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Automated Extraction of Inductive Invariants to Aid Model Checking

Michael L. Case, Alan Mishchenko, Robert K. Brayton
2007 Formal Methods in Computer Aided Design (FMCAD'07)  
We present a way to automatically extract inductive invariants from a design and then prove them.  ...  In this work, we develop a new method for systematically exploring the space of candidate inductive invariants, which allows us to find and prove invariants that are few in number and immediately help  ...  ACKNOWLEDGMENTS The authors would like to acknowledge the Semiconductor Research Corporation (SRC) for their support through contracts 1361.001 and 1444.001.  ... 
doi:10.1109/fmcad.2007.4401996 fatcat:dyhkrmzcxffcdmbmwszzn5gewq

Automated Extraction of Inductive Invariants to Aid Model Checking

Michael L. Case, Alan Mishchenko, Robert K. Brayton
2007 Formal Methods in Computer Aided Design (FMCAD'07)  
We present a way to automatically extract inductive invariants from a design and then prove them.  ...  In this work, we develop a new method for systematically exploring the space of candidate inductive invariants, which allows us to find and prove invariants that are few in number and immediately help  ...  ACKNOWLEDGMENTS The authors would like to acknowledge the Semiconductor Research Corporation (SRC) for their support through contracts 1361.001 and 1444.001.  ... 
doi:10.1109/famcad.2007.12 dblp:conf/fmcad/CaseMB07 fatcat:kktqxjcpsnbupmzo2pxl3d425q

k-Inductive Invariant Checking for Graph Transformation Systems [chapter]

Johannes Dyck, Holger Giese
2017 Lecture Notes in Computer Science  
While our technique takes care of the inductive step (verifying the k-inductive invariant), the base of induction for traces of length k − 1 from an initial graph is established with the model checker  ...  We present our formal approach to k-inductive invariant checking in Section 4. In Section 5, we evaluate our algorithm and approach, before summarizing our results in Section 6.  ...  As its central contribution, this report then presents a formal approach and algorithm to verify graph constraints as k-inductive invariants.  ... 
doi:10.1007/978-3-319-61470-0_9 fatcat:jzlax4qgwvdfdpifrwkvlnvt3y

Formal Verification of Invariants for Attributed Graph Transformation Systems Based on Nested Attributed Graph Conditions [chapter]

Sven Schneider, Johannes Dyck, Holger Giese
2020 Lecture Notes in Computer Science  
To this end, we formalize a symbolic analysis algorithm based on k-induction using Isabelle, apply it to GTSs and GCs over typed attributed graphs, develop support to single out some spurious counterexamples  ...  We propose an analysis procedure for establishing state-invariants for GTSs that are given by nested graph conditions (GCs).  ...  We then applied this analysis approach to typed attributed GTSs by abstracting graphs by nested graph conditions (GCs) and by applying k-induction on these GCs.  ... 
doi:10.1007/978-3-030-51372-6_15 fatcat:3i4dhzxuhffxjpnrz4hqdugtxm

Symbolic invariant verification for systems with dynamic structural adaptation

Basil Becker, Dirk Beyer, Holger Giese, Florian Klein, Daniela Schilling
2006 Proceeding of the 28th international conference on Software engineering - ICSE '06  
The system state is modeled as a graph, system transitions are modeled as rule applications in a graph transformation system, and safety properties of the system are encoded as inductive invariants (permitting  ...  We developed a symbolic verification procedure that allows us to perform the computation on an efficient BDD-based graph manipulation engine, and we report performance results for several examples.  ...  ) and a set of forbidden graphs F whether ΦF is an inductive invariant of S.  ... 
doi:10.1145/1134285.1134297 dblp:conf/icse/BeckerBGKS06 fatcat:zikgtsesvvcahjbctzxtcfbi6i

Structural Counter Abstraction [chapter]

Kshitij Bansal, Eric Koskinen, Thomas Wies, Damien Zufferey
2013 Lecture Notes in Computer Science  
We have implemented our work in a prototype tool and used it to automatically prove liveness properties of complex concurrent systems, including nonblocking algorithms such as Treiber's stack and several  ...  They can model a wide range of concurrent infinite-state systems including those with dynamic thread creation, dynamically changing communication topology, and complex shared heap structures.  ...  Our algorithmic technique of computing a numerical abstraction from an inductive invariant, introduced in this paper, promises applications beyond liveness properties.  ... 
doi:10.1007/978-3-642-36742-7_5 fatcat:xhaslsqws5dvjnlwb3syfl6ray

Inductive Invariant Checking with Partial Negative Application Conditions [chapter]

Johannes Dyck, Holger Giese
2015 Lecture Notes in Computer Science  
Acknowledgments We would like to thank the group of Annegret Habel, in particular the authors of the SeekSat/ProCon tool [15] , for allowing us to do the comparison and Leen Lambers for her work on behavior  ...  Inductive Invariant Checking Our inductive invariant checking algorithm consists of four basic steps: 1) From a composed forbidden pattern and a rule set, we create all pairs of individual forbidden patterns  ...  Inductive invariants are properties whose validity before the application of a graph rule implies their validity thereafter.  ... 
doi:10.1007/978-3-319-21145-9_15 fatcat:k4elpfx7rfdytni53adx5gibbe

Fixed-Point Definability and Polynomial Time [chapter]

Martin Grohe
2009 Lecture Notes in Computer Science  
Example Connectedness of graphs, satisfiability of Boolean circuits, the language {a n b n | n ≥ 0} 6 Abstract Logics A logic L consists of a set of sentences and a semantics that associates a property  ...  Abstract Logics A logic L consists of a set of sentences and a semantics that associates a property P φ of finite structures with each sentence φ.  ...  Application to Isomorphism Testing The k-dimensional Weisfeiler-Leman Algorithm (k-WL) is a simple combinatorial algorithm for testing isomorphism of graphs, based on an iterative "color refinement" on  ... 
doi:10.1007/978-3-642-04027-6_4 fatcat:qajggupey5dq7gnn6mp2ehekny

The Dynamic Vertex Minimum Problem and Its Application to Clustering-Type Approximation Algorithms [chapter]

Harold N. Gabow, Seth Pettie
2002 Lecture Notes in Computer Science  
Introduction Many approximation algorithms are applications of the primal-dual algorithm of Goemans and Williamson GW 11 .  ...  Here and throughout this paper n and m denote the numberofvertices and edges in the given graph, respectively.  ...  Because of this our algorithm gives the best known time bound On 2 for these applications of the GW algorithm 11 : 4-approximation for the exact tree, exact path and exact cycle partitioning problems;  ... 
doi:10.1007/3-540-45471-3_20 fatcat:cprn67x7hbbctmb5k33att6vqi

XARK

Manuel Arenaz, Juan Touriño, Ramon Doallo
2008 ACM Transactions on Programming Languages and Systems  
The application of recognition techniques is limited to string matching and replacement.  ...  Examples of applications are variable renaming and one-to-one translation between language constructs.  ...  the induction variable and an invariant.  ... 
doi:10.1145/1391956.1391959 fatcat:3tz46mhfq5ditfl6l2c27yholq

FAR-Cubicle — A new reachability algorithm for Cubicle

Sylvain Conchon, Amit Goel, Sava Krstic, Rupak Majumdar, Mattias Roux
2017 2017 Formal Methods in Computer Aided Design (FMCAD)  
We show the effectiveness and limitations of this algorithm and tradeoffs that results from it.  ...  Our algorithm iteratively builds an abstract reachability graph refining the set of reachable states from counterexamples. Refining is made through counterexample approximation.  ...  This algorithm, based on both IC3 [2] and Lazy Abstraction [3] , builds an inductive invariant by unwinding a graph (Section 3) building a forward abstract reachability of our system.  ... 
doi:10.23919/fmcad.2017.8102256 dblp:conf/fmcad/ConchonGKMR17 fatcat:6pmzxfqax5eenn5hajwisrylie

A proof system for graph (non)-isomorphism verification [article]

Milan Banković, Ivan Drecun, Filip Marić
2022 arXiv   pre-print
We analyze a state-of-the-art graph canonical labelling algorithm (described by McKay and Piperno) and formulate it in a form of a formal proof system.  ...  In order to be able to apply graph canonical labelling and isomorphism checking within interactive theorem provers, either these checking algorithms must be mechanically verified, or their results must  ...  We are very grateful to the anonymous reviewers whose insightful comments and remarks helped us to make this text much better.  ... 
arXiv:2112.14303v2 fatcat:mat2usyahzegpfxouwqvp6ujxa

Loop summarization using state and transition invariants

Daniel Kroening, Natasha Sharygina, Stefano Tonetta, Aliaksei Tsitovich, Christoph M. Wintersteiger
2012 Formal methods in system design  
This paper presents algorithms for program abstraction based on the principle of loop summarization, which, unlike traditional program approximation approaches (e.g., abstract interpretation), does not  ...  This allows for an effective exploitation of problemspecific abstract domains for summarization and, as a consequence, the precision of an abstract model may be tailored to specific verification needs.  ...  obtain an inductive invariant from a candidate.  ... 
doi:10.1007/s10703-012-0176-y fatcat:2mbdjpgqebfgxpjjfptuavj5ru

State of the art of graph-based data mining

Takashi Washio, Hiroshi Motoda
2003 SIGKDD Explorations  
ACKNOWLEDGEMENTS The authors express our deep appreciation to the reviewers and editors of this article .  ...  This framework is applicable to graph-based mining . Subgraphs and/or relations among subgraphs are pregenerated by using a graph-based mining approach, and stored in an inductive database.  ...  The newly emerging approach collects many graph invariants on a graph G, and forms a feature vector XG consisting of the graph invariants .  ... 
doi:10.1145/959242.959249 fatcat:dlwyoas4gnbbbff375bmtmcenq

Unsupervised Learning of a Probabilistic Grammar for Object Detection and Parsing

Long Zhu, Yuanhao Chen, Alan L. Yuille
2006 Neural Information Processing Systems  
Our approach is invariant to the scale and rotation of the objects. We illustrate our approach using thirteen objects from the Caltech 101 database.  ...  Moreover, our approach is very general and can be applied to a large range of objects and structures.  ...  Keck Foundation, NSF grant number 0413214, and NIH grant RO1 EY015261.  ... 
dblp:conf/nips/ZhuCY06 fatcat:jhv2clz6ifdlhg55xl6gdtrtki
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