6 research outputs found
LNCS
We present the tool Quasy, a quantitative synthesis tool. Quasy takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. The user can choose between a system that satisfies and optimizes the specifications (a) under all possible environment behaviors or (b) under the most-likely environment behaviors given as a probability distribution on the possible input sequences. Quasy solves these two quantitative synthesis problems by reduction to instances of 2-player games and Markov Decision Processes (MDPs) with quantitative winning objectives. Quasy can also be seen as a game solver for quantitative games. Most notable, it can solve lexicographic mean-payoff games with 2 players, MDPs with mean-payoff objectives, and ergodic MDPs with mean-payoff parity objectives
Symblicit Exploration and Elimination for Probabilistic Model Checking
Binary decision diagrams can compactly represent vast sets of states,
mitigating the state space explosion problem in model checking. Probabilistic
systems, however, require multi-terminal diagrams storing rational numbers.
They are inefficient for models with many distinct probabilities and for
iterative numeric algorithms like value iteration. In this paper, we present a
new "symblicit" approach to checking Markov chains and related probabilistic
models: We first generate a decision diagram that symbolically collects all
reachable states and their predecessors. We then concretise states one-by-one
into an explicit partial state space representation. Whenever all predecessors
of a state have been concretised, we eliminate it from the explicit state space
in a way that preserves all relevant probabilities and rewards. We thus keep
few explicit states in memory at any time. Experiments show that very large
models can be model-checked in this way with very low memory consumption
Synthesizing Systems with Optimal Average-Case Behavior for Ratio Objectives
We show how to automatically construct a system that satisfies a given
logical specification and has an optimal average behavior with respect to a
specification with ratio costs.
When synthesizing a system from a logical specification, it is often the case
that several different systems satisfy the specification. In this case, it is
usually not easy for the user to state formally which system she prefers. Prior
work proposed to rank the correct systems by adding a quantitative aspect to
the specification. A desired preference relation can be expressed with (i) a
quantitative language, which is a function assigning a value to every possible
behavior of a system, and (ii) an environment model defining the desired
optimization criteria of the system, e.g., worst-case or average-case optimal.
In this paper, we show how to synthesize a system that is optimal for (i) a
quantitative language given by an automaton with a ratio cost function, and
(ii) an environment model given by a labeled Markov decision process. The
objective of the system is to minimize the expected (ratio) costs. The solution
is based on a reduction to Markov Decision Processes with ratio cost functions
which do not require that the costs in the denominator are strictly positive.
We find an optimal strategy for these using a fractional linear program.Comment: In Proceedings iWIGP 2011, arXiv:1102.374
Decision diagrams: Extensions and applications to reachability analysis
Symbolic data structures and algorithms are increasingly popular tools for the analysis of complex systems. Given a high-level model of a system, such as a Petri Net, we can automatically verify certain properties about it. In this thesis, we develop data structures and techniques that can be used to improve such analyses.
First, we show how decision diagrams can be used efficiently in traditional explicit generation algorithms. Next, we show how symbolic reachability analysis can be used to detect deadlocks in Petri Nets. We also present a symbolic approach that can detect deadlocks in unbounded Petri Nets.
Finally, we introduce a new type of decision diagram, ESRBDD, that combines multiple reduction rules, is canonical, and produces a more compact representation than previous efforts. We show that operations on ESRBDDs are at least as efficient as those on the underlying decision diagrams and introduce extensions to ESRBDDs that improve on their compactness and operational efficiency