5,154 research outputs found
Improving search order for reachability testing in timed automata
Standard algorithms for reachability analysis of timed automata are sensitive
to the order in which the transitions of the automata are taken. To tackle this
problem, we propose a ranking system and a waiting strategy. This paper
discusses the reason why the search order matters and shows how a ranking
system and a waiting strategy can be integrated into the standard reachability
algorithm to alleviate and prevent the problem respectively. Experiments show
that the combination of the two approaches gives optimal search order on
standard benchmarks except for one example. This suggests that it should be
used instead of the standard BFS algorithm for reachability analysis of timed
automata
Setting port numbers for fast graph exploration
International audienceWe consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of arbitrary size and arbitrary maximum degree. In anonymous graphs, nodes are not labeled but edges are labeled in a local manner (called {\em local orientation}) so that the automaton is able to distinguish them. Precisely, the edges incident to a node are given port numbers from to , where is the degree of~. Periodic graph exploration means visiting every node infinitely often. We are interested in the length of the period, i.e., the maximum number of edge traversals between two consecutive visits of any node by the automaton in the same state and entering the node by the same port. This problem is unsolvable if local orientations are set arbitrarily. Given this impossibility result, we address the following problem: what is the mimimum function such that there exist an algorithm for setting the local orientation, and a finite automaton using it, such that the automaton explores all graphs of size within the period ? The best result so far is the upper bound , by Dobrev et al. [SIROCCO 2005], using an automaton with no memory (i.e. only one state). In this paper we prove a better upper bound . Our automaton uses three states but performs periodic exploration independently of its starting position and initial state
Exploring an Infinite Space with Finite Memory Scouts
Consider a small number of scouts exploring the infinite -dimensional grid
with the aim of hitting a hidden target point. Each scout is controlled by a
probabilistic finite automaton that determines its movement (to a neighboring
grid point) based on its current state. The scouts, that operate under a fully
synchronous schedule, communicate with each other (in a way that affects their
respective states) when they share the same grid point and operate
independently otherwise. Our main research question is: How many scouts are
required to guarantee that the target admits a finite mean hitting time?
Recently, it was shown that is an upper bound on the answer to this
question for any dimension and the main contribution of this paper
comes in the form of proving that this bound is tight for .Comment: Added (forgotten) acknowledgement
Verification of Timed Automata Using Rewrite Rules and Strategies
ELAN is a powerful language and environment for specifying and prototyping
deduction systems in a language based on rewrite rules controlled by
strategies. Timed automata is a class of continuous real-time models of
reactive systems for which efficient model-checking algorithms have been
devised. In this paper, we show that these algorithms can very easily be
prototyped in the ELAN system. This paper argues through this example that
rewriting based systems relying on rules and strategies are a good framework to
prototype, study and test rather efficiently symbolic model-checking
algorithms, i.e. algorithms which involve combination of graph exploration
rules, deduction rules, constraint solving techniques and decision procedures
Better abstractions for timed automata
We consider the reachability problem for timed automata. A standard solution
to this problem involves computing a search tree whose nodes are abstractions
of zones. These abstractions preserve underlying simulation relations on the
state space of the automaton. For both effectiveness and efficiency reasons,
they are parametrized by the maximal lower and upper bounds (LU-bounds)
occurring in the guards of the automaton. We consider the aLU abstraction
defined by Behrmann et al. Since this abstraction can potentially yield
non-convex sets, it has not been used in implementations. We prove that aLU
abstraction is the biggest abstraction with respect to LU-bounds that is sound
and complete for reachability. We also provide an efficient technique to use
the aLU abstraction to solve the reachability problem.Comment: Extended version of LICS 2012 paper (conference paper till v6). in
Information and Computation, available online 27 July 201
Using non-convex approximations for efficient analysis of timed automata
The reachability problem for timed automata asks if there exists a path from
an initial state to a target state. The standard solution to this problem
involves computing the zone graph of the automaton, which in principle could be
infinite. In order to make the graph finite, zones are approximated using an
extrapolation operator. For reasons of efficiency in current algorithms
extrapolation of a zone is always a zone and in particular it is convex.
In this paper, we propose to solve the reachability problem without such
extrapolation operators. To ensure termination, we provide an efficient
algorithm to check if a zone is included in the so called region closure of
another. Although theoretically better, closure cannot be used in the standard
algorithm since a closure of a zone may not be convex.
An additional benefit of the proposed approach is that it permits to
calculate approximating parameters on-the-fly during exploration of the zone
graph, as opposed to the current methods which do it by a static analysis of
the automaton prior to the exploration. This allows for further improvements in
the algorithm. Promising experimental results are presented.Comment: Extended version of FSTTCS 2011 pape
Building a Nest by an Automaton
A robot modeled as a deterministic finite automaton has to build a structure from material available to it. The robot navigates in the infinite oriented grid Z x Z. Some cells of the grid are full (contain a brick) and others are empty. The subgraph of the grid induced by full cells, called the field, is initially connected. The (Manhattan) distance between the farthest cells of the field is called its span. The robot starts at a full cell. It can carry at most one brick at a time. At each step it can pick a brick from a full cell, move to an adjacent cell and drop a brick at an empty cell. The aim of the robot is to construct the most compact possible structure composed of all bricks, i.e., a nest. That is, the robot has to move all bricks in such a way that the span of the resulting field be the smallest.
Our main result is the design of a deterministic finite automaton that accomplishes this task and subsequently stops, for every initially connected field, in time O(sz), where s is the span of the initial field and z is the number of bricks. We show that this complexity is optimal
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