Inclusion dynamics hybrid automata

Abstract

Hybrid systems are dynamical systems with the ability to describe mixed discrete-continuous evolution of a wide range of systems. Consequently, at first glance, hybrid systems appear powerful but recalcitrant, neither yielding to analysis and reasoning through a purely continuous-time modeling as with systems of differential equations, nor open to inferential processes commonly used for discrete state-transition systems such as finite state automata. A convenient and popular model, called hybrid automata, was introduced to model them and has spurred much interest on its tractability as a tool for inference and model checking in a general setting. Intuitively, a hybrid automaton is simply a "finite-state" automaton with each state augmented by continuous variables, which evolve according to a set of well-defined continuous laws, each specified separately for each state. This article investigates both the notion of hybrid automaton and the model checking problem over such a structure. In particular, it relates first-order theories and analysis results on multivalued maps and reduces the bounded reachability problem for hybrid automata whose continuous laws are expressed by inclusions (x ′ ∈ f (x, t)) to a decidability problem for first-order formulæ over the reals. Furthermore, the paper introduces a class of hybrid automata for which the reachability problem can be decided and shows that the problem of deciding whether a hybrid automaton belongs to this class can be again decided using first-order formulæ over the reals. Despite the fact that the bisimulation quotient for this class of hybrid automata can be infinite, we show that our techniques permit effective model checking for a nontrivial fragment of CTL. © 2008 Elsevier Inc. All rights reserved

ϵ-Semantics computations on biological systems

“…Differently from [12], we require that Dyn (v) p, q, 0 implies p = q. Intuitively, this means that if we are in p at time 0, we can reach a point different from p through a continuous dynamic only if we let the time flow.…”

“…Intuitively, this means that if we are in p at time 0, we can reach a point different from p through a continuous dynamic only if we let the time flow. This assumption will allow us to both get continuity of the flow at time 0 and slightly simplify the reachability formulae with respect to the ones defined in [12].…”

“…However, there exist non functional automata for which this is not the case. Hybrid automata in Michael's form [12] generalize functional automata still admitting a reduction of the continuous reachability problem over them to a satisfiability problem. On the one hand, they allow to express dynamics involving unknown parameters, which may be useful in many practical applications (e.g., systems biology).…”

Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology

“…In Casagrande et al (2005bCasagrande et al ( , 2008, we introduced the Semi-Algebraic Constant reset Hybrid Automata (SACoRe), which extended o-minimal automata over the reals, in the case of flows obtained from nonautonomous systems of differential inclusions. SACoRe automata were shown to admit decision procedures for reachability and model checking for a limited fragment of CTL, which they achieved by combining Tarski's decidability result over the reals with Michael's selection theorem.…”

“…A few remarks are in order, especially in the context of classes of automata that my research group introduced in Casagrande et al (2005aCasagrande et al ( ,b, 2008 in its effort to discover the right formalisms to take us beyond the linear hybrid systems. These, unlike many of the earlier generalizations, do not admit finite bisimulation quotients (a default approach of attack in this area).…”