We give an overview of GRIP, a symmetry reduction tool for the probabilistic model checker PRISM, together with experimental results for a selection of example specifications. An Overview of GRIPGRIP (generic representatives in PRISM), introduced in [1], is a symmetry reduction tool for the PRISM model checker [6]. GRIP is based on the generic representatives approach of [2], which aims to overcome the inherent problem of combining symmetry reduction with symbolic state-space representation. We present an overview of GRIP version 2.0 (referred to henceforth as GRIP), an improved version of the original tool, and compare GRIP to PRISM-symm, an alternative symmetry reduction tool for PRISM [5]. GRIP, together with the PRISM examples used for experiments in Section 3 can be downloaded from our website [4].The top panel of Figure 1 shows a simple leader election protocol in PRISM, adapted from [1]. The underlying model here is a Markov decision process (MDP). GRIP works by translating this specification into a reduced form, as shown in the bottom-left panel of the figure. The reduced specification abstracts away from specific modules, instead using a single generic module comprised of variables which count the number of modules in each potential local state. Symmetric temporal properties can also be translated into reduced form. PRISM can then be used, unchanged, to check reduced properties of a reduced specification. New Features of GRIPThe original version of GRIP required specifications to consist of multiple instantiations of a single symmetric module type, specified using a single local state variable. This model of computation is in keeping with the presentation of the generic representatives approach for non-probabilistic model checking [2]. While a wide class of symmetric systems can, in theory, be specified in this way, accurately modelling complex protocols via a single state variable quickly becomes impractical. GRIP now supports: multiple local state variables; a wide range of arithmetic and boolean expressions over these variables; communication via shared global variables, and multiple asymmetric modules in parallel with a single family of symmetric modules. In addition, GRIP handles models with continuous time Markov chain (CTMC) semantics.Multiple local variables can result in a large number of local states, which translates to many counters in the specification output by GRIP. This in turn can lead to large MTBDDs (the symbolic data structure used by PRISM). To combat this, we have implemented an optimisation suggested in [3]: we use PRISM for local reachability analysis during the translation process, to reduce the number of counters in the output specification. In addition, since the sum of counter variables should always equal N (the number of symmetric modules), the last counter variable can be eliminated and replaced with the formulaThis second optimisation offers a modest reduction in MTBDD size. The bottom-right panel of Figure 1 shows the effect of these optimisations: local reachabi...
The main problems of school course timetabling are time, curriculum, and classrooms. In addition there are other problems that vary from one institution to another. This paper is intended to solve the problem of satisfying the teachers' preferred schedule in a way that regards the importance of the teacher to the supervising institute, i.e. his score according to some criteria. Genetic algorithm (GA) has been presented as an elegant method in solving timetable problem (TTP) in order to produce solutions with no conflict. In this paper, we consider the analytic hierarchy process (AHP) to efficiently obtain a score for each teacher, and consequently produce a GA-based TTP solution that satisfies most of the teachers' preferences.
International audienceStochastic automata networks (Sans) are high-level formalisms for modeling very large and complex Markov chains in a compact and structured manner. To date, the exponential distribution has been the only distribution used to model the passage of time in the evolution of the different San components. In this paper we show how phase-type distributions may be incorporated into Sans thereby providing the wherewithal by which arbitrary distributions can be used which in turn leads to an improved ability for more accurately modeling numerous real phenomena. The approach we develop is to take a San model containing phase-type distributions and to translate it into another, stochastically equivalent, San model having only exponential distributions. In the San formalism, it is the events that are responsible for firing transitions and our procedure is to associate a stochastic automaton with each event having a phase-type distribution. This automaton models the distribution of time until the event occurs. In this way, the size of the elementary matrices remain small, because the size of the automata are small: the automata are either those of the original San, or are those associated with the phase-type events and are of size k, the number of phases in the representation of the distribution
The production of video has increased and expanded dramatically. There is a need to reach accurate video classification. In our work, we use deep learning as a mean to accelerate the video retrieval task by classifying them into categories. We classify a video depending on the text extracted from it. We trained our model using fastText, a library for efficient text classification and representation learning, and tested our model on 15000 videos. Experimental results show that our approach is efficient and has good performance. Our technique can be used on huge datasets. It produces a model that can be used to classify any video into a specific category very quickly.
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