Pub Date : 2010-09-30DOI: 10.1109/PDMC-HIBI.2010.19
M. Burkitt, D. Walker, D. Romano, A. Fazeli
Extracting information about the structure of biological tissue from static image data is a complex task which requires a series of computationally intensive operations. Here we present how the power of multi-core CPUs and massively parallel GPUs have been utilised to extract information about the shape, size and path followed by the mammalian oviduct, called the fallopian tube in humans, from histology images, to create a realistic 3D virtual organ for use in predictive computational models. Histology images from a mouse oviduct were processed, using a combination of GPU and multi-core CPU techniques, to identify the individual cross-sections and determine the 3D path that the tube follows through the tissue. This information was then related back to the histology images, linking the 2D cross-sections with their corresponding 3D position along the oviduct. Measurements were then taken from the images and used to computationally generate a series of linear 2D spline cross-sections for the length of the oviduct, which were bound to the 3D path of the tube using a novel particle system based technique that provides smooth resolution of self intersections and crossovers from adjacent sections. This results in a unique 3D model of the oviduct, which is based on measurements of histology slides and therefore grounded in reality. The GPU is used for the processor intensive operations of image processing and particle physics based simulations, significantly reducing the time required to generate a complete model. A set of models created using this technique is being used to investigate the influence that the 3D structure of the oviductal environment has on sperm transport and navigation.
{"title":"Using the GPU and Multi-core CPU to Generate a 3D Oviduct through Feature Extraction from Histology Slides","authors":"M. Burkitt, D. Walker, D. Romano, A. Fazeli","doi":"10.1109/PDMC-HIBI.2010.19","DOIUrl":"https://doi.org/10.1109/PDMC-HIBI.2010.19","url":null,"abstract":"Extracting information about the structure of biological tissue from static image data is a complex task which requires a series of computationally intensive operations. Here we present how the power of multi-core CPUs and massively parallel GPUs have been utilised to extract information about the shape, size and path followed by the mammalian oviduct, called the fallopian tube in humans, from histology images, to create a realistic 3D virtual organ for use in predictive computational models. Histology images from a mouse oviduct were processed, using a combination of GPU and multi-core CPU techniques, to identify the individual cross-sections and determine the 3D path that the tube follows through the tissue. This information was then related back to the histology images, linking the 2D cross-sections with their corresponding 3D position along the oviduct. Measurements were then taken from the images and used to computationally generate a series of linear 2D spline cross-sections for the length of the oviduct, which were bound to the 3D path of the tube using a novel particle system based technique that provides smooth resolution of self intersections and crossovers from adjacent sections. This results in a unique 3D model of the oviduct, which is based on measurements of histology slides and therefore grounded in reality. The GPU is used for the processor intensive operations of image processing and particle physics based simulations, significantly reducing the time required to generate a complete model. A set of models created using this technique is being used to investigate the influence that the 3D structure of the oviductal environment has on sperm transport and navigation.","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"75 1","pages":"78-87"},"PeriodicalIF":0.0,"publicationDate":"2010-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85966444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-09-30DOI: 10.1109/PDMC-HIBI.2010.11
D. Bosnacki, S. Edelkamp, Damian Sulewski, Anton Wijs
We present an extension of the model checker PRISM for (general purpose) graphics processing units (GPUs). The extension is based on parallel algorithms for probabilistic model checking which are tuned for GPUs. In particular, we parallelize the parts of the algorithms that boil down to linear algebraic operations, like solving systems of linear equations and matrix vector multiplication. These computations are performed very efficiently on GPGPUs which results inconsiderable runtime improvements compared to the standard versions of PRISM. We evaluated the extension of PRISM on several case studies in which we observed significant speedup over the standard CPU implementation of the tool.
{"title":"GPU-PRISM: An Extension of PRISM for General Purpose Graphics Processing Units","authors":"D. Bosnacki, S. Edelkamp, Damian Sulewski, Anton Wijs","doi":"10.1109/PDMC-HIBI.2010.11","DOIUrl":"https://doi.org/10.1109/PDMC-HIBI.2010.11","url":null,"abstract":"We present an extension of the model checker PRISM for (general purpose) graphics processing units (GPUs). The extension is based on parallel algorithms for probabilistic model checking which are tuned for GPUs. In particular, we parallelize the parts of the algorithms that boil down to linear algebraic operations, like solving systems of linear equations and matrix vector multiplication. These computations are performed very efficiently on GPGPUs which results inconsiderable runtime improvements compared to the standard versions of PRISM. We evaluated the extension of PRISM on several case studies in which we observed significant speedup over the standard CPU implementation of the tool.","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"41 1","pages":"17-19"},"PeriodicalIF":0.0,"publicationDate":"2010-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80580278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-09-30DOI: 10.1109/PDMC-HIBI.2010.20
V. Belcastro, D. Bernardo, F. Gregoretti, G. Oliva
A Gene Regulatory Network links pairs of genes through an edge if they physically or functionally interact."Reverse engineering", a gene regulatory network means to infer the edges between genes from the available experimental data. Transcriptional responses (i.e. gene expression profiles obtained through micro array experiments) are often used to reverse-engineer a network of genes. Reverse-engineering consists in analyzing transcriptional responses to a set of treatments and adding an edge between genes if their expressions show a coordinated behavior on a subset of the treatments, according to some underlying model of gene regulation. Mammalian cells contain tens of thousands of genes, and it is necessary to analyze hundreds of transcriptional responses in order to have acceptable statistical evidence of interactions between genes. There currently exist several ready-to-use software packages able to infer gene networks, but few can be used to infer large-size networks from thousands of transcriptional responses as the dimension of the problem leads to high computational costs and memory requirements. We propose to exploit parallel computing techniques to overcome this problem. In this work, we designed and developed a parallel computing algorithm to reverse engineer large-scale gene regulatory networks from tens of thousands of gene expression profiles. The algorithm is based on computing pair-wise Mutual Information between each gene-pair. We successfully tested it to infer the Mus Musculus (mouse) gene regulatory network in liver from 312 expression profiles collected from a public Internet repository. Each profile measures the expression of 45,101 genes (more specifically, transcripts). We analyzed all of the possible gene-pairs for a total amount of about 1 billion identifying about 60 millions edges. We used a hierarchical clustering algorithm to discover communities within the gene network, and found a modular structure that highlights genes involved in the same biological functions.
{"title":"Parallel Computing Algorithms for Reverse-Engineering and Analysis of Genome-Wide Gene Regulatory Networks from Gene Expression Profiles","authors":"V. Belcastro, D. Bernardo, F. Gregoretti, G. Oliva","doi":"10.1109/PDMC-HIBI.2010.20","DOIUrl":"https://doi.org/10.1109/PDMC-HIBI.2010.20","url":null,"abstract":"A Gene Regulatory Network links pairs of genes through an edge if they physically or functionally interact.\"Reverse engineering", a gene regulatory network means to infer the edges between genes from the available experimental data. Transcriptional responses (i.e. gene expression profiles obtained through micro array experiments) are often used to reverse-engineer a network of genes. Reverse-engineering consists in analyzing transcriptional responses to a set of treatments and adding an edge between genes if their expressions show a coordinated behavior on a subset of the treatments, according to some underlying model of gene regulation. Mammalian cells contain tens of thousands of genes, and it is necessary to analyze hundreds of transcriptional responses in order to have acceptable statistical evidence of interactions between genes. There currently exist several ready-to-use software packages able to infer gene networks, but few can be used to infer large-size networks from thousands of transcriptional responses as the dimension of the problem leads to high computational costs and memory requirements. We propose to exploit parallel computing techniques to overcome this problem. In this work, we designed and developed a parallel computing algorithm to reverse engineer large-scale gene regulatory networks from tens of thousands of gene expression profiles. The algorithm is based on computing pair-wise Mutual Information between each gene-pair. We successfully tested it to infer the Mus Musculus (mouse) gene regulatory network in liver from 312 expression profiles collected from a public Internet repository. Each profile measures the expression of 45,101 genes (more specifically, transcripts). We analyzed all of the possible gene-pairs for a total amount of about 1 billion identifying about 60 millions edges. We used a hierarchical clustering algorithm to discover communities within the gene network, and found a modular structure that highlights genes involved in the same biological functions.","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"14 1","pages":"88-94"},"PeriodicalIF":0.0,"publicationDate":"2010-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82509852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-09-30DOI: 10.1109/PDMC-HIBI.2010.24
Andreas Sand, Christian N. S. Pedersen, T. Mailund, Asbjorn Tolbol Brask
We present a C++ library for constructing and analyzing general hidden Markov models. The library consists of a number of template classes and generic functions, parameterized with the precision of floating point types and different types of hardware acceleration.
{"title":"HMMlib: A C++ Library for General Hidden Markov Models Exploiting Modern CPUs","authors":"Andreas Sand, Christian N. S. Pedersen, T. Mailund, Asbjorn Tolbol Brask","doi":"10.1109/PDMC-HIBI.2010.24","DOIUrl":"https://doi.org/10.1109/PDMC-HIBI.2010.24","url":null,"abstract":"We present a C++ library for constructing and analyzing general hidden Markov models. The library consists of a number of template classes and generic functions, parameterized with the precision of floating point types and different types of hardware acceleration.","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"57 1","pages":"126-134"},"PeriodicalIF":0.0,"publicationDate":"2010-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86432487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
F. Peschanski, Hanna Klaudel, Raymond R. Devillers
This paper presents the Pi-graphs, a visual paradigm for the modelling and verification of mobile systems. The language is a graphical variant of the Pi-calculus with iterators to express non-terminating behaviors. The operational semantics of Pi-graphs use ground notions of labelled transition and bisimulation, which means standard verification techniques can be applied. We show that bisimilarity is decidable for the proposed semantics, a result obtained thanks to an original notion of causal clock as well as the automatic garbage collection of unused names.
{"title":"A Decidable Characterization of a Graphical Pi-calculus with Iterators","authors":"F. Peschanski, Hanna Klaudel, Raymond R. Devillers","doi":"10.4204/EPTCS.39.4","DOIUrl":"https://doi.org/10.4204/EPTCS.39.4","url":null,"abstract":"This paper presents the Pi-graphs, a visual paradigm for the modelling and verification of mobile systems. The language is a graphical variant of the Pi-calculus with iterators to express non-terminating behaviors. The operational semantics of Pi-graphs use ground notions of labelled transition and bisimulation, which means standard verification techniques can be applied. We show that bisimilarity is decidable for the proposed semantics, a result obtained thanks to an original notion of causal clock as well as the automatic garbage collection of unused names.","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"35 1","pages":"47-61"},"PeriodicalIF":0.0,"publicationDate":"2010-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87262463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present an extension of two policy-iteration based algorithms on weighted graphs (viz., Markov Decision Problems and Max-Plus Algebras). This extension allows us to solve the following inverse problem: considering the weights of the graph to be unknown constants or parameters, we suppose that a reference instantiation of those weights is given, and we aim at computing a constraint on the parameters under which an optimal policy for the reference instantiation is still optimal. The original algorithm is thus guaranteed to behave well around the reference instantiation, which provides us with some criteria of robustness. We present an application of both methods to simple examples. A prototype implementation has been done.
{"title":"An Inverse Method for Policy-Iteration Based Algorithms","authors":"L. Fribourg, É. André","doi":"10.4204/EPTCS.10.4","DOIUrl":"https://doi.org/10.4204/EPTCS.10.4","url":null,"abstract":"We present an extension of two policy-iteration based algorithms on weighted graphs (viz., Markov Decision Problems and Max-Plus Algebras). This extension allows us to solve the following inverse problem: considering the weights of the graph to be unknown constants or parameters, we suppose that a reference instantiation of those weights is given, and we aim at computing a constraint on the parameters under which an optimal policy for the reference instantiation is still optimal. The original algorithm is thus guaranteed to behave well around the reference instantiation, which provides us with some criteria of robustness. We present an application of both methods to simple examples. A prototype implementation has been done.","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"11 22 1","pages":"44-61"},"PeriodicalIF":0.0,"publicationDate":"2009-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90567467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in particular, for such systems having a finite description, each state of the system is a configuration of some machine. Then most algorithmic approaches rely on the structure of these configurations. Such characterisations are said internal. In order to apply algorithms detecting a structural property (like identifying connected components) one may have first to transform the system in order to fit the description needed for the algorithm. The problem of internal characterisation is that it hides structural properties, and each solution becomes ad hoc relatively to the form of the configurations. On the contrary, external characterisations avoid explicit naming of the vertices. Such characterisation are mostly defined via graph transformations. In this paper we present two kind of external characterisations: deterministic graph rewriting, which in turn characterise regular graphs, deterministic context-free languages, and rational graphs. Inverse substitution from a generator (like the complete binary tree) provides characterisation for prefix-recognizable graphs, the Caucal Hierarchy and rational graphs. We illustrate how these characterisation provide an efficient tool for the representation of infinite state systems.
{"title":"On external presentations of infinite graphs","authors":"Christophe Morvan","doi":"10.4204/EPTCS.10.2","DOIUrl":"https://doi.org/10.4204/EPTCS.10.2","url":null,"abstract":"The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in particular, for such systems having a finite description, each state of the system is a configuration of some machine. Then most algorithmic approaches rely on the structure of these configurations. Such characterisations are said internal. In order to apply algorithms detecting a structural property (like identifying connected components) one may have first to transform the system in order to fit the description needed for the algorithm. The problem of internal characterisation is that it hides structural properties, and each solution becomes ad hoc relatively to the form of the configurations. On the contrary, external characterisations avoid explicit naming of the vertices. Such characterisation are mostly defined via graph transformations. In this paper we present two kind of external characterisations: deterministic graph rewriting, which in turn characterise regular graphs, deterministic context-free languages, and rational graphs. Inverse substitution from a generator (like the complete binary tree) provides characterisation for prefix-recognizable graphs, the Caucal Hierarchy and rational graphs. We illustrate how these characterisation provide an efficient tool for the representation of infinite state systems.","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"14 1","pages":"23-35"},"PeriodicalIF":0.0,"publicationDate":"2009-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84386691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Visibly pushdown automata (VPA), introduced by Alur and Madhusuan in 2004, is a subclass of pushdown automata whose stack behavior is completely determined by the input symbol according to a fixed partition of the input alphabet. Since its introduce, VPAs have been shown to be useful in various context, e.g., as specification formalism for verification and as automaton model for processing XML streams. Due to high complexity, however, implementation of formal verification based on VPA framework is a challenge. In this paper we consider the problem of implementing VPA-based model checking algorithms. For doing so, we first present an improvement on upper bound for determinization of VPA. Next, we propose simple on-the-fly algorithms to check universality and inclusion problems of this automata class. Then, we implement the proposed algorithms in a prototype tool. Finally, we conduct experiments on randomly generated VPAs. The experimental results show that the proposed algorithms are considerably faster than the standard ones.
{"title":"A Tighter Bound for the Determinization of Visibly Pushdown Automata","authors":"Nguyen Van Tang","doi":"10.4204/EPTCS.10.5","DOIUrl":"https://doi.org/10.4204/EPTCS.10.5","url":null,"abstract":"Visibly pushdown automata (VPA), introduced by Alur and Madhusuan in 2004, is a subclass of pushdown automata whose stack behavior is completely determined by the input symbol according to a fixed partition of the input alphabet. Since its introduce, VPAs have been shown to be useful in various context, e.g., as specification formalism for verification and as automaton model for processing XML streams. Due to high complexity, however, implementation of formal verification based on VPA framework is a challenge. In this paper we consider the problem of implementing VPA-based model checking algorithms. For doing so, we first present an improvement on upper bound for determinization of VPA. Next, we propose simple on-the-fly algorithms to check universality and inclusion problems of this automata class. Then, we implement the proposed algorithms in a prototype tool. Finally, we conduct experiments on randomly generated VPAs. The experimental results show that the proposed algorithms are considerably faster than the standard ones.","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"39 1","pages":"62-76"},"PeriodicalIF":0.0,"publicationDate":"2009-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80528403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Introduction Model checking has been widely successful in validating and debugging hardware de- signs and communication protocols. However, state-space explosion is an intrinsic problem which limits the applicability of model checking tools. To overcome this limitation software model checkers have suggested different approaches, among which abstraction methods have been highly esteemed. modern techniques. Among others, predicate abstraction is a prominent technique which has been widely used in modern model checking. This technique has been shown to enhance the effectiveness of the reachability computation technique in infinite-state systems. In this te chnique an infinite-state system is represented abstractly by a finite-state system, where states of the abst ract model correspond to the truth valuations of a chosen set of atomic predicates. Predicate abstraction was first introduced in (8) as a method for auto- matically determining invariant properties of infinite-st ate systems. This technique involves abstracting a concrete transition system using a set of formulas called predicates which usually denote some state properties of the concrete system. The practical applicability of predicate abstraction is im peded by two problems. First, predicates need to be provided manually (11, 7). This means that the selection of appropriate abstraction predicates is based on a user-driven trial-and-error process. The high degree of user intervention also stands in the way of a seamless integration into practical software development processes. Second, very often the abstraction is too coarse in order to allow relevant system properties to be verified. This calls for abstrac- tion refinement (6), often following a counterexample guide d abstraction refinement scheme (5, 3). Real time models are one example of systems with a large state space as time adds much complexity to the system. In this event, recently there have been increasing number of research to provide a means for the abstraction of such models. It is the objective of this paper to provide support for an automated predicate abstraction technique for concurrent dense real-time models according to the timed automaton model of (1). We propose a method to generate an efficient set of pred icates than a manual, ad-hoc process would be able to provide. We use the results from our recent work (2) to analyze the behavior of the system under verification to discover its local state invari ants and to remove transitions that can never be traversed. We then describe a method to compute a predicate abstraction based on these state invariants. We use information regarding the control state labels as well as the newly computed invariants in the considered control states when determining the abstraction predicates. We have developed a prototype
{"title":"Automated Predicate Abstraction for Real-Time Models","authors":"Bahareh Badban, S. Leue, J. Smaus","doi":"10.4204/EPTCS.10.3","DOIUrl":"https://doi.org/10.4204/EPTCS.10.3","url":null,"abstract":"Introduction Model checking has been widely successful in validating and debugging hardware de- signs and communication protocols. However, state-space explosion is an intrinsic problem which limits the applicability of model checking tools. To overcome this limitation software model checkers have suggested different approaches, among which abstraction methods have been highly esteemed. modern techniques. Among others, predicate abstraction is a prominent technique which has been widely used in modern model checking. This technique has been shown to enhance the effectiveness of the reachability computation technique in infinite-state systems. In this te chnique an infinite-state system is represented abstractly by a finite-state system, where states of the abst ract model correspond to the truth valuations of a chosen set of atomic predicates. Predicate abstraction was first introduced in (8) as a method for auto- matically determining invariant properties of infinite-st ate systems. This technique involves abstracting a concrete transition system using a set of formulas called predicates which usually denote some state properties of the concrete system. The practical applicability of predicate abstraction is im peded by two problems. First, predicates need to be provided manually (11, 7). This means that the selection of appropriate abstraction predicates is based on a user-driven trial-and-error process. The high degree of user intervention also stands in the way of a seamless integration into practical software development processes. Second, very often the abstraction is too coarse in order to allow relevant system properties to be verified. This calls for abstrac- tion refinement (6), often following a counterexample guide d abstraction refinement scheme (5, 3). Real time models are one example of systems with a large state space as time adds much complexity to the system. In this event, recently there have been increasing number of research to provide a means for the abstraction of such models. It is the objective of this paper to provide support for an automated predicate abstraction technique for concurrent dense real-time models according to the timed automaton model of (1). We propose a method to generate an efficient set of pred icates than a manual, ad-hoc process would be able to provide. We use the results from our recent work (2) to analyze the behavior of the system under verification to discover its local state invari ants and to remove transitions that can never be traversed. We then describe a method to compute a predicate abstraction based on these state invariants. We use information regarding the control state labels as well as the newly computed invariants in the considered control states when determining the abstraction predicates. We have developed a prototype","PeriodicalId":31175,"journal":{"name":"Infinity","volume":"60 1","pages":"36-43"},"PeriodicalIF":0.0,"publicationDate":"2009-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73952856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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