Inclusion dynamics hybrid automata

  • Authors:

  • Alberto Casagrande;Carla Piazza;Alberto Policriti;Bud Mishra

  • Affiliations:

  • DIMI, Università di Udine, Via delle Scienze, 206, 33100 Udine, Italy and DISA, Università di Udine, Via delle Scienze, 208, 33100 Udine, Italy and Istituto di Genomica Applicata, Via J. ...;DIMI, Università di Udine, Via delle Scienze, 206, 33100 Udine, Italy;DIMI, Università di Udine, Via delle Scienze, 206, 33100 Udine, Italy and Istituto di Genomica Applicata, Via J.Linussio, 51, 33100 Udine, Italy;Courant Institute of Mathematical Sciences, NYU, New York, NY, USA and NYU School of Medicine, 550 First Avenue, New York, NY 10016, USA

  • Venue:
  • Information and Computation
  • Year:
  • 2008

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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 formulaeover 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 formulaeover 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.