Efficient modelling, generation and analysis of Markov Automata

Abstract

Quantitative model checking is concerned with the verification of both quantitative and qualitative properties over models incorporating quantitative information. Increases in expressivity of the models involved allow more types of systems to be analysed, but also raise the difficulty of their efficient analysis.Three years ago, the Markov automaton (MA) was introduced as a generalisation of probabilistic automata and interactive Markov chains, supporting nondeterminism, discrete probabilistic choice as well as stochastic timing (Markovian rates). Later, the tool IMCA was developed to compute time-bounded reachability probabilities, expected times and long-run averages for sets of goal states within an MA. However, an efficient formalism for modelling and generating MAs was still lacking. Additionally, the omnipresent state space explosion also threatened the analysability of these models. This thesis solves the first problem and contributes significantly to the solution of the second.

Modelling and Analysis of Markov Reward Automata

“…The Markov Automata Process Algebra (MAPA) language allows MAs to be generated in an efficient and effective manner [31]. It is based on µCRL [16], allowing the standard process-algebraic constructs such as nondeterministic choice and action prefix to be used in a data-rich context: processes are equipped with a set of variables over user-definable data types, and actions can be parameterised based on the values of these variables.…”

“…Action-based rewards are just added as decorations to the actions in the process-algebraic specification: we use a[r] • x:D f : p to denote an action a having reward r, continuing as process p (where the variable x gets a value from its domain D based on a probabilistic expression f ). We refer to [31] for a detailed exposition of the syntax and semantics of MAPA; this is trivially generalised to incorporate the action-based rewards.…”

“…Recent work also demonstrated that MAs (and hence MRAs as well) are suitable for modelling and analysing distributed algorithms such as a leader election protocol, performance models such as a polling system and hardware models such as a processor grid [31].…”

“…Notions of strong, weak and branching bisimulation were defined to equate behaviourally equivalent MAs [15,28,12,31], and the process-algebraic language MAPA was introduced for easily specifying large MAs in a concise manner [32]. Several types of reduction techniques [34,33] have been defined for the MAPA language and implemented in the tool SCOOP, optimising specifications to decrease the state space of the corresponding MAs while staying bisimilar [30,18].…”

Qualitative and quantitative information flow analysis for multi-threaded programs

“…A probability space (Ω, F, P) is defined in a standard way [88], where Ω is the sample space, F is a set of events, and P is the unique measure on F [86]. The sample space Ω is a set of all possible outcomes of the probabilistic experiment.…”