Permissive strategies in timed automata and games

Timed automata are a convenient framework for modelling and reasoning about real-time systems. While these models are now well-understood, they do not offer a convenient way of taking timing imprecisions into account. Several solutions (e.g. parametric guard enlargement) have been proposed over the last ten years to take such imprecisions into account. In this paper, we propose a novel approach for handling robust reachability, based on permissive strategies. While classical strategies propose to play an action at an exact point in time, permissive strategies consider intervals of possible dates when to play the selected action. In other words, the controller specifies an interval of time delays for actions to be executed in a more flexible way. With such a permissive strategy, we associate a penalty, which is the inverse of the length of the proposed interval, and accumulates along the run. We show that in that setting, optimal strategies can be computed in polynomial time for one-clock timed automata

Stochastic Timed Automata

A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a stochastic timed automaton A and a property $\Phi$, we want to decide whether A satisfies $\Phi$ with probability 1. In this paper, we identify several classes of automata and of properties for which this can be decided. The proof relies on the construction of a finite abstraction, called the thick graph, that we interpret as a finite Markov chain, and for which we can decide the almost-sure model-checking problem. Correctness of the abstraction holds when automata are almost-surely fair, which we show, is the case for two large classes of systems, single- clock automata and so-called weak-reactive automata. Techniques employed in this article gather tools from real-time verification and probabilistic verification, as well as topological games played on timed automata.Comment: 40 pages + appendi

Timed Automata Robustness Analysis via Model Checking

Timed automata (TA) have been widely adopted as a suitable formalism to model time-critical systems. Furthermore, contemporary model-checking tools allow the designer to check whether a TA complies with a system specification. However, the exact timing constants are often uncertain during the design phase. Consequently, the designer is often able to build a TA with a correct structure, however, the timing constants need to be tuned to satisfy the specification. Moreover, even if the TA initially satisfies the specification, it can be the case that just a slight perturbation during the implementation causes a violation of the specification. Unfortunately, model-checking tools are usually not able to provide any reasonable guidance on how to fix the model in such situations. In this paper, we propose several concepts and techniques to cope with the above mentioned design phase issues when dealing with reachability and safety specifications

Tools and Algorithms for the Construction and Analysis of Systems

This book is Open Access under a CC BY licence. The LNCS 11427 and 11428 proceedings set constitutes the proceedings of the 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019. The total of 42 full and 8 short tool demo papers presented in these volumes was carefully reviewed and selected from 164 submissions. The papers are organized in topical sections as follows: Part I: SAT and SMT, SAT solving and theorem proving; verification and analysis; model checking; tool demo; and machine learning. Part II: concurrent and distributed systems; monitoring and runtime verification; hybrid and stochastic systems; synthesis; symbolic verification; and safety and fault-tolerant systems

Parametric updates in parametric timed automata

We introduce a new class of Parametric Timed Automata (PTAs) where we allow clocks to be compared to parameters in guards, as in classic PTAs, but also to be updated to parameters. We focus here on the EF-emptiness problem: "is the set of parameter valuations for which some given location is reachable in the instantiated timed automaton empty?". This problem is well-known to be undecidable for PTAs, and so it is for our extension. Nonetheless, if we update all clocks each time we compare a clock with a parameter and each time we update a clock to a parameter, we obtain a syntactic subclass for which we can decide the EF-emptiness problem and even perform the exact synthesis of the set of rational valuations such that a given location is reachable. To the best of our knowledge, this is the first non-trivial subclass of PTAs, actually even extended with parametric updates, for which this is possible

Realizability of embedded controllers: from hybrid models to correct implementations

Un controller embedded \ue8 un dispositivo (ovvero, un'opportuna combinazione di componenti hardware e software) che, immerso in un ambiente dinamico, deve reagire alle variazioni ambientali in tempo reale. I controller embedded sono largamente adottati in molti contesti della vita moderna, dall'automotive all'avionica, dall'elettronica di consumo alle attrezzature mediche. La correttezza di tali controller \ue8 indubbiamente cruciale. Per la progettazione e per la verifica di un controller embedded, spesso sorge la necessit\ue0 di modellare un intero sistema che includa sia il controller, sia il suo ambiente circostante. La natura di tale sistema \ue8 ibrido. Esso, infatti, \ue8 ottenuto integrando processi ad eventi discreti (i.e., il controller) e processi a tempo continuo (i.e., l'ambiente). Sistemi di questo tipo sono chiamati cyber-physical (CPS) o sistemi ibridi. Le dinamiche di tali sistemi non possono essere rappresentati efficacemente utilizzando o solo un modello (i.e., rappresentazione) discreto o solo un modello continuo. Diversi tipi di modelli possono sono stati proposti per descrivere i sistemi ibridi. Questi si concentrano su obiettivi diversi: modelli dettagliati sono eccellenti per la simulazione del sistema, ma non sono adatti per la sua verifica; modelli meno dettagliati sono eccellenti per la verifica, ma non sono convenienti per i successivi passi di raffinamento richiesti per la progettazione del sistema, e cos\uec via. Tra tutti questi modelli, gli Automi Ibridi (HA) [8, 77] rappresentano il formalismo pi\uf9 efficace per la simulazione e la verifica di sistemi ibridi. In particolare, un automa ibrido rappresenta i processi ad eventi discreti per mezzo di macchine a stati finiti (FSM), mentre i processi a tempo continuo sono rappresentati mediante variabili "continue" la cui dinamica \ue8 specificata da equazioni differenziali ordinarie (ODE) o loro generalizzazioni (e.g., inclusioni differenziali). Sfortunatamente, a causa della loro particolare semantica, esistono diverse difficolt\ue0 nel raffinare un modello basato su automi ibridi in un modello realizzabile e, di conseguenza, esistono difficolt\ue0 nell'automatizzare il flusso di progettazione di sistemi ibridi a partire da automi ibridi. Gli automi ibridi, infatti, sono considerati dispositivi "perfetti e istantanei". Essi adottano una nozione di tempo e di variabili basata su insiemi "densi" (i.e., l'insieme dei numeri reali). Pertanto, gli automi ibridi possono valutare lo stato (i.e., i valori delle variabili) del sistema in ogni istante, ovvero in ogni infinitesimo di tempo, e con la massima precisione. Inoltre, sono in grado di eseguire computazioni o reagire ad eventi di sincronizzazione in modo istantaneo, andando a cambiare la modalit\ue0 di funzionamento del sistema senza alcun ritardo. Questi aspetti sono convenienti a livello di modellazione, ma nessun dispositivo hardware/software potrebbe implementare correttamente tali comportamenti, indipendentemente dalle sue prestazioni. In altre parole, il controller modellato potrebbe non essere implementabile, ovvero, esso potrebbe non essere realizzabile affatto. Questa tesi affronta questo problema proponendo una metodologia completa e gli strumenti necessari per derivare da modelli basati su automi ibridi, modelli realizzabili e le corrispondenti implementazioni corrette. In un modello realizzabile, il controller analizza lo stato del sistema ad istanti temporali discreti, tipicamente fissati dalla frequenza di clock del processore installato sul dispositivo che implementa il controller. Lo stato del sistema \ue8 dato dai valori delle variabili rilevati dai sensori. Questi valori vengono digitalizzati con precisione finita e propagati al controller che li elabora per decidere se cambiare la modalit\ue0 di funzionamento del sistema. In tal caso, il controller genera segnali che, una volta trasmessi agli attuatori, determineranno il cambiamento della modalit\ue0 di funzionamento del sistema. \uc8 necessario tener presente che i sensori e gli attuatori introducono ritardi che seppur limitati, non possono essere trascurati.An embedded controller is a reactive device (e.g., a suitable combination of hardware and software components) that is embedded in a dynamical environment and has to react to environment changes in real time. Embedded controllers are widely adopted in many contexts of modern life, from automotive to avionics, from consumer electronics to medical equipment. Noticeably, the correctness of such controllers is crucial. When designing and verifying an embedded controller, often the need arises to model the controller and also its surrounding environment. The nature of the obtained system is hybrid because of the inclusion of both discrete-event (i.e., controller) and continuous-time (i.e., environment) processes whose dynamics cannot be characterized faithfully using either a discrete or continuous model only. Systems of this kind are named cyber-physical (CPS) or hybrid systems. Different types of models may be used to describe hybrid systems and they focus on different objectives: detailed models are excellent for simulation but not suitable for verification, high-level models are excellent for verification but not convenient for refinement, and so forth. Among all these models, hybrid automata (HA) [8, 77] have been proposed as a powerful formalism for the design, simulation and verification of hybrid systems. In particular, a hybrid automaton represents discrete-event processes by means of finite state machines (FSM), whereas continuous-time processes are represented by using real-numbered variables whose dynamics is specified by (ordinary) differential equation (ODE) or their generalizations (e.g., differential inclusions). Unfortunately, when the high-level model of the hybrid system is a hybrid automaton, several difficulties should be solved in order to automate the refinement phase in the design flow, because of the classical semantics of hybrid automata. In fact, hybrid automata can be considered perfect and instantaneous devices. They adopt a notion of time and evaluation of continuous variables based on dense sets of values (usually R, i.e., Reals). Thus, they can sample the state (i.e., value assignments on variables) of the hybrid system at any instant in such a dense set R 650. Further, they are capable of instantaneously evaluating guard constraints or reacting to incoming events by performing changes in the operating mode of the hybrid system without any delay. While these aspects are convenient at the modeling level, any model of an embedded controller that relies for its correctness on such precision and instantaneity cannot be implemented by any hardware/software device, no matter how fast it is. In other words, the controller is un-realizable, i.e., un-implementable. This thesis proposes a complete methodology and a framework that allows to derive from hybrid automata proved correct in the hybrid domain, correct realizable models of embedded controllers and the related discrete implementations. In a realizable model, the controller samples the state of the environment at periodic discrete time instants which, typically, are fixed by the clock frequency of the processor implementing the controller. The state of the environment consists of the current values of the relevant variables as observed by the sensors. These values are digitized with finite precision and reported to the controller that may decide to switch the operating mode of the environment. In such a case, the controller generates suitable output signals that, once transmitted to the actuators, will effect the desired change in the operating mode. It is worth noting that the sensors will report the current values of the variables and the actuators will effect changes in the rates of evolution of the variables with bounded delays

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency

Shrinking timed automata

We define and study a new approach to the implementability of timed automata, where the semantics is perturbed by imprecisions and finite frequency of the hardware. In order to circumvent these effects, we introduce parametric shrinking of clock constraints, which corresponds to tightening these. We propose symbolic procedures to decide the existence of (and then compute) parameters under which the shrunk version of a given timed automaton is non-blocking and can time-abstract simulate the exact semantics. We then define an implementation semantics for timed automata with a digital clock and positive reaction times, and show that for shrinkable timed automata, non-blockingness and time-abstract simulation are preserved in implementation