2,698 research outputs found
Generalized Property-Directed Reachability for Hybrid Systems
Generalized property-directed reachability (GPDR) belongs to the family of
the model-checking techniques called IC3/PDR. It has been successfully applied
to software verification; for example, it is the core of Spacer, a
state-of-the-art Horn-clause solver bundled with Z3. However, it has yet to be
applied to hybrid systems, which involve a continuous evolution of values over
time. As the first step towards GPDR- based model checking for hybrid systems,
this paper formalizes HGPDR, an adaptation of GPDR to hybrid systems, and
proves its soundness. We also implemented a semi-automated proof-of-concept
verifier, which allows a user to provide hints to guide verification steps.Comment: To appear in VMCAI 202
PrIC3: Property Directed Reachability for MDPs
IC3 has been a leap forward in symbolic model checking. This paper proposes
PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic
model checking of MDPs. Our main focus is to develop the theory underlying
PrIC3. Alongside, we present a first implementation of PrIC3 including the key
ingredients from IC3 such as generalization, repushing, and propagation
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
Synthesis of Switching Protocols from Temporal Logic Specifications
We propose formal means for synthesizing switching protocols that determine the sequence in which the modes of a switched system are activated to satisfy certain high-level specifications in linear temporal logic. The synthesized protocols are robust against exogenous disturbances on the continuous dynamics. Two types of finite transition systems, namely under- and over-approximations, that abstract the behavior of the underlying continuous dynamics are defined. In particular, we show that the discrete synthesis problem for an under-approximation can be formulated as a model checking problem, whereas that for an over-approximation can be transformed into a two-player game. Both of these formulations are amenable to efficient, off-the-shelf software tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the nonlinear switched system. Moreover, the proposed framework can be straightforwardly extended to accommodate specifications that require reacting to possibly adversarial external events. Finally, these results are illustrated using three examples from different application domains
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications
Cellular automata (CAs) are dynamical systems which exhibit complex global
behavior from simple local interaction and computation. Since the inception of
cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention
of several researchers over various backgrounds and fields for modelling
different physical, natural as well as real-life phenomena. Classically, CAs
are uniform. However, non-uniformity has also been introduced in update
pattern, lattice structure, neighborhood dependency and local rule. In this
survey, we tour to the various types of CAs introduced till date, the different
characterization tools, the global behaviors of CAs, like universality,
reversibility, dynamics etc. Special attention is given to non-uniformity in
CAs and especially to non-uniform elementary CAs, which have been very useful
in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin
Towards Cancer Hybrid Automata
This paper introduces Cancer Hybrid Automata (CHAs), a formalism to model the
progression of cancers through discrete phenotypes. The classification of
cancer progression using discrete states like stages and hallmarks has become
common in the biology literature, but primarily as an organizing principle, and
not as an executable formalism. The precise computational model developed here
aims to exploit this untapped potential, namely, through automatic verification
of progression models (e.g., consistency, causal connections, etc.),
classification of unreachable or unstable states and computer-generated
(individualized or universal) therapy plans. The paper builds on a
phenomenological approach, and as such does not need to assume a model for the
biochemistry of the underlying natural progression. Rather, it abstractly
models transition timings between states as well as the effects of drugs and
clinical tests, and thus allows formalization of temporal statements about the
progression as well as notions of timed therapies. The model proposed here is
ultimately based on hybrid automata, and we show how existing controller
synthesis algorithms can be generalized to CHA models, so that therapies can be
generated automatically. Throughout this paper we use cancer hallmarks to
represent the discrete states through which cancer progresses, but other
notions of discretely or continuously varying state formalisms could also be
used to derive similar therapies.Comment: In Proceedings HSB 2012, arXiv:1208.315
Triggered Clause Pushing for IC3
We propose an improvement of the famous IC3 algorithm for model checking
safety properties of finite state systems. We collect models computed by the
SAT-solver during the clause propagation phase of the algorithm and use them as
witnesses for why the respective clauses could not be pushed forward. It only
makes sense to recheck a particular clause for pushing when its witnessing
model falsifies a newly added clause. Since this trigger test is both
computationally cheap and sufficiently precise, we can afford to keep clauses
pushed as far as possible at all times. Experiments indicate that this strategy
considerably improves IC3's performance.Comment: 4 page
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