79 research outputs found
Does Church-Turing thesis apply outside computer science?
We analyze whether Church-Turing thesis can be applied to mathematical and physical systems. We find the factors that allow to a class of systems to reach a Turing or a super-Turing computational power. We illustrate our general statements by some more concrete theorems on hybrid and stochastic systems
Simple Algorithm for Simple Timed Games
version 1.1We propose a subclass of timed game automata (TGA), called Task TGA, representing networks of communicating tasks where the system can choose when to start the task and the environment can choose the duration of the task. We search to solve finite-horizon reachability games on Task TGA by building strategies in the form of Simple Temporal Networks with Uncertainty (STNU). Such strategies have the advantage of being very succinct due to the partial order reduction of independent tasks. We show that the existence of such strategies is an NP-complete problem. A practical consequence of this result is a fully forward algorithm for building STNU strategies. Potential applications of this work are planning and scheduling under temporal uncertainty
Entropy Games and Matrix Multiplication Games
Two intimately related new classes of games are introduced and studied:
entropy games (EGs) and matrix multiplication games (MMGs). An EG is played on
a finite arena by two-and-a-half players: Despot, Tribune and the
non-deterministic People. Despot wants to make the set of possible People's
behaviors as small as possible, while Tribune wants to make it as large as
possible.An MMG is played by two players that alternately write matrices from
some predefined finite sets. One wants to maximize the growth rate of the
product, and the other to minimize it. We show that in general MMGs are
undecidable in quite a strong sense.On the positive side, EGs correspond to a
subclass of MMGs, and we prove that such MMGs and EGs are determined, and that
the optimal strategies are simple. The complexity of solving such games is in
NP\&coNP.Comment: Accepted to STACS 201
SPeeDI - a verification tool for polygonal hybrid systems
Hybrid systems combining discrete and continuous dynamics arise as mathematical models of various artificial and natural systems, and as an approximation to
complex continuous systems. A very important problem in the analysis of the behavior of hybrid systems is reachability. It is well-known that for most non-trivial
subclasses of hybrid systems this and all interesting verification problems are undecidable. Most of the proved decidability results rely on stringent hypothesis
that lead to the existence of a finite and computable partition of the state space
into classes of states which are equivalent with respect to reachability. This is
the case for classes of rectangular automata [1] and hybrid automata with linear
vector fields [2]. Most implemented computational procedures resort to (forward
or backward) propagation of constraints, typically (unions of convex) polyhedra
or ellipsoids [3, 4, 5]. In general, these techniques provide semi-decision procedures, that is, if the given final set of states is reachable, they will terminate,
otherwise they may fail to. Maybe the major drawback of set-propagation, reachset approximation procedures is that they pay little attention to the geometric
properties of the specific (class of) systems under analysis.peer-reviewe
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