Marcus Größer
Dresden University of Technology
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Publication
Featured researches published by Marcus Größer.
Lecture Notes in Computer Science | 2004
Frank Ciesinski; Marcus Größer
In this survey we motivate, define and explain model checking of probabilistic deterministic and nondeterministic systems using the probabilistic computation tree logics PCTL and PCTL *. Juxtapositions to non-deterministic computation tree logic are made and algorithms are presented.
foundations of software science and computation structure | 2008
Christel Baier; Nathalie Bertrand; Marcus Größer
Probabilistic Buchi automata (PBA) are finite-state acceptors for infinite words where all choices are resolved by fixed distributions and where the accepted language is defined by the requirement that the measure of the accepting runs is positive. The main contribution of this paper is a complementation operator for PBA and a discussion on several algorithmic problems for PBA. All interesting problems, such as checking emptiness or equivalence for PBA or checking whether a finite transition system satisfies a PBA-specification, turn out to be undecidable. An important consequence of these results are several undecidability results for stochastic games with incomplete information, modelled by partially-observable Markov decision processes and ω-regular winning objectives. Furthermore, we discuss an alternative semantics for PBA where it is required that almost all runs for an accepted word are accepting, which turns out to be less powerful, but has a decidable emptiness problem.
foundations of software technology and theoretical computer science | 2007
Christel Baier; Nathalie Bertrand; Patricia Bouyer; Thomas Brihaye; Marcus Größer
Like most models used in model-checking, timed automata are an idealized mathematical model used for representing systems with strong timing requirements. In such mathematical models, properties can be violated, due to unlikely (sequences of) events. We propose two new semantics for the satisfaction of LTL formulas, one based on probabilities, and the other one based on topology, to rule out these sequences. We prove that the two semantics are equivalent and lead to a PSPACE-Complete model-checking problem for LTL over finite executions.
Archive | 2009
Christel Baier; Marcus Größer; Frank Ciesinski
This chapter is about the verification of Markov decision processes (MDPs) which incorporate one of the fundamental models for reasoning about probabilistic and nondeterministic phenomena in reactive systems. MDPs have their roots in the field of operations research and are nowadays used in a wide variety of areas including verification, robotics, planning, controlling, reinforcement learning, economics and semantics of randomized systems. Furthermore, MDPs served as the basis for the introduction of probabilistic automata which are related to weighted automata. We describe the use of MDPs as an operational model for randomized systems, e.g., systems that employ randomized algorithms, multi-agent systems or systems with unreliable components or surroundings. In this context we outline the theory of verifying ω-regular properties of such operational models. As an integral part of this theory we use ω-automata, i.e., finite-state automata over finite alphabets that accept languages of infinite words. Additionally, basic concepts of important reduction techniques are sketched, namely partial order reduction of MDPs and quotient system reduction of the numerical problem that arises in the verification of MDPs. Furthermore we present several undecidability and decidability results for the controller synthesis problem for partially observable MDPs.
measurement and modeling of computer systems | 2005
Christel Baier; Frank Ciesinski; Marcus Größer
Markov decision processes (MDP) can serve as operational model for probabilistic distributed systems and yield the basis for model checking algorithms against qualitative or quantitative properties. In this paper, we summarize the main steps of a quantitative analysis for a given MDP and formula of linear temporal logic, give an introduction to the modelling language ProbMela which provides a simple and intuitive way to describe complex systems with a MDP-semantics and present the basic features of the MDP model checker LiQuor.
Archive | 2004
Christel Baier; Marcus Größer; Martin Leucker; Benedikt Bollig; Frank Ciesinski
Controller synthesis addresses the question of how to limit the internal behavior of a given implementation to meet its specification, regardless of the behavior enforced by the environment. In this paper, we consider a model with probabilism and nondeterminism where the nondeterministic choices in some states are assumed to be controllable, while the others are under the control of an unpredictable environment. We first consider probabilistic computation tree logic as specification formalism, discuss the role of strategy-types for the controller and show the NP-hardness of the controller synthesis problem. The second part of the paper presents a controller synthesis algorithm for automata-specifications which relies on a reduction to the synthesis problem for PCTL with fairness.
Logical Methods in Computer Science | 2014
Nathalie Bertrand; Patricia Bouyer; Thomas Brihaye; Quentin Menet; Christel Baier; Marcus Größer; Marcin Jurdzinski
A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a stochastic timed automaton A and a property
international workshop on model checking software | 2008
Frank Ciesinski; Christel Baier; Marcus Größer; David Parker
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foundations of software technology and theoretical computer science | 2006
Marcus Größer; Gethin Norman; Christel Baier; Frank Ciesinski; Marta Z. Kwiatkowska; David Parker
, we want to decide whether A satisfies
DCFS | 2009
Christel Baier; Nathalie Bertrand; Marcus Größer
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