337 research outputs found
Revisiting Reachability in Timed Automata
We revisit a fundamental result in real-time verification, namely that the
binary reachability relation between configurations of a given timed automaton
is definable in linear arithmetic over the integers and reals. In this paper we
give a new and simpler proof of this result, building on the well-known
reachability analysis of timed automata involving difference bound matrices.
Using this new proof, we give an exponential-space procedure for model checking
the reachability fragment of the logic parametric TCTL. Finally we show that
the latter problem is NEXPTIME-hard
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
Revisiting Robustness in Priced Timed Games
Priced timed games are optimal-cost reachability games played between two
players---the controller and the environment---by moving a token along the
edges of infinite graphs of configurations of priced timed automata. The goal
of the controller is to reach a given set of target locations as cheaply as
possible, while the goal of the environment is the opposite. Priced timed games
are known to be undecidable for timed automata with or more clocks, while
they are known to be decidable for automata with clock.
In an attempt to recover decidability for priced timed games Bouyer, Markey,
and Sankur studied robust priced timed games where the environment has the
power to slightly perturb delays proposed by the controller. Unfortunately,
however, they showed that the natural problem of deciding the existence of
optimal limit-strategy---optimal strategy of the controller where the
perturbations tend to vanish in the limit---is undecidable with or more
clocks. In this paper we revisit this problem and improve our understanding of
the decidability of these games. We show that the limit-strategy problem is
already undecidable for a subclass of robust priced timed games with or
more clocks. On a positive side, we show the decidability of the existence of
almost optimal strategies for the same subclass of one-clock robust priced
timed games by adapting a classical construction by Bouyer at al. for one-clock
priced timed games
Model checking embedded system designs
We survey the basic principles behind the application of model checking to controller verification and synthesis. A promising development is the area of guided model checking, in which the state space search strategy of the model checking algorithm can be influenced to visit more interesting sets of states first. In particular, we discuss how model checking can be combined with heuristic cost functions to guide search strategies. Finally, we list a number of current research developments, especially in the area of reachability analysis for optimal control and related issues
Fast algorithms for handling diagonal constraints in timed automata
A popular method for solving reachability in timed automata proceeds by
enumerating reachable sets of valuations represented as zones. A na\"ive
enumeration of zones does not terminate. Various termination mechanisms have
been studied over the years. Coming up with efficient termination mechanisms
has been remarkably more challenging when the automaton has diagonal
constraints in guards.
In this paper, we propose a new termination mechanism for timed automata with
diagonal constraints based on a new simulation relation between zones.
Experiments with an implementation of this simulation show significant gains
over existing methods.Comment: Shorter version of this article to appear in CAV 201
Revisiting Local Time Semantics for Networks of Timed Automata
We investigate a zone based approach for the reachability problem in timed automata. The challenge is to alleviate the size explosion of the search space when considering networks of timed automata working in parallel. In the timed setting this explosion is particularly visible as even different interleavings of local actions of processes may lead to different zones. Salah et al. in 2006 have shown that the union of all these different zones is also a zone. This observation was used in an algorithm which from time to time detects and aggregates these zones into a single zone.
We show that such aggregated zones can be calculated more efficiently using the local time semantics and the related notion of local zones proposed by Bengtsson et al. in 1998. Next, we point out a flaw in the existing method to ensure termination of the local zone graph computation. We fix this with a new algorithm that builds the local zone graph and uses abstraction techniques over (standard) zones for termination. We evaluate our algorithm on standard examples. On various examples, we observe an order of magnitude decrease in the search space. On the other examples, the algorithm performs like the standard zone algorithm
Revisiting Synthesis for One-Counter Automata
We study the (parameter) synthesis problem for one-counter automata with
parameters. One-counter automata are obtained by extending classical
finite-state automata with a counter whose value can range over non-negative
integers and be tested for zero. The updates and tests applicable to the
counter can further be made parametric by introducing a set of integer-valued
variables called parameters. The synthesis problem for such automata asks
whether there exists a valuation of the parameters such that all infinite runs
of the automaton satisfy some omega-regular property. Lechner showed that (the
complement of) the problem can be encoded in a restricted one-alternation
fragment of Presburger arithmetic with divisibility. In this work (i) we argue
that said fragment, called AERPADPLUS, is unfortunately undecidable.
Nevertheless, by a careful re-encoding of the problem into a decidable
restriction of AERPADPLUS, (ii) we prove that the synthesis problem is
decidable in general and in N2EXP for several fixed omega-regular properties.
Finally, (iii) we give a polynomial-space algorithm for the special case of the
problem where parameters can only be used in tests, and not updates, of the
counter
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