We present PROPhESY, a tool for analyzing parametric Markov chains (MCs). It can compute a ration... more We present PROPhESY, a tool for analyzing parametric Markov chains (MCs). It can compute a rational function (i.e., a fraction of two polynomials in the model parameters) for reachability and expected reward objectives. Our tool outperforms state-of-the-art tools and supports the novel feature of conditional probabilities. PROPhESY supports incremental automatic parameter synthesis (using SMT techniques) to determine " safe " and " unsafe " regions of the parameter space. All values in these regions give rise to instantiated MCs satisfying or violating the (conditional) probability or expected reward objective. PROPhESY features a web front-end supporting visualization and user-guided parameter synthesis. Experimental results show that PROPhESY scales to MCs with millions of states and several parameters.
We investigate the semantic intricacies of conditioning, a main feature in probabilistic programm... more We investigate the semantic intricacies of conditioning, a main feature in probabilistic programming. We provide a weakest (liberal) pre-condition (w(l)p) semantics for the elementary probabilistic programming language pGCL extended with conditioning. We prove that quantitative weakest (liberal) pre-conditions coincide with conditional (liberal) expected rewards in Markov chains and show that semantically conditioning is a truly conservative extension. We present two program transformations which entirely eliminate conditioning from any program and prove their correctness using the w(l)p-semantics. Finally, we show how the w(l)p-semantics can be used to determine conditional probabilities in a parametric anonymity protocol and show that an inductive w(l)p-semantics for conditioning in non-deterministic probabilistic programs cannot exist.
Generation of counterexamples is a highly important task in the model checking process. In contra... more Generation of counterexamples is a highly important task in the model checking process. In contrast to, e., g., digital circuits where counterexamples typically consist of a single path leading to a critical state of the system, in the probabilistic setting counterexamples may consist of a large number of paths. In order to be able to handle large systems and to use the capabilities of modern SAT-solvers, bounded model checking (BMC) for discrete-time Markov chains was established. In this paper we introduce the usage of SMT-solving over ...
COMICS is a stand-alone tool which performs model checking and the generation of counterexamples ... more COMICS is a stand-alone tool which performs model checking and the generation of counterexamples for discrete-time Markov Chains (DTMCs). For an input DTMC COMICS computes an abstract system that carries the model checking information and uses this result to compute a critical subsystem, which induces a counterexample. This abstract subsystem can be refined and concretized hierarchically. The tool comes with a command line version as well as a graphical user interface which allows the user to interactively ...
We propose a new approach to compute counterexamples for violated ω-regular properties of discret... more We propose a new approach to compute counterexamples for violated ω-regular properties of discrete-time Markov chains. Whereas most approaches compute a set of system paths as a counterexample, we determine a critical subsystem that already violates the given property. In earlier work methods have been introduced to compute such subsystems for safety properties, based on a search for shortest paths. In this paper we use mixed integer linear programming to determine minimal critical subsystems for arbitrary ω- ...
We present PROPhESY, a tool for analyzing parametric Markov chains (MCs). It can compute a ration... more We present PROPhESY, a tool for analyzing parametric Markov chains (MCs). It can compute a rational function (i.e., a fraction of two polynomials in the model parameters) for reachability and expected reward objectives. Our tool outperforms state-of-the-art tools and supports the novel feature of conditional probabilities. PROPhESY supports incremental automatic parameter synthesis (using SMT techniques) to determine " safe " and " unsafe " regions of the parameter space. All values in these regions give rise to instantiated MCs satisfying or violating the (conditional) probability or expected reward objective. PROPhESY features a web front-end supporting visualization and user-guided parameter synthesis. Experimental results show that PROPhESY scales to MCs with millions of states and several parameters.
We investigate the semantic intricacies of conditioning, a main feature in probabilistic programm... more We investigate the semantic intricacies of conditioning, a main feature in probabilistic programming. We provide a weakest (liberal) pre-condition (w(l)p) semantics for the elementary probabilistic programming language pGCL extended with conditioning. We prove that quantitative weakest (liberal) pre-conditions coincide with conditional (liberal) expected rewards in Markov chains and show that semantically conditioning is a truly conservative extension. We present two program transformations which entirely eliminate conditioning from any program and prove their correctness using the w(l)p-semantics. Finally, we show how the w(l)p-semantics can be used to determine conditional probabilities in a parametric anonymity protocol and show that an inductive w(l)p-semantics for conditioning in non-deterministic probabilistic programs cannot exist.
Generation of counterexamples is a highly important task in the model checking process. In contra... more Generation of counterexamples is a highly important task in the model checking process. In contrast to, e., g., digital circuits where counterexamples typically consist of a single path leading to a critical state of the system, in the probabilistic setting counterexamples may consist of a large number of paths. In order to be able to handle large systems and to use the capabilities of modern SAT-solvers, bounded model checking (BMC) for discrete-time Markov chains was established. In this paper we introduce the usage of SMT-solving over ...
COMICS is a stand-alone tool which performs model checking and the generation of counterexamples ... more COMICS is a stand-alone tool which performs model checking and the generation of counterexamples for discrete-time Markov Chains (DTMCs). For an input DTMC COMICS computes an abstract system that carries the model checking information and uses this result to compute a critical subsystem, which induces a counterexample. This abstract subsystem can be refined and concretized hierarchically. The tool comes with a command line version as well as a graphical user interface which allows the user to interactively ...
We propose a new approach to compute counterexamples for violated ω-regular properties of discret... more We propose a new approach to compute counterexamples for violated ω-regular properties of discrete-time Markov chains. Whereas most approaches compute a set of system paths as a counterexample, we determine a critical subsystem that already violates the given property. In earlier work methods have been introduced to compute such subsystems for safety properties, based on a search for shortest paths. In this paper we use mixed integer linear programming to determine minimal critical subsystems for arbitrary ω- ...
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