This paper presents algorithms for the automatic synthesis of real-time controllers by finding a winning strategy for certain games defined by the timed-automata of Alur and Dill. In such games, the outcome depends on the players' actions as well as on their timing. We believe that these results will pave the way for the application of program synthesis techniques to the construction of real-time embedded systems from their specifications.

On the synthesis of discrete controllers for timed systems

We revisit the problem of computing controlled invariant sets for controllable discrete-time linear systems. Inspired by previous work by the authors, our main idea works in two moves: the problem is lifted to a higher dimensional space, where we provide a closed-form expression for a set whose projection back onto the original space is proven to be controlled invariant. We propose two methods in which the key insight is computing controlled invariant sets by considering periodic control policies. The first method considers hyperboxes that are rendered recurrent and essentially improves computational performance of the authors' previous work, while computing the same sets. The second method relaxes the assumption of recurrent hyper-boxes and yields substantially larger controlled invariant sets as shown in case studies. These methods do not rely on iterative computations and their scalability is illustrated in several examples, which show that none of the methods is strictly better than the other.

An enhanced hierarchy for (robust) controlled invariance

Robust Linear Temporal Logic (rLTL) was crafted to incorporate the notion of robustness into Linear-time Temporal Logic (LTL) specifications. Technically, robustness was formalized in the logic rLTL via 5 different truth values and it led to an increase in the time complexity of the associated model checking problem. In general, model checking an rLTL formula relies on constructing a generalized Buchi automaton of size 5 | φ | where | φ | denotes the length of an rLTL formula φ. It was recently shown that the size of this automaton can be reduced to 3 | φ | (and even smaller) when the formulas to be model checked come from a fragment of rLTL. In this paper, we introduce Evrostos, the first tool for model checking formulas in this fragment. We also present several empirical studies, based on models and LTL formulas reported in the literature, confirming that rLTL model checking for the aforementioned fragment incurs in a time overhead that makes the verification of rLTL practical.

https://dl.acm.org/doi/pdf/10.1145/3302504.3311812

Evrostos: the rLTL verifier

We study the temporal robustness of stochastic signals. This topic is of particular interest in interleaving processes such as multi-agent systems where communication and individual agents induce timing uncertainty. For a deterministic signal and a given specification, we first introduce the synchronous and the asynchronous temporal robustness to quantify the signal’s robustness with respect to synchronous and asynchronous time shifts in its sub-signals. We then define the temporal robustness risk by investigating the temporal robustness of the realizations of a stochastic signal. This definition can be interpreted as the risk associated with a stochastic signal to not satisfy a specification robustly in time. In this definition, general forms of specifications such as signal temporal logic specifications are permitted. We show how the temporal robustness risk is estimated from data for the value-at-risk. The usefulness of the temporal robustness risk is underlined by both theoretical and empirical evidence. In particular, we provide various numerical case studies including a T-intersection scenario in autonomous driving.

/pdf/temporal-robustness-of-stochastic-signals-7kzp1thx.pdf

Temporal Robustness of Stochastic Signals

Runtime monitoring is commonly used to detect the violation of desired properties in safety critical cyber-physical systems by observing its executions. Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties based on a three-valued semantics: the formula is already satisfied by the given prefix, it is already violated, or it is still undetermined, i.e., it can still be satisfied and violated by appropriate extensions. However, a wide range of formulas are not monitorable under this approach, meaning that they have a prefix for which satisfaction and violation will always remain undetermined no matter how it is extended. In particular, Bauer et al. report that 44% of the formulas they consider in their experiments fall into this category. Recently, a robust semantics for LTL was introduced to capture different degrees by wich a property can be violated. In this paper we introduce a robust semantics for finite strings and show its potential in monitoring: every formula considered by Bauer et al. is monitorable under our approach. Furthermore, we discuss which properties that come naturally in LTL monitoring --- such as the realizability of all truth values --- can be transferred to the robust setting. Lastly, we show that LTL formulas with robust semantics can be monitored by deterministic automata and report on a prototype implementation.

From LTL to rLTL monitoring: improved monitorability through robust semantics

Robust Linear Temporal Logic (rLTL) was crafted to incorporate the notion of robustness into Linear-time Temporal Logic specifications. Robustness is ubiquitous in control systems and translates the intuitive notion that “small” violations of environment assumptions should only lead to “small” violations of system guarantees. This notion was formalized in the logic rLTL via 5 different truth values and it led to an increase in the time complexity of the associated model checking problem. In this paper we identify and analyze a fragment of rLTL for which the model checking problem can be solved using generalized Biichi automata with at most $3^{\vert \varphi\vert }$ states where $\vert \varphi \vert$ denotes the length of an rLTL formula $\varphi$ . This is a substantial improvement over the previously known bound of $5^{\vert \varphi \vert}$ and close to the tight upper bound $2^{\vert \varphi\vert }$ for LTL.

https://par.nsf.gov/servlets/purl/10122208

Verifying rLTL formulas: now faster than ever before!

While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we introduce the logic rLTL which provides a means to formally reason about both correctness and robustness in system design. Furthermore, we identify a large fragment of rLTL for which the verification problem can be efficiently solved, i.e., verification can be done by using an automaton, recognizing the behaviors described by the rLTL formula $\varphi$, of size at most $\mathcal{O} \left( 3^{ |\varphi|} \right)$, where $|\varphi|$ is the length of $\varphi$. This result improves upon the previously known bound of $\mathcal{O}\left(5^{|\varphi|} \right)$ for rLTL verification and is closer to the LTL bound of $\mathcal{O}\left( 2^{|\varphi|} \right)$. The usefulness of this fragment is demonstrated by a number of case studies showing its practical significance in terms of expressiveness, the ability to describe robustness, and the fine-grained information that rLTL brings to the process of system verification. Moreover, these advantages come at a low computational overhead with respect to LTL verification.

Being correct is not enough: efficient verification using robust linear temporal logic.

In this paper we revisit the problem of computing controlled invariant sets for controllable discrete-time linear systems and present a novel hierarchy for their computation. The key insight is to lift the problem to a higher dimensional space where the maximal controlled invariant set can be computed exactly and in closed-form for the lifted system. By projecting this set into the original space we obtain a controlled invariant set that is a subset of the maximal controlled invariant set for the original system. Building upon this insight we describe in this paper a hierarchy of spaces where the original problem can be lifted into so as to obtain a sequence of increasing controlled invariant sets. The algorithm that results from the proposed hierarchy does not rely on iterative computations. We illustrate the performance of the proposed method on a variety of scenarios exemplifying its appeal.

/pdf/a-simple-hierarchy-for-computing-controlled-invariant-sets-242aameyyf.pdf

Tzanis Anevlavis

Papers

An enhanced hierarchy for (robust) controlled invariance

Evrostos: the rLTL verifier

Verifying rLTL formulas: now faster than ever before!

Being correct is not enough: efficient verification using robust linear temporal logic.

A simple hierarchy for computing controlled invariant sets