A theory of robust omega-regular software synthesis

Abstract

A key property for systems subject to uncertainty in their operating environment is robustness: ensuring that unmodeled but bounded disturbances have only a proportionally bounded effect upon the behaviors of the system. Inspired by ideas from robust control and dissipative systems theory, we present a formal definition of robustness as well as algorithmic tools for the design of optimally robust controllers for ω-regular properties on discrete transition systems. Formally, we define metric automata-automata equipped with a metric on states-and strategies on metric automata which guarantee robustness for ω-regular properties. We present fixed-point algorithms to construct optimally robust strategies in polynomial time. In contrast to strategies computed by classical graph theoretic approaches, the strategies computed by our algorithm ensure that the behaviors of the controlled system gracefully degrade under the action of disturbances; the degree of degradation is parameterized by the magnitude of the disturbance. We show an application of our theory to the design of controllers that tolerate infinitely many transient errors provided they occur infrequently enough.

A Small Gain Theorem for Parametric Assume-Guarantee Contracts

“…Smallgain conditions are leveraged by Rungger et al [21] for com-positional construction of approximate discrete abstractions of continuous systems and Dallal et al [6] to design customized compositional abstractions for a persistency specification. Majumdar et al [16] argue that graceful degradation in performance in the presence of errors is a desirable property to enforce in systems. Bloem et al [4] advocate for objectives with quantitative measures of "goodness" to distinguish between control strategies that both satisfy a Boolean specification.…”

Robustness Analysis of Finite Precision Implementations

“…Robustness has also been discussed in the context of synthesis and validation of control systems, in [19,24]. The formalization is based on automata theoretic methods, providing a convenient definition of a metric between Büchi automata.…”

Robustness Analysis of String Transducers

“…Also, unlike our distance metrics, their distances are measured using cost functions that map each string to a nonnegative integer. In [16,3,1], the authors develop different notions of robustness for reactive systems, with ω-regular specifications, interacting with uncertain environments. In [7], the authors present a polynomial-time algorithm to decide robustness of sequential circuits modeled as Mealy machines, w.r.t.…”