Search results for "Reachability"
showing 7 items of 17 documents
Deciding reachability for planar multi-polynomial systems
1996
In this paper we investigate the decidability of the reachability problem for planar non-linear hybrid systems. A planar hybrid system has the property that its state space corresponds to the standard Euclidean plane, which is partitioned into a finite number of (polyhedral) regions. To each of these regions is assigned some vector field which governs the dynamical behaviour of the system within this region. We prove the decidability of point to point and region to region reachability problems for planar hybrid systems for the case when trajectories within the regions can be described by polynomials of arbitrary degree.
Verification of scope-dependent hierarchical state machines
2008
AbstractA hierarchical state machine (Hsm) is a finite state machine where a vertex can either expand to another hierarchical state machine (box) or be a basic vertex (node). Each node is labeled with atomic propositions. We study an extension of such model which allows atomic propositions to label also boxes (Shsm). We show that Shsms can be exponentially more succinct than Shsms and verification is in general harder by an exponential factor. We carefully establish the computational complexity of reachability, cycle detection, and model checking against general Ltl and Ctl specifications. We also discuss some natural and interesting restrictions of the considered problems for which we can …
Varieties and Covarieties of Languages (Extended Abstract)
2013
AbstractBecause of the isomorphism (X×A)→X≅X→(A→X), the transition structure of a deterministic automaton with state set X and with inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. This algebra-coalgebra duality goes back to Arbib and Manes, who formulated it as a duality between reachability and observability, and is ultimately based on Kalmanʼs duality in systems theory between controllability and observability. Recently, it was used to give a new proof of Brzozowskiʼs minimization algorithm for deterministic automata. Here we will use the algebra-coalgebra duality of automata as a common perspective for the study of both varieties and covarieties, which are …
H∞ sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameters
2015
This paper is devoted to the investigation of H ∞ sliding mode control (SMC) for uncertain neutral stochastic systems with Markovian jumping parameters and time-varying delays. A sliding surface functional is firstly constructed. Then, the sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite-time interval. The sufficient conditions for asymptotically stochastic stability of sliding mode dynamics with a given disturbance attenuation level are presented in terms of linear matrix inequalities (LMIs). Finally, an example is provided to illustrate the efficiency of the proposed method.
Modular Strategies for Recursive Game Graphs
2006
AbstractMany problems in formal verification and program analysis can be formalized as computing winning strategies for two-player games on graphs. In this paper, we focus on solving games in recursive game graphs which can model the control flow in sequential programs with recursive procedure calls. While such games can be viewed as the pushdown games studied in the literature, the natural notion of winning in our framework requires the strategies to be modular with only local memory; that is, resolution of choices within a module does not depend on the context in which the module is invoked, but only on the history within the current invocation of the module. While reachability in (global…
Decidability of bisimulation equivalences for parallel timer processes
1993
In this paper an abstract model of parallel timer processes (PTPs), allowing specification of temporal quantitative constraints on the behaviour of real time systems, is introduced. The parallel timer processes are defined in a dense time domain and are able to model both concurrent (with delay intervals overlapping on the time axis) and infinite behaviour. Both the strong and weak (abstracted from internal actions) bisimulation equivalence problems for PTPs are proved decidable. It is proved also that, if one provides the PTP model additionally with memory cells for moving timer value information along the time axis, the bisimulation equivalence (and even the vertex reachability) problems …
Finite automata on timed ω-trees
2003
AbstractIn the last decade Alur and Dill introduced a model of automata on timed ω-sequences which extends the traditional models of finite automata. In this paper, we present a theory of timed ω-trees which extends both the theory of timed ω-sequences and the theory of ω-trees. The main motivation is to introduce a new way of specifying real-time systems and provide tools for studying decidability problems in related fields. We focus on the decision problems and their applications in system verification and synthesis.