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Counterexample-Guided Refinement of Template Polyhedra [chapter]

Sergiy Bogomolov, Goran Frehse, Mirco Giacobbe, Thomas A. Henzinger
2017 Lecture Notes in Computer Science  
Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions.  ...  While previously, the choice of directions has been left to the user or a heuristic, we present a method for the automatic discovery of directions that generalize and eliminate spurious counterexamples  ...  Counterexample-guided methods have been developed, but not for template polyhedra [15, 4, 19, 7] . Second, they partition and bound the time domain.  ... 
doi:10.1007/978-3-662-54577-5_34 fatcat:ps4gevekdreuzoknnsvuox5cxq

Space-Time Interpolants [chapter]

Goran Frehse, Mirco Giacobbe, Thomas A. Henzinger
2018 Lecture Notes in Computer Science  
Template polyhedra, on the other hand, can be adapted flexibly and can be unbounded, but sound template refinement for unbounded reachability analysis has been implemented only for systems with piecewise  ...  Promising abstraction techniques usually employ interval methods or template polyhedra.  ...  Checking this is a crucial element of a counterexample-guided abstraction refinement routine.  ... 
doi:10.1007/978-3-319-96145-3_25 fatcat:3kqrmpawv5bvdbxm4fkd7vnzeu

Lifting CDCL to Template-Based Abstract Domains for Program Verification [chapter]

Rajdeep Mukherjee, Peter Schrammel, Leopold Haller, Daniel Kroening, Tom Melham
2017 Lecture Notes in Computer Science  
This is the first instantiation of CDCL with a template polyhedra abstract domain.  ...  We instantiate the model search and conflict analysis algorithms with an abstract domain of template polyhedra, strictly generalizing CDCL from the Boolean lattice to a richer lattice structure.  ...  ACDLP is implemented in C++ on top of the CPROVER [12] framework as an extension of 2LS [27] and consists of around 9 KLOC. The template polyhedra domain is implemented in C++ in 10 KLOC.  ... 
doi:10.1007/978-3-319-68167-2_21 fatcat:vr627k7yrrahhabdsuvlfro7am

Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis [chapter]

Anastasiia Izycheva, Eva Darulova, Helmut Seidl
2020 Lecture Notes in Computer Science  
Unlike previous approaches that rely on policy iteration, linear algebra or semi-definite programming, we propose a heuristic procedure based on simulation and counterexample-guided refinement.  ...  Our procedure generates invariants of the form of a convex polynomial inequality that tightly bounds the values of loop variables.  ...  We use concrete executions and polynomial approximation in order to obtain candidate invariants which, when combined with counterexample-guided refinement, allows us to synthesize invariants for floating-point  ... 
doi:10.1007/978-3-030-65474-0_8 fatcat:g62rmena2ranrmrobp6jmwqhde

Lifting CDCL to Template-based Abstract Domains for Program Verification [article]

Rajdeep Mukherjee, Peter Schrammel, Leopold Haller, Daniel Kroening, Tom Melham
2017 arXiv   pre-print
This is the first instantiation of CDCL with a template polyhedra abstract domain.  ...  We instantiate the model search and conflict analysis algorithms to an abstract domain of template polyhedra, strictly generalizing CDCL from the Boolean lattice to a richer lattice structure.  ...  Template Polyhedra Abstract Domain An abstract value of the template polyhedra domain [26] represents a set X of values of the vector x of numerical (bitvector) variables NVars of their respective data  ... 
arXiv:1707.02011v1 fatcat:sxk2gznl5rbn7juasvhbmtmbmy

Efficient Dynamic Error Reduction for Hybrid Systems Reachability Analysis [chapter]

Stefan Schupp, Erika Ábrahám
2018 Lecture Notes in Computer Science  
In this paper we propose a CEGAR approach that takes as input a user-defined ordered list of search configurations, which are used to dynamically refine the search tree along potentially spurious counterexamples  ...  Naturally, faster computations come with less precision and more spurious counterexamples.  ...  In [6] the authors present a method to automatically derive template directions when using template polyhedra as a state set representation in a CEGAR refinement fashion during analysis.  ... 
doi:10.1007/978-3-319-89963-3_17 fatcat:mfjnx36pgzgxlajzknckxomhzu

Counterexample Guided Abstraction Refinement for Stability Analysis [chapter]

Pavithra Prabhakar, Miriam García Soto
2016 Lecture Notes in Computer Science  
In this paper, we present a counterexample guided abstraction refinement (Cegar) algorithm for stability analysis of polyhedral hybrid systems.  ...  We compare the Cegar algorithm with Averist and report experimental results demonstrating the benefits of counterexample guided refinement.  ...  BES-2013-065076 from the Spanish Ministry of Economy and Competitiveness to Miriam García Soto.  ... 
doi:10.1007/978-3-319-41528-4_27 fatcat:xgzagrysqfa7towyqz2ajwnteq

From Tests to Proofs [chapter]

Ashutosh Gupta, Rupak Majumdar, Andrey Rybalchenko
2009 Lecture Notes in Computer Science  
The strengthening comes in the form of additional linear constraints that trigger a series of simplifications in the solver, and make solving more scalable.  ...  We describe the design and implementation of an automatic invariant generator for imperative programs.  ...  In the counterexample-guided abstraction refinement (CEGAR) approach [1, 16] , one starts with a set of predicates, and uses spurious counterexamples produced by model checking to dynamically discover  ... 
doi:10.1007/978-3-642-00768-2_24 fatcat:tk6pva566vdnnalassuia6gnz4

From tests to proofs

Ashutosh Kumar Gupta, Rupak Majumdar, Andrey Rybalchenko
2012 International Journal on Software Tools for Technology Transfer (STTT)  
The strengthening comes in the form of additional linear constraints that trigger a series of simplifications in the solver, and make solving more scalable.  ...  We describe the design and implementation of an automatic invariant generator for imperative programs.  ...  In the counterexample-guided abstraction refinement (CEGAR) approach [1, 16] , one starts with a set of predicates, and uses spurious counterexamples produced by model checking to dynamically discover  ... 
doi:10.1007/s10009-012-0267-5 fatcat:mw6t5dizbzcfxdoxcvse4dowhu

Data-driven Numerical Invariant Synthesis with Automatic Generation of Attributes [article]

Ahmed Bouajjani and Wael-Amine Boutglay and Peter Habermehl
2022 arXiv   pre-print
The main issue we address is the discovery of relevant attributes to be used in the learning process of numerical invariants. We define a method for solving this problem guided by the data sample.  ...  The generalization mechanism of the decision tree learning from the constraints of the separator allows the inference of general invariants, accurate enough for proving the targeted property.  ...  In more theoretical work, an abstract learning framework for synthesis, introduced in [20] , incorporates the principle of CEGIS (counterexample-guided inductive synthesis).  ... 
arXiv:2205.14943v2 fatcat:2ag7fvwevbf5rasonc4dkascwi

On the decidability of the existence of polyhedral invariants in transition systems

David Monniaux
2018 Acta Informatica  
For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear (in)equalities.  ...  Forty years of research on convex polyhedral invariants have focused, on the one hand, on identifying "easier" subclasses, on the other hand on heuristics for finding general convex polyhedra.  ...  Here, we instead consider the problem that abstract interpreters (or other classes of tools, for instance those based on counterexample-guided abstraction refinement) solve heuristically: finding an invariant  ... 
doi:10.1007/s00236-018-0324-y fatcat:joojwuxvvzguddmcv2gmaz7aru

On the decidability of the existence of polyhedral invariants in transition systems [article]

David Monniaux
2018 arXiv   pre-print
Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties.For numerical properties, a classical class of invariants is convex polyhedra: solution  ...  sets of system of linear (in)equalities.Forty years of research on convex polyhedral invariants have focused, on the one hand, on identifying "easier" subclasses, on the other hand on heuristics for finding  ...  Here, we instead consider the problem that abstract interpreters (or other classes of tools, for instance those based on counterexample-guided abstraction refinement) solve heuristically: finding an invariant  ... 
arXiv:1709.04382v2 fatcat:yenlr65wcfbb7msi5ek4kyofci

Sum of Abstract Domains [chapter]

Gianluca Amato, Simone Di Nardo Di Maio, Francesca Scozzari
2015 Lecture Notes in Computer Science  
We provide a general framework equipped with all the necessary abstract operators for static analysis of imperative languages.  ...  In the abstract interpretation theory, program properties are encoded by abstract domains, and the combination of abstract domains leads to new properties to be analyzed.  ...  polyhedra template [16] .  ... 
doi:10.1007/978-3-319-17524-9_4 fatcat:x7zrpecxmrgzrghbkt3lzvr4t4

Unbounded-Time Safety Verification of Guarded LTI Models with Inputs by Abstract Acceleration

Dario Cattaruzza, Alessandro Abate, Peter Schrammel, Daniel Kroening
2020 Journal of automated reasoning  
concrete counterexamples for refinement based on the given safety specification.  ...  We achieve this using counterexample-guided Abstract Acceleration: this approach over-approximates the reachability tube of the LTI model over an unbounded time horizon by using abstraction, possibly finding  ...  Acknowledgements University of Oxford; We would like to thank Colas Le Guernic for his constructive  ... 
doi:10.1007/s10817-020-09562-z pmid:33678930 pmcid:PMC7900086 fatcat:sqhhutyr4bao3fdpbyhn3s3qae

Decision Tree Learning in CEGIS-Based Termination Analysis [chapter]

Satoshi Kura, Hiroshi Unno, Ichiro Hasuo
2021 Lecture Notes in Computer Science  
Our algorithm is integrated into the workflow of CounterExample Guided Inductive Synthesis (CEGIS).  ...  Our main novelty is in the design of a synthesizer: building on top of a usual decision tree learning algorithm, our algorithm detects cycles in a set of example transitions and uses them for refining  ...  We study synthesis of ranking functions by CounterExample Guided Inductive Synthesis (CEGIS) [29] .  ... 
doi:10.1007/978-3-030-81688-9_4 fatcat:idnriwqpo5fv3i5ts6h23f7chi
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