PReMo : An Analyzer for P robabilistic Re cursive Mo dels
نویسندگان
چکیده
This paper describes PReMo, a tool for analyzing Recursive Markov Chains, and their controlled/game extensions: (1-exit) Recursive Markov Decision Processes and Recursive Simple Stochastic Games. Introduction. Recursive Markov Chains (RMCs) [4, 5] are a natural abstract model of probabilistic procedural programs and other systems involving recursion and probability. They are formally equivalent to probabilistic Pushdown Systems (pPDSs) ([2, 3]), and they define a class of infinite-state Markov chains that generalize a number of well studied stochastic models such as Stochastic Context-Free Grammars (SCFGs) and Multi-Type Branching Processes. In a series of recent papers ([4–7]), the second author and M. Yannakakis have developed algorithms for analysis and model checking of RMCs and their controlled and game extensions: 1-exit Recursive Markov Decision Processes (1-RMDPs) and 1-exit Recursive Simple Stochastic Games (1-RSSGs). These extensions allow modelling of nondeterministic and interactive behavior. In this paper we describe PReMo, a software tool for analysing models based on RMCs, 1-RMDPs, and 1-RSSGs. PReMo allows these models to be specified in several different input formats, including a simple imperative-style language for specifying RMCs and RSSGs, and an input format for SCFGs. For RMCs/RSSGs, PReMo generates a graphical depiction of the model, useful for visualizing small models (see Figure 1). PReMo has implementations of numerical algorithms for a number of analyses of RMCs and 1-RSSGs. From an RMC, PReMo generates a corresponding system of nonlinear polynomial equations, whose Least Fixed Point (LFP) solution gives precisely the termination probabilities for vertex-exit pairs in the RMC. For 1-RSSGs, it generates a system of nonlinear min-max equations, whose LFP gives the values of the termination game starting at each vertex. Computation of termination probabilities is a key ingredient for model checking and other analyses for RMCs and pPDSs ([4, 5, 2]). PReMo provides a number of optimized numerical algorithms for computing termination probabilities. Methods provided include both dense and sparse versions of a decomposed Newton’s method developed in [4], as well as versions of value iteration, optimized using nonlinear generalizations of Gauss-Seidel and SOR techniques. The latter methods also apply to analysis of 1-RSSGs. In addition to computing termination probabilities, PReMo can compute the (maximum/minimum/game) expected termination time in 1-RMCs, 1-RMDPs, and 1-RSSGs. It does so by generating a different monotone system of linear
منابع مشابه
Delineation of enriched zones of Mo, Cu and Re by concentration-volume fractal model in Nowchun Mo-Cu porphyry deposit, SE Iran
The purpose of this study is to identify the enriched zones of Cu, Mo and Re in Nowchun Mo-Cu porphyry deposit (SE Iran) based on subsurface data and using of concentration–volume (C–V) fractal model. The C-V model illustrates four and five geochemical zones based on Mo and Cu distributions respectively and there are three geochemical populations for Re. The main mineralization for Mo, Cu and R...
متن کاملExact Solutions for Some Discrete Models of the Boltzmann Equation
Abs tra ct. For the simplest of the disc rete mod els of the Boltzmann equations , the Broad well model, exact solutions have been obtained by Co rnille [15.16] in the form of bisolitons. In the present paper, we build exact solutions for more co mplex mod els. 1. Introduction For t he las t twenty years, t he st udy of disc rete mo de ls of t he Bolt zm ann equat ion h as attract ed t he atten...
متن کاملThe Open Inventor Toolkit and the PREMO Standard
REPORTRAPPORT The open inventor toolkit and the PREMO standard Abstract PREMO is an emerging international standard for the presentations of multimedia objects including computer graphics. Open Inventor TM is a commercially available \de facto" standard for interactive computer graphics packaged as a library of objects. In this paper, we consider whether the concepts and objects of PREMO are su...
متن کاملRelating the primitive hierarchy of the PREMO standard to the standard reference model for intelligent multimedia presentation systems
The need for a suitable classification of media types arises for several reasons when building or comparing multimedia systems. Within an Intelligent Multimedia Presentation Systems (IMMPS) it is necessary to formulate and encode design knowledge for decision making on the appropriate medium in which to present information and for the generation of the presentation. It is also required in order...
متن کاملInvestigating the behaviour of PREMO synchronizable objects
PREMO stands for Presentation Environment for Multimedia Objects and is a major new standard under development within ISO/IEC. It addresses the creation of, presentation of and interaction with all forms of information using single or multiple media. The PREMO standard (u.d.) is currently described using english with an additional formal speciication in Object-Z. Such a state based speciication...
متن کامل