31 research outputs found
CHARDA: Causal Hybrid Automata Recovery via Dynamic Analysis
We propose and evaluate a new technique for learning hybrid automata
automatically by observing the runtime behavior of a dynamical system. Working
from a sequence of continuous state values and predicates about the
environment, CHARDA recovers the distinct dynamic modes, learns a model for
each mode from a given set of templates, and postulates causal guard conditions
which trigger transitions between modes. Our main contribution is the use of
information-theoretic measures (1)~as a cost function for data segmentation and
model selection to penalize over-fitting and (2)~to determine the likely causes
of each transition. CHARDA is easily extended with different classes of model
templates, fitting methods, or predicates. In our experiments on a complex
videogame character, CHARDA successfully discovers a reasonable
over-approximation of the character's true behaviors. Our results also compare
favorably against recent work in automatically learning probabilistic timed
automata in an aircraft domain: CHARDA exactly learns the modes of these
simpler automata.Comment: 7 pages, 2 figures. Accepted for IJCAI 201
Analysis of Non-Linear Probabilistic Hybrid Systems
This paper shows how to compute, for probabilistic hybrid systems, the clock
approximation and linear phase-portrait approximation that have been proposed
for non probabilistic processes by Henzinger et al. The techniques permit to
define a rectangular probabilistic process from a non rectangular one, hence
allowing the model-checking of any class of systems. Clock approximation, which
applies under some restrictions, aims at replacing a non rectangular variable
by a clock variable. Linear phase-approximation applies without restriction and
yields an approximation that simulates the original process. The conditions
that we need for probabilistic processes are the same as those for the classic
case.Comment: In Proceedings QAPL 2011, arXiv:1107.074
Approximate probabilistic verification of hybrid systems
Hybrid systems whose mode dynamics are governed by non-linear ordinary
differential equations (ODEs) are often a natural model for biological
processes. However such models are difficult to analyze. To address this, we
develop a probabilistic analysis method by approximating the mode transitions
as stochastic events. We assume that the probability of making a mode
transition is proportional to the measure of the set of pairs of time points
and value states at which the mode transition is enabled. To ensure a sound
mathematical basis, we impose a natural continuity property on the non-linear
ODEs. We also assume that the states of the system are observed at discrete
time points but that the mode transitions may take place at any time between
two successive discrete time points. This leads to a discrete time Markov chain
as a probabilistic approximation of the hybrid system. We then show that for
BLTL (bounded linear time temporal logic) specifications the hybrid system
meets a specification iff its Markov chain approximation meets the same
specification with probability . Based on this, we formulate a sequential
hypothesis testing procedure for verifying -approximately- that the Markov
chain meets a BLTL specification with high probability. Our case studies on
cardiac cell dynamics and the circadian rhythm indicate that our scheme can be
applied in a number of realistic settings
The Reach-Avoid Problem for Constant-Rate Multi-Mode Systems
A constant-rate multi-mode system is a hybrid system that can switch freely
among a finite set of modes, and whose dynamics is specified by a finite number
of real-valued variables with mode-dependent constant rates. Alur, Wojtczak,
and Trivedi have shown that reachability problems for constant-rate multi-mode
systems for open and convex safety sets can be solved in polynomial time. In
this paper, we study the reachability problem for non-convex state spaces and
show that this problem is in general undecidable. We recover decidability by
making certain assumptions about the safety set. We present a new algorithm to
solve this problem and compare its performance with the popular sampling based
algorithm rapidly-exploring random tree (RRT) as implemented in the Open Motion
Planning Library (OMPL).Comment: 26 page
Weak Singular Hybrid Automata
The framework of Hybrid automata, introduced by Alur, Courcourbetis,
Henzinger, and Ho, provides a formal modeling and analysis environment to
analyze the interaction between the discrete and the continuous parts of
cyber-physical systems. Hybrid automata can be considered as generalizations of
finite state automata augmented with a finite set of real-valued variables
whose dynamics in each state is governed by a system of ordinary differential
equations. Moreover, the discrete transitions of hybrid automata are guarded by
constraints over the values of these real-valued variables, and enable
discontinuous jumps in the evolution of these variables. Singular hybrid
automata are a subclass of hybrid automata where dynamics is specified by
state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed
that for even very restricted subclasses of singular hybrid automata, the
fundamental verification questions, like reachability and schedulability, are
undecidable. In this paper we present \emph{weak singular hybrid automata}
(WSHA), a previously unexplored subclass of singular hybrid automata, and show
the decidability (and the exact complexity) of various verification questions
for this class including reachability (NP-Complete) and LTL model-checking
(PSPACE-Complete). We further show that extending WSHA with a single
unrestricted clock or extending WSHA with unrestricted variable updates lead to
undecidability of reachability problem
Safe Schedulability of Bounded-Rate Multi-Mode Systems
Bounded-rate multi-mode systems (BMMS) are hybrid systems that can switch
freely among a finite set of modes, and whose dynamics is specified by a finite
number of real-valued variables with mode-dependent rates that can vary within
given bounded sets. The schedulability problem for BMMS is defined as an
infinite-round game between two players---the scheduler and the
environment---where in each round the scheduler proposes a time and a mode
while the environment chooses an allowable rate for that mode, and the state of
the system changes linearly in the direction of the rate vector. The goal of
the scheduler is to keep the state of the system within a pre-specified safe
set using a non-Zeno schedule, while the goal of the environment is the
opposite. Green scheduling under uncertainty is a paradigmatic example of BMMS
where a winning strategy of the scheduler corresponds to a robust
energy-optimal policy. We present an algorithm to decide whether the scheduler
has a winning strategy from an arbitrary starting state, and give an algorithm
to compute such a winning strategy, if it exists. We show that the
schedulability problem for BMMS is co-NP complete in general, but for two
variables it is in PTIME. We also study the discrete schedulability problem
where the environment has only finitely many choices of rate vectors in each
mode and the scheduler can make decisions only at multiples of a given clock
period, and show it to be EXPTIME-complete.Comment: Technical report for a paper presented at HSCC 201
Reasoning about transfinite sequences
We introduce a family of temporal logics to specify the behavior of systems
with Zeno behaviors. We extend linear-time temporal logic LTL to authorize
models admitting Zeno sequences of actions and quantitative temporal operators
indexed by ordinals replace the standard next-time and until future-time
operators. Our aim is to control such systems by designing controllers that
safely work on -sequences but interact synchronously with the system in
order to restrict their behaviors. We show that the satisfiability problem for
the logics working on -sequences is EXPSPACE-complete when the
integers are represented in binary, and PSPACE-complete with a unary
representation. To do so, we substantially extend standard results about LTL by
introducing a new class of succinct ordinal automata that can encode the
interaction between the different quantitative temporal operators.Comment: 38 page