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Solving Invariant Generation for Unsolvable Loops [article]

Daneshvar Amrollahi, Ezio Bartocci, George Kenison, Laura Kovács, Marcel Moosbrugger, Miroslav Stankovič
2022 arXiv   pre-print
In this paper we establish a technique for invariant synthesis for loops that are not solvable, termed unsolvable loops.  ...  Whilst the problem is in general undecidable, the goal is settled for restricted classes of loops.  ...  for program variables by solving the recurrences; and (iii) compute polynomial invariants by eliminating the loop counter n from the closed-forms.  ... 
arXiv:2206.06943v1 fatcat:bw7kuqfumbgdxokiylozk4txxe

PKind: A parallel k-induction based model checker

Temesghen Kahsai, Cesare Tinelli
2011 Electronic Proceedings in Theoretical Computer Science  
PKind is a novel parallel k-induction-based model checker of invariant properties for finite- or infinite-state Lustre programs.  ...  Its architecture, which is strictly message-based, is designed to minimize synchronization delays and easily accommodate the incorporation of incremental invariant generators to enhance basic k-induction  ...  Looking at the previously unsolved benchmarks, with a timeout of 100s, both invariant generation modes solve 66% of them.  ... 
doi:10.4204/eptcs.72.6 fatcat:4ecasevjirb7zfm76o43bozrs4

Instantiation-Based Invariant Discovery [chapter]

Temesghen Kahsai, Yeting Ge, Cesare Tinelli
2011 Lecture Notes in Computer Science  
We present a general scheme for automated instantiation-based invariant discovery.  ...  Our experimental results show that both specializations are able to quickly produce invariants from a variety of synchronous systems which prove quite useful in proving safety properties for these systems  ...  that remain unsolved, either because KIND-INV was not able to generate an invariant for them or because the generated invariant is not helpful.  ... 
doi:10.1007/978-3-642-20398-5_15 fatcat:a25yhwi6znd73firfcmsf3ij64

SynRG: Syntax Guided Synthesis of Expressions with Alternating Quantifiers [article]

Elizabeth Polgreen, Sanjit A. Seshia
2020 arXiv   pre-print
Program synthesis techniques have been used to automate the generation of loop invariants in code, synthesize function summaries, and to assist programmers via program sketching.  ...  We present SynRG, a synthesis algorithm based on restricting the synthesis problem to generate candidate solutions with quantification over a finite domain, and then generalizing these candidate solutions  ...  The benchmarks we are unable to solve are unsolvable for one of two reasons: Linear relationships between array indices: Firstly, we were unable to solve some examples due to constant difference relationships  ... 
arXiv:2007.10519v2 fatcat:js7k2z2fzfdfjap4s2rjgba6ry

Page 1321 of Automation and Remote Control Vol. 53, Issue 9 [page]

1992 Automation and Remote Control  
Let us list some unsolved problems. 1. Weighted Sensitivity Problem. Synthesize a controller that minimizes the reactivity of the closed-loop system subject to robustness constraints.  ...  closed-loop transfer functions, C, is the bound on the uncertainty of the open-loop transfer function, and C; is the reactivity of the closed-loop system with respect to additive noise.  ... 

A Heuristic Approach to Program Verification

Shmuel Katz, Zohar Manna
1973 International Joint Conference on Artificial Intelligence  
), and another in which we generate the inductive assertion directly from the statements of the loop (bottom-up approach).  ...  We present various heuristic techniques for use in proving the correctness of computer programs.  ...  Clearly, any conjunct in the inductive assertion of a loop must be an invariant of the loop.  ... 
dblp:conf/ijcai/KatzM73 fatcat:vvm5vgydd5bmvmfwslfthef7am

The Cutting Pattern Problem for Tetrahedral Mesh Generation [chapter]

Xiaotian Yin, Wei Han, Xianfeng Gu, Shing-Tung Yau
2011 Proceedings of the 20th International Meshing Roundtable  
For all the proposed algorithms, the convergence is validated and the complexity is analyzed.  ...  For each type of boundary conditions, we provide efficient algorithms to compute valid assignments if there is any, or report the obstructions otherwise.  ...  The authors would like to acknowledge and thank the anonymous reviewers for their insightful and constructive comments.  ... 
doi:10.1007/978-3-642-24734-7_12 dblp:conf/imr/YinHGY11 fatcat:scr6r6rtnbeofnzefuuupx2wla

Page 2038 of Mathematical Reviews Vol. 57, Issue 5 [page]

1979 Mathematical Reviews  
It appears to the reviewer that the approach presented can be applied, in at least some cases, both for time-invariant and for time-varying linear systems, but that a number of questions remain unsolved  ...  The author derives a canonical expression for the closed-loop transfer function matrix of a linear, time-invariant feedback sys- tem of the standard form.  ... 


Jiang Ming, Dongpeng Xu, Li Wang, Dinghao Wu
2015 Proceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security - CCS '15  
This paper introduces LOOP, a Logic Oriented Opaque Predicate detection tool for obfuscated binary code.  ...  We have developed a prototype of LOOP and evaluated it with a range of common utilities and obfuscated malicious programs. Our experimental results demonstrate the efficacy and generality of LOOP.  ...  ACKNOWLEDGMENTS We thank the ACM CCS 2015 anonymous reviewers and Bill Harris for their valuable feedback.  ... 
doi:10.1145/2810103.2813617 dblp:conf/ccs/MingXWW15 fatcat:ect2muhnsvejthbgktnpbeiqn4

Fast Downward Aidos: Code and Planner Abstract [article]

Jendrik Seipp, Florian Pommerening, Silvan Sievers, Martin Wehrle, Chris Fawcett, Yusra Alkhazraji
2020 Zenodo  
See the included file for instructions on how to run the planner.  ...  Three variants of the planner participated in the 2016 Unsolvability International Planning Competition and all of them proved more tasks unsolvable than all other competitors.  ...  We are especially grateful to Malte Helmert, not only for his work on Fast Downward, but also for many fruitful discussions about the unsolvability IPC.  ... 
doi:10.5281/zenodo.4058212 fatcat:qn5rhddkizbofpeuisv6oopkre

LoopInvGen: A Loop Invariant Generator based on Precondition Inference [article]

Saswat Padhi and Rahul Sharma and Todd Millstein
2019 arXiv   pre-print
We describe the LoopInvGen tool for generating loop invariants that can provably guarantee correctness of a program with respect to a given specification.  ...  In contrast to existing techniques, LoopInvGen is not restricted to a fixed set of features -- atomic predicates that are composed together to build complex loop invariants.  ...  ACKNOWLEDGMENT We thank the organizers of SyGuS-Comp for making all the solvers and benchmarks publicly available.  ... 
arXiv:1707.02029v4 fatcat:mywfv2j3x5c7vdkxpvq67cjx5e

Topology: The Poincaré conjecture proved

Ian Stewart
1986 Nature  
invariants may be constructed using 'loops' (actually spheres) of higher dimension.  ...  And their pioneering effort paves the way, at last, for a detailed understanding not just of the threesphere, but of three-manifolds in general.  ... 
doi:10.1038/320517a0 fatcat:r6uvfelpkze6pdsiqvybznftki

The Static Analysis of Linear Loops

Michael Lvov, Yulia Tarasich
2015 International Conference on Information and Communication Technologies in Education, Research, and Industrial Applications  
In the first part of the paper, we consider the problem of generation of polynomial invariants of iterative loops with operator of initialization of loop and non-singular linear operator in the loop body  ...  In the article we also show the algorithm for calculating the basic invariants for linear operator of the Jordan cell, and an algorithm for calculating the basic invariants of diagonalizable linear operator  ...  In [16] [17] , general iterative methods are used to solve the problem of searching for linear invariant inequalities.  ... 
dblp:conf/icteri/LvovT15 fatcat:uibpm2dec5glnnekjcampz6pha

Learning Nonlinear Loop Invariants with Gated Continuous Logic Networks (Extended Version) [article]

Jianan Yao, Gabriel Ryan, Justin Wong, Suman Jana, Ronghui Gu
2020 arXiv   pre-print
We incorporate these methods into a nonlinear loop invariant inference system that can learn general nonlinear loop invariants.  ...  Recently, data-driven methods for loop invariant inference have shown promise, especially on linear invariants.  ...  Acknowledgements The authors are grateful to our shepherd, Aditya Kanade, and the anonymous reviewers for valuable feedbacks that improved this paper significantly.  ... 
arXiv:2003.07959v4 fatcat:j3m343yaqjbyhjwadw4swoes4u

Non-Local Properties in Euclidean Quantum Gravity [chapter]

Giampiero Esposito
1996 Quantum Field Theory Under the Influence of External Conditions  
In the one-loop approximation for Euclidean quantum gravity, the boundary  ...  Dowker, Hugh Luckock, Ian Moss, Stephen Poletti and Dmitri Vassilevich for correspondence.  ...  Acknowledgments I am indebted to Peter D'Eath, Alexander Kamenshchik, Igor Mishakov and Giuseppe Pollifrone for scientic collaboration on the evaluation of trace anomalies, and to Andrei Barvinsky, Stuart  ... 
doi:10.1007/978-3-663-01204-7_41 fatcat:ykwvx4v6uffibci7oucqszoiya
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