AbstractThis paper surveys the analysis of parametric Markov models whose transitions are labelled with functions over a finite set parameters. These symbolic representations uncountable many concrete probabilistic models, each obtained by instantiating We consider various problems for given logical specification \(\varphi \): do all parameter instantiations within region values satisfy \)?, wh...

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 t...

ion-Based Parameter Synthesis for Multiaffine Systems Sergiy Bogomolov1(B), Christian Schilling, Ezio Bartocci, Gregory Batt, Hui Kong, and Radu Grosu 1 IST Austria, Klosterneuburg, Austria [email protected] 2 University of Freiburg, Freiburg im Breisgau, Germany 3 Vienna University of Technology, Vienna, Austria 4 INRIA Paris-Rocquencourt, Paris, France Abstract. Multiaffine hybrid au...

We show how to synthesise parameter values under which a given property, expressed in a certain extension of CTL called RTCTLP, holds in a parametric timed Kripke structure. Similarly as in fixed-point symbolic model checking approach, we introduce special operators which stabilise on the solution. The process of stabilisation is essentially a translation from RTCTLP parameter synthesis problem...

We provide a subclass of parametric timed automata (PTA) that we can actually and efficiently analyze, and we argue that it retains most of the practical usefulness of PTA. The currently most useful known subclass of PTA, L/U automata, has a strong syntactical restriction for practical purposes, and we show that the associated theoretical results are mixed. We therefore advocate for a different...

Probabilistic modelling has proved useful to analyseperformance, reliability and energy usage of distributed ornetworked systems. We consider parametric probabilistic models,in which probabilities are specified as expressions over a setof parameters, rather than concrete values. We address theparameter synthesis problem for parametric Markov decisionprocesses and paramet...

An account is presented on investigation of the effects of synthesis parameters, i.e., reaction sources, silica to alumina ratio, acid molar ratio and crystallization conditions on the crystallinity, morphology and particle size of SAPO-34. The synthesis conditions were designed to produce small particles with narrow size range. The prepared samples were characterized by XRD and SE...