., whether at least one parameter valuation
allows to reach some given discrete state, is undecidable.
Lower-bound/upper-bound parametric timed automata (L/U-PTAs) achieve
decidability for reachability properties by enforcing a separation of
parameters used as upper bounds in the automaton constraints, and those used as
lower bounds.
In this paper, we first study reachability. We exhibit a subclass of PTAs
(namely integer-points PTAs) with bounded rational-valued parameters for which
the parametric reachability emptiness problem is decidable. Using this class,
we present further results improving the boundary between decidability and
undecidability for PTAs and their subclasses such as L/U-PTAs.
We then study liveness. We prove that:
(1) the existence of at least one parameter valuation for which there exists
an infinite run in an L/U-PTA is PSPACE-complete;
(2) the existence of a parameter valuation such that the system has a
deadlock is however undecidable;
(3) the problem of the existence of a valuation for which a run remains in a
given set of locations exhibits a very thin border between decidability and
undecidability.Comment: This manuscript is an extended version of two conference papers
published in the proceedings of ICFEM 2016 and ACSD 201
Reachability and liveness in parametric timed automata
We study timed systems in which some timing features are unknown parameters.
Parametric timed automata (PTAs) are a classical formalism for such systems but
for which most interesting problems are undecidable. Notably, the parametric
reachability emptiness problem, i.e., the emptiness of the parameter valuations
set allowing to reach some given discrete state, is undecidable.
Lower-bound/upper-bound parametric timed automata (L/U-PTAs) achieve
decidability for reachability properties by enforcing a separation of
parameters used as upper bounds in the automaton constraints, and those used as
lower bounds.
In this paper, we first study reachability. We exhibit a subclass of PTAs
(namely integer-points PTAs) with bounded rational-valued parameters for which
the parametric reachability emptiness problem is decidable. Using this class,
we present further results improving the boundary between decidability and
undecidability for PTAs and their subclasses such as L/U-PTAs.
We then study liveness. We prove that:
(1) deciding the existence of at least one parameter valuation for which
there exists an infinite run in an L/U-PTA is PSpace-complete;
(2) the existence of a parameter valuation such that the system has a
deadlock is however undecidable;
(3) the problem of the existence of a valuation for which a run remains in a
given set of locations exhibits a very thin border between decidability and
undecidability
Formal methods applied to the analysis of phylogenies: Phylogenetic model checking
Los árboles filogenéticos son abstracciones útiles para modelar y caracterizar la evolución de un conjunto de especies o poblaciones respecto del tiempo. La proposición, verificación y generalización de hipótesis sobre un árbol filogenético inferido juegan un papel importante en el estudio y comprensión de las relaciones evolutivas. Actualmente, uno de los principales objetivos cientÃficos es extraer o descubrir los mensajes biológicos implÃcitos y las propiedades estructurales subyacentes en la filogenia. Por ejemplo, la integración de información genética en una filogenia ayuda al descubrimiento de genes conservados en todo o parte del árbol, la identificación de posiciones covariantes en el ADN o la estimación de las fechas de divergencia entre especies. Consecuentemente, los árboles ayudan a comprender el mecanismo que gobierna la deriva evolutiva. Hoy en dÃa, el amplio espectro de métodos y herramientas heterogéneas para el análisis de filogenias enturbia y dificulta su utilización, además del fuerte acoplamiento entre la especificación de propiedades y los algoritmos utilizados para su evaluación (principalmente scripts ad hoc). Este problema es el punto de arranque de esta tesis, donde se analiza como solución la posibilidad de introducir un entorno formal de verificación de hipótesis que, de manera automática y modular, estudie la veracidad de dichas propiedades definidas en un lenguaje genérico e independiente (en una lógica formal asociada) sobre uno de los múltiples softwares preparados para ello. La contribución principal de la tesis es la propuesta de un marco formal para la descripción, verificación y manipulación de relaciones causales entre especies de forma independiente del código utilizado para su valoración. Para ello, exploramos las caracterÃsticas de las técnicas de model checking, un paradigma en el que una especificación expresada en lógica temporal se verifica con respecto a un modelo del sistema que representa una implementación a un cierto nivel de detalle. Se ha aplicado satisfactoriamente en la industria para el modelado de sistemas y su verificación, emergiendo del ámbito de las ciencias de la computación. Las contribuciones concretas de la tesis han sido: A) La identificación e interpretación de los árboles filogeneticos como modelos de la evolución, adaptados al entorno de las técnicas de model checking. B) La definición de una lógica temporal que captura las propiedades filogenéticas habituales junto con un método de construcción de propiedades. C) La clasificación de propiedades filogenéticas, identificando categorÃas de propiedades según estén centradas en la estructura del árbol, en las secuencias o sean hÃbridas. D) La extensión de las lógicas y modelos para contemplar propiedades cuantitativas de tiempo, probabilidad y de distancias. E) El desarrollo de un entorno para la verificación de propiedades booleanas, cuantitativas y paramétricas. F) El establecimiento de los principios para la manipulación simbolica de objetos filogenéticos, p. ej., clados. G) La explotación de las herramientas de model checking existentes, detectando sus problemas y carencias en el campo de filogenia y proponiendo mejoras. H) El desarrollo de técnicas "ad hoc" para obtener ganancia de complejidad alrededor de dos frentes: distribución de los cálculos y datos, y el uso de sistemas de información. Los puntos A-F se centran en las aportaciones conceptuales de nuestra aproximación, mientras que los puntos G-H enfatizan la parte de herramientas e implementación. Los contenidos de la tesis están contrastados por la comunidad cientÃfica mediante las siguientes publicaciones en conferencias y revistas internacionales. La introducción de model checking como entorno formal para analizar propiedades biológicas (puntos A-C) ha llevado a la publicación de nuestro primer artÃculo de congreso [1]. En [2], desarrollamos la verificación de hipótesis filogenéticas sobre un árbol de ejemplo construido a partir de las relaciones impuestas por un conjunto de proteÃnas codificadas por el ADN mitocondrial humano (ADNmt). En ese ejemplo, usamos una herramienta automática y genérica de model checking (punto G). El artÃculo de revista [7] resume lo básico de los artÃculos de congreso previos y extiende la aplicación de lógicas temporales a propiedades filogenéticas no consideradas hasta ahora. Los artÃculos citados aquà engloban los contenidos presentados en las Parte I--II de la tesis. El enorme tamaño de los árboles y la considerable cantidad de información asociada a los estados (p.ej., la cadena de ADN) obligan a la introducción de adaptaciones especiales en las herramientas de model checking para mantener un rendimiento razonable en la verificación de propiedades y aliviar también el problema de la explosión de estados (puntos G-H). El artÃculo de congreso [3] presenta las ventajas de rebanar el ADN asociado a los estados, la partición de la filogenia en pequeños subárboles y su distribución entre varias máquinas. Además, la idea original del model checking rebanado se complementa con la inclusión de una base de datos externa para el almacenamiento de secuencias. El artÃculo de revista [4] reúne las nociones introducidas en [3] junto con la implementación y resultados preliminares presentados [5]. Este tema se corresponde con lo presentado en la Parte III de la tesis. Para terminar, la tesis reaprovecha las extensiones de las lógicas temporales con tiempo explÃcito y probabilidades a fin de manipular e interrogar al árbol sobre información cuantitativa. El artÃculo de congreso [6] ejemplifica la necesidad de introducir probabilidades y tiempo discreto para el análisis filogenético de un fenotipo real, en este caso, el ratio de distribución de la intolerancia a la lactosa entre diversas poblaciones arraigadas en las hojas de la filogenia. Esto se corresponde con el CapÃtulo 13, que queda englobado dentro de las Partes IV--V. Las Partes IV--V completan los conceptos presentados en ese artÃculo de conferencia hacia otros dominios de aplicación, como la puntuación de árboles, y tiempo continuo (puntos E-F). La introducción de parámetros en las hipótesis filogenéticas se plantea como trabajo futuro. Referencias [1] Roberto Blanco, Gregorio de Miguel Casado, José Ignacio Requeno, and José Manuel Colom. Temporal logics for phylogenetic analysis via model checking. In Proceedings IEEE International Workshop on Mining and Management of Biological and Health Data, pages 152-157. IEEE, 2010. [2] José Ignacio Requeno, Roberto Blanco, Gregorio de Miguel Casado, and José Manuel Colom. Phylogenetic analysis using an SMV tool. In Miguel P. Rocha, Juan M. Corchado RodrÃguez, Florentino Fdez-Riverola, and Alfonso Valencia, editors, Proceedings 5th International Conference on Practical Applications of Computational Biology and Bioinformatics, volume 93 of Advances in Intelligent and Soft Computing, pages 167-174. Springer, Berlin, 2011. [3] José Ignacio Requeno, Roberto Blanco, Gregorio de Miguel Casado, and José Manuel Colom. Sliced model checking for phylogenetic analysis. In Miguel P. Rocha, Nicholas Luscombe, Florentino Fdez-Riverola, and Juan M. Corchado RodrÃguez, editors, Proocedings 6th International Conference on Practical Applications of Computational Biology and Bioinformatics, volume 154 of Advances in Intelligent and Soft Computing, pages 95-103. Springer, Berlin, 2012. [4] José Ignacio Requeno and José Manuel Colom. Model checking software for phylogenetic trees using distribution and database methods. Journal of Integrative Bioinformatics, 10(3):229-233, 2013. [5] José Ignacio Requeno and José Manuel Colom. Speeding up phylogenetic model checking. In Mohd Saberi Mohamad, Loris Nanni, Miguel P. Rocha, and Florentino Fdez-Riverola, editors, Proceedings 7th International Conference on Practical Applications of Computational Biology and Bioinformatics, volume 222 of Advances in Intelligent Systems and Computing, pages 119-126. Springer, Berlin, 2013. [6] José Ignacio Requeno and José Manuel Colom. Timed and probabilistic model checking over phylogenetic trees. In Miguel P. Rocha et al., editors, Proceedings 8th International Conference on Practical Applications of Computational Biology and Bioinformatics, Advances in Intelligent and Soft Computing. Springer, Berlin, 2014. [7] José Ignacio Requeno, Gregorio de Miguel Casado, Roberto Blanco, and José Manuel Colom. Temporal logics for phylogenetic analysis via model checking. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 10(4):1058-1070, 2013
On the verification of parametric and real-time systems
2009 - 2010Parametric and Real-Time Systems play a central role in the theory underlying
the Verification and Synthesis problems.
Real-time systems are present everywhere and are used in safety critical
applications, such as flight controllers. Failures in such systems can be
very expensive and even life threatening and, moreover, they are quite
hard to design and verify. For these reasons, the development of formal
methods for the modeling and analysis of safety-critical systems is
an active area of computer science research.
The standard formalism used to specify the wished behaviour of a realtime
system is temporal logic. Traditional temporal logics, such as linear
temporal logic (LTL), allow only qualitative assertions about the temporal
ordering of events. However, in several circumstances, for assessing the
efficiency of the system being modeled, it may be useful to have additional
quantitative guarantees. An extension of LTL with a real-time semantics
is given by the Metric Interval Temporal Logic (MITL), where changes
of truth values happen according to a splitting of the line of non-negative
reals into intervals.
However, even with quantitative temporal logics, we would actually like
to find out what quantitative bounds can be placed on the logic operators.
In this thesis we face with the above problem proposing a parametric
extension of MITL, that is the parametric metric interval temporal logic
(PMITL), which allows to introduce parameters within intervals . For this
logic, we study decision problems which are the analogous of satisfiability,
validity and model-checking problems for non-parametric temporal
logic. PMITL turns out to be decidable and we show that, when parameter
valuations give only non-singular sets, the considered problems are all
decidable, EXPSPACE-complete, and have the same complexity as in MITL.
Moreover, we investigate the computational complexity of these problems
for natural fragments of PMITL, and show that in meaningful fragments
of the logic they are PSPACE-complete.
We also consider a remarkable problem expressed by queries where the
values that each parameter may assume are either existentially or universally
quantified. We solve this problem in several cases and we propose an
algorithm in EXPSPACE.
Another interesting application of the temporal logic is when it is used
to express specification of concurrent programs, where programs and properties
are formalized as regular languages of infinite words. In this case,
the verification problem (whether the program satisfies the specification)
corresponds to solve the language inclusion problem.
In the second part of this thesis we consider the Synthesis problem for realtime
systems, investigating the applicability of automata constructions that
avoid determinization for solving the language inclusion problem and the
realizability problem for real-time logics. Since Safra’s determinization
procedure is difficult to implement, we present Safraless algorithms for
automata on infinite timed words. [edited by author]IX n.s