1,626 research outputs found
Game theoretic controller synthesis for multi-robot motion planning Part I : Trajectory based algorithms
We consider a class of multi-robot motion planning problems where each robot
is associated with multiple objectives and decoupled task specifications. The
problems are formulated as an open-loop non-cooperative differential game. A
distributed anytime algorithm is proposed to compute a Nash equilibrium of the
game. The following properties are proven: (i) the algorithm asymptotically
converges to the set of Nash equilibrium; (ii) for scalar cost functionals, the
price of stability equals one; (iii) for the worst case, the computational
complexity and communication cost are linear in the robot number
From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity
The equivalence of finite automata and regular expressions dates back to the
seminal paper of Kleene on events in nerve nets and finite automata from 1956.
In the present paper we tour a fragment of the literature and summarize results
on upper and lower bounds on the conversion of finite automata to regular
expressions and vice versa. We also briefly recall the known bounds for the
removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free
nondeterministic devices. Moreover, we report on recent results on the average
case descriptional complexity bounds for the conversion of regular expressions
to finite automata and brand new developments on the state elimination
algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527
Sparse Positional Strategies for Safety Games
We consider the problem of obtaining sparse positional strategies for safety
games. Such games are a commonly used model in many formal methods, as they
make the interaction of a system with its environment explicit. Often, a
winning strategy for one of the players is used as a certificate or as an
artefact for further processing in the application. Small such certificates,
i.e., strategies that can be written down very compactly, are typically
preferred. For safety games, we only need to consider positional strategies.
These map game positions of a player onto a move that is to be taken by the
player whenever the play enters that position. For representing positional
strategies compactly, a common goal is to minimize the number of positions for
which a winning player's move needs to be defined such that the game is still
won by the same player, without visiting a position with an undefined next
move. We call winning strategies in which the next move is defined for few of
the player's positions sparse.
Unfortunately, even roughly approximating the density of the sparsest
strategy for a safety game has been shown to be NP-hard. Thus, to obtain sparse
strategies in practice, one either has to apply some heuristics, or use some
exhaustive search technique, like ILP (integer linear programming) solving. In
this paper, we perform a comparative study of currently available methods to
obtain sparse winning strategies for the safety player in safety games. We
consider techniques from common knowledge, such as using ILP or SAT
(satisfiability) solving, and a novel technique based on iterative linear
programming. The results of this paper tell us if current techniques are
already scalable enough for practical use.Comment: In Proceedings SYNT 2012, arXiv:1207.055
DecSerFlow: Towards a Truly Declarative Service Flow Language
The need for process support in the context of web services
has triggered the development of many languages, systems, and standards.
Industry has been developing software solutions and proposing
standards such as BPEL, while researchers have been advocating the
use of formal methods such as Petri nets and pi-calculus. The languages
developed for service flows, i.e., process specification languages for web
services, have adopted many concepts from classical workflow management
systems. As a result, these languages are rather procedural and
this does not fit well with the autonomous nature of services. Therefore,
we propose DecSerFlow as a Declarative Service Flow Language. DecSerFlow
can be used to specify, enact, and monitor service flows. The
language is extendible (i.e., constructs can be added without changing
the engine or semantical basis) and can be used to enforce or to check the
conformance of service flows. Although the language has an appealing
graphical representation, it is grounded in temporal logic
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