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Policy Iteration-Based Conditional Termination and Ranking Functions [chapter]

Damien Massé
2014 Lecture Notes in Computer Science  
We show that it can work on programs admitting a specific kind of segmented ranking functions, and that the results can be checked by the construction of a disjunctive ranking relation.  ...  This method is not based on ranking functions and does not directly provide a ranking relation, which makes the comparison with existing approaches difficult.  ...  Policy iteration Policy or strategy iteration [10, 18, 19] is a method to compute the least (or greatest) fixpoint of specific classes of monotonic operators.  ... 
doi:10.1007/978-3-642-54013-4_25 fatcat:qrikdn3ylbbbvnl7cegsy3c4ny

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
However, applying data-driven inference to nonlinear loop invariants is challenging due to the large numbers of and magnitudes of high-order terms, the potential for overfitting on a small number of samples  ...  We incorporate these methods into a nonlinear loop invariant inference system that can learn general nonlinear loop 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

Why does Astrée scale up?

Patrick Cousot, Radhia Cousot, Jérôme Feret, Laurent Mauborgne, Antoine Miné, Xavier Rival
2009 Formal methods in system design  
What makes ASTRÉE such an innovative tool is its scalability, while retaining the required precision, when it is used to analyze a specific class of programs: that of reactive control-command software.  ...  ASTRÉE was the first static analyzer able to prove automatically the total absence of runtime errors of actual industrial programs of hundreds of thousand lines.  ...  They feature a lower and predictable quadratic-memory and cubic-time complexity, as well as a fast yet sound floating-point implementation [44] .  ... 
doi:10.1007/s10703-009-0089-6 fatcat:lf5bl7rtznfjtlriqu62gvs35m

Geometric Quantifier Elimination Heuristics for Automatically Generating Octagonal and Max-plus Invariants [chapter]

Deepak Kapur, Zhihai Zhang, Matthias Horbach, Hengjun Zhao, Qi Lu, ThanhVu Nguyen
2013 Lecture Notes in Computer Science  
automatic generation of a subclass of disjunctive invariants for imperative programs as well.  ...  This approach has been generalized to consider disjunctive invariants of the similar form, expressed using maximum function (such as max(x + a, y + b, z + c, d) ≤ max(x + e, y + f, z + g, h)), thus enabling  ...  To keep the quantifier elimination procedure fast (quadratic in the number of program variables), the verification condition is approximated using a geometric heuristic (Section 2.5). 4.  ... 
doi:10.1007/978-3-642-36675-8_11 fatcat:azi6olpq6fbllpgacgoeqhvzle

An Algorithm Inspired by Constraint Solvers to Infer Inductive Invariants in Numeric Programs [chapter]

Antoine Miné, Jason Breck, Thomas Reps
2016 Lecture Notes in Computer Science  
This paper addresses the problem of proving a given invariance property ϕ of a loop in a numeric program, by inferring automatically a stronger inductive invariant ψ.  ...  As in abstract interpretation, it computes the effect of a loop using a numeric abstract domain.  ...  a novel search algorithm inspired from constraint programming, and (ii) proposes a novel method to introduce disjunctions.  ... 
doi:10.1007/978-3-662-49498-1_22 fatcat:54lc5y7cljgnbdenlu2tlcm6xa

Timing analysis enhancement for synchronous program

Pascal Raymond, Claire Maiza, Catherine Parent-Vigouroux, Fabienne Carrier
2013 Proceedings of the 21st International conference on Real-Time Networks and Systems - RTNS '13  
Thus, a large part of semantic information, known at the design level, is lost due to the compilation scheme (typically organized in two stages, from high-level model to C, and then binary code).  ...  We integrate an existing verification tool to check the feasibility of the worst-case path.  ...  , while abstracting away real-time concerns (does the system compute fast enough?).  ... 
doi:10.1145/2516821.2516841 dblp:conf/rtns/RaymondMPC13 fatcat:ab4hras6zzfanpbt6pk3jsf2de

Liveness by Invisible Invariants [chapter]

Yi Fang, Kenneth L. McMillan, Amir Pnueli, Lenore D. Zuck
2006 Lecture Notes in Computer Science  
The method of Invisible Invariants was developed in order to verify safety properties of parametrized systems in a fully automatic manner.  ...  In this paper, we apply the method of invisible invariant to "bounded response" properties, i.e., liveness properties of the type p =⇒ ½ q that are bounded -once a p-state is reached, it takes a bounded  ...  However, the invisible ranking method requires numerous auxiliary construct, some (especially the pre-order) are at times hard to compute. The method proposed here is much simpler.  ... 
doi:10.1007/11888116_26 fatcat:mr5ph4prsvgl3gm6zmxhufhtvm

Extending Constraint-Only Representation of Polyhedra with Boolean Constraints [chapter]

Alexey Bakhirkin, David Monniaux
2018 Lecture Notes in Computer Science  
We propose a new relational abstract domain for analysing programs with numeric and Boolean variables.  ...  This way, an abstract element can still be seen as an implicit map from a partition of B m to convex polyhedra (similar to a BddApron element), but we do not have to duplicate storage and computations  ...  "Raytracing" [24] is a fast method to identify redundancies, but it degenerates into the conventional linear programming approach in the worst case).  ... 
doi:10.1007/978-3-319-99725-4_10 fatcat:efrs4fdk3jegtcjoyoayzo24qm

On theorem proving for program checking

Maria Paola Bonacina
2010 Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '10  
This article is a survey of recent results, related works and new challenges in automated theorem proving for program checking.  ...  The aim is to give some historical perspective, albeit necessarily incomplete, and highlight some of the turning points that made crucial advances possible.  ...  Introduction The design of computer programs that check whether other computer programs satisfy given properties is a central quest in computer science.  ... 
doi:10.1145/1836089.1836090 dblp:conf/ppdp/Bonacina10 fatcat:mh3666vskfcxvgnisxp7hnwvi4

Learning invariants using decision trees and implication counterexamples

Pranav Garg, Daniel Neider, P. Madhusudan, Dan Roth
2016 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016  
We implement the learners and an appropriate teacher, and show that they are scalable, efficient and convergent in synthesizing adequate inductive invariants in a suite of more than 50 programs.  ...  Inductive invariants can be robustly synthesized using a learning model where the teacher is a program verifier who instructs the learner through concrete program configurations, classified as positive  ...  Additionally, the tool searches for numerical invariants that have constant thresholds that belong to a small bag of values (typically of size three to five) that are mined from the program code.  ... 
doi:10.1145/2837614.2837664 dblp:conf/popl/0001NMR16 fatcat:jyemnddvovfchguduprxl54ygi

Learning invariants using decision trees and implication counterexamples

Pranav Garg, Daniel Neider, P. Madhusudan, Dan Roth
2016 SIGPLAN notices  
We implement the learners and an appropriate teacher, and show that they are scalable, efficient and convergent in synthesizing adequate inductive invariants in a suite of more than 50 programs.  ...  Inductive invariants can be robustly synthesized using a learning model where the teacher is a program verifier who instructs the learner through concrete program configurations, classified as positive  ...  Additionally, the tool searches for numerical invariants that have constant thresholds that belong to a small bag of values (typically of size three to five) that are mined from the program code.  ... 
doi:10.1145/2914770.2837664 fatcat:spjkoqyf45eolbwqxwzftfasxu

Relational Abstractions for Continuous and Hybrid Systems [chapter]

Sriram Sankaranarayanan, Ashish Tiwari
2011 Lecture Notes in Computer Science  
A relational abstraction is obtained by replacing the continuous dynamics in each mode by a binary transition relation that relates a state of the system to any state that can potentially be reached at  ...  We present the basic underpinnings of our approach and demonstrate its use on many benchmark systems to derive simple and usable abstractions.  ...  Progress invariants were used to compute complexity bounds of programs.  ... 
doi:10.1007/978-3-642-22110-1_56 fatcat:q4d5uqvzljdi7p6uc6lxpcpeqi

A Logical Product Approach to Zonotope Intersection [chapter]

Khalil Ghorbal, Eric Goubault, Sylvie Putot
2010 Lecture Notes in Computer Science  
This fixes a known drawback of zonotopic methods, as used for reachability analysis for hybrid sys- tems as well as for invariant generation in abstract interpretation: intersection of zonotopes are not  ...  We describe some examples and an im- plementation of our method in the APRON library, and discuss some further in- teresting combinations of zonotopes with non-linear or non-convex domains such as quadratic  ...  Introduction Zonotopic abstractions are known to give fast and accurate over-approximations in invariant synthesis for static analysis of programs, as introduced by the authors [10, 11, 7] , as well as  ... 
doi:10.1007/978-3-642-14295-6_22 fatcat:opdbpzxj35ai7aif3chrbdwbea

Verification and falsification of programs with loops using predicate abstraction

Daniel Kroening, Georg Weissenbacher
2009 Formal Aspects of Computing  
We present a novel technique that speeds up the detection of long counterexamples as well as the verification of programs with loops.  ...  In many cases, predicate abstraction suffers from the need for at least one predicate for each iteration of a loop construct in the program.  ...  Thomas Wahl deserves a special note of thanks for his thorough reading and his insightful comments on this paper.  ... 
doi:10.1007/s00165-009-0110-2 fatcat:wwd3wjrylbb6vceuyavmythcv4

A Quantifier Elimination Algorithm for Linear Real Arithmetic [chapter]

David Monniaux
2008 Lecture Notes in Computer Science  
The quantifier elimination algorithm presented in the paper is compared, on examples arising from program analysis problems and on random examples, to several other implementations, all of which cannot  ...  We propose a new quantifier elimination algorithm for the theory of linear real arithmetic.  ...  Examples produced from problems of program analysis following our method for the parametric computation of least invariants.  ... 
doi:10.1007/978-3-540-89439-1_18 fatcat:y2eqvag35fhojc77awt3qgmyxm
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