511 research outputs found
Revisiting Underapproximate Reachability for Multipushdown Systems
Boolean programs with multiple recursive threads can be captured as pushdown
automata with multiple stacks. This model is Turing complete, and hence, one is
often interested in analyzing a restricted class that still captures useful
behaviors. In this paper, we propose a new class of bounded under
approximations for multi-pushdown systems, which subsumes most existing
classes. We develop an efficient algorithm for solving the under-approximate
reachability problem, which is based on efficient fix-point computations. We
implement it in our tool BHIM and illustrate its applicability by generating a
set of relevant benchmarks and examining its performance. As an additional
takeaway, BHIM solves the binary reachability problem in pushdown automata. To
show the versatility of our approach, we then extend our algorithm to the timed
setting and provide the first implementation that can handle timed
multi-pushdown automata with closed guards.Comment: 52 pages, Conference TACAS 202
A Theory of Sampling for Continuous-time Metric Temporal Logic
This paper revisits the classical notion of sampling in the setting of
real-time temporal logics for the modeling and analysis of systems. The
relationship between the satisfiability of Metric Temporal Logic (MTL) formulas
over continuous-time models and over discrete-time models is studied. It is
shown to what extent discrete-time sequences obtained by sampling
continuous-time signals capture the semantics of MTL formulas over the two time
domains. The main results apply to "flat" formulas that do not nest temporal
operators and can be applied to the problem of reducing the verification
problem for MTL over continuous-time models to the same problem over
discrete-time, resulting in an automated partial practically-efficient
discretization technique.Comment: Revised version, 43 pages
Permissive strategies in timed automata and games
Timed automata are a convenient framework for modelling and reasoning about real-time systems. While these models are now well-understood, they do not offer a convenient way of taking timing imprecisions into account. Several solutions (e.g. parametric guard enlargement) have been proposed over the last ten years to take such imprecisions into account. In this paper, we propose a novel approach for handling robust reachability, based on permissive strategies. While classical strategies propose to play an action at an exact point in time, permissive strategies consider intervals of possible dates when to play the selected action. In other words, the controller specifies an interval of time delays for actions to be executed in a more flexible way. With such a permissive strategy, we associate a penalty, which is the inverse of the length of the proposed interval, and accumulates along the run. We show that in that setting, optimal strategies can be computed in polynomial time for one-clock timed automata
Simple Priced Timed Games Are Not That Simple
Priced timed games are two-player zero-sum games played on priced timed
automata (whose locations and transitions are labeled by weights modeling the
costs of spending time in a state and executing an action, respectively). The
goals of the players are to minimise and maximise the cost to reach a target
location, respectively. We consider priced timed games with one clock and
arbitrary (positive and negative) weights and show that, for an important
subclass of theirs (the so-called simple priced timed games), one can compute,
in exponential time, the optimal values that the players can achieve, with
their associated optimal strategies. As side results, we also show that
one-clock priced timed games are determined and that we can use our result on
simple priced timed games to solve the more general class of so-called
reset-acyclic priced timed games (with arbitrary weights and one-clock)
Path Checking for MTL and TPTL over Data Words
Metric temporal logic (MTL) and timed propositional temporal logic (TPTL) are
quantitative extensions of linear temporal logic, which are prominent and
widely used in the verification of real-timed systems. It was recently shown
that the path checking problem for MTL, when evaluated over finite timed words,
is in the parallel complexity class NC. In this paper, we derive precise
complexity results for the path-checking problem for MTL and TPTL when
evaluated over infinite data words over the non-negative integers. Such words
may be seen as the behaviours of one-counter machines. For this setting, we
give a complete analysis of the complexity of the path-checking problem
depending on the number of register variables and the encoding of constraint
numbers (unary or binary). As the two main results, we prove that the
path-checking problem for MTL is P-complete, whereas the path-checking problem
for TPTL is PSPACE-complete. The results yield the precise complexity of model
checking deterministic one-counter machines against formulae of MTL and TPTL
Platform-Specific Code Generation from Platform-Independent Timed Models
Many safety-critical real-time embedded systems need to meet stringent timing constraints such as preserving delay bounds between input and output events. In model-based development, a system is often implemented by using a code generator to automatically generate source code from system models, and integrating the generated source code with a platform. It is challenging to guarantee that the implemented systems preserve required timing constraints, because the timed behavior of the source code and the platform is closely intertwined. In this paper, we address this challenge by proposing a model transformation approach for the code generation. Our approach compensates the platform-processing delays by adjusting the timing parameters in system models, based on an Integer Linear Programming problem formulation. We demonstrate the usefulness of our approach via a case study of infusion pump systems. Experimental results show that the code generated using our approach can better preserve the timing constraints
Safe Neighborhood Computation for Hybrid System Verification
For the design and implementation of engineering systems, performing
model-based analysis can disclose potential safety issues at an early stage.
The analysis of hybrid system models is in general difficult due to the
intrinsic complexity of hybrid dynamics. In this paper, a simulation-based
approach to formal verification of hybrid systems is presented.Comment: In Proceedings HAS 2014, arXiv:1501.0540
Timed Basic Parallel Processes
Timed basic parallel processes (TBPP) extend communication-free Petri nets (aka. BPP or commutative context-free grammars) by a global notion of time. TBPP can be seen as an extension of timed automata (TA) with context-free branching rules, and as such may be used to model networks of independent timed automata with process creation. We show that the coverability and reachability problems (with unary encoded target multiplicities) are PSPACE-complete and EXPTIME-complete, respectively. For the special case of 1-clock TBPP, both are NP-complete and hence not more complex than for untimed BPP. This contrasts with known super-Ackermannian-completeness and undecidability results for general timed Petri nets. As a result of independent interest, and basis for our NP upper bounds, we show that the reachability relation of 1-clock TA can be expressed by a formula of polynomial size in the existential fragment of linear arithmetic, which improves on recent results from the literature
Optimal Control for Multi-mode Systems with Discrete Costs
This paper studies optimal time-bounded control in multi-mode systems with
discrete costs. Multi-mode systems are an important subclass of linear hybrid
systems, in which there are no guards on transitions and all invariants are
global. Each state has a continuous cost attached to it, which is linear in the
sojourn time, while a discrete cost is attached to each transition taken. We
show that an optimal control for this model can be computed in NEXPTIME and
approximated in PSPACE. We also show that the one-dimensional case is simpler:
although the problem is NP-complete (and in LOGSPACE for an infinite time
horizon), we develop an FPTAS for finding an approximate solution.Comment: extended version of a FORMATS 2017 pape
Verification and Parameter Synthesis for Real-Time Programs using Refinement of Trace Abstraction
We address the safety verification and synthesis problems for real-time
systems. We introduce real-time programs that are made of instructions that can
perform assignments to discrete and real-valued variables. They are general
enough to capture interesting classes of timed systems such as timed automata,
stopwatch automata, time(d) Petri nets and hybrid automata.
We propose a semi-algorithm using refinement of trace abstractions to solve
both the reachability verification problem and the parameter synthesis problem
for real-time programs.
All of the algorithms proposed have been implemented and we have conducted a
series of experiments, comparing the performance of our new approach to
state-of-the-art tools in classical reachability, robustness analysis and
parameter synthesis for timed systems. We show that our new method provides
solutions to problems which are unsolvable by the current state-of-the-art
tools
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