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Fixpoint Guided Abstraction Refinement for Alternating Automata [chapter]

Pierre Ganty, Nicolas Maquet, Jean-François Raskin
2009 Lecture Notes in Computer Science  
In this paper, we develop and evaluate two new algorithms for checking emptiness of alternating automata. Those algorithms build on previous works.  ...  Second, they are abstract algorithms with built-in refinement operators based on techniques that exploit information computed by abstract fixed points (and not counter-examples as it is usually the case  ...  Abstraction Refinement Algorithm This section presents two fixpoint-guided abstraction refinement algorithms for AFA.  ... 
doi:10.1007/978-3-642-02979-0_19 fatcat:4y2ikuv6obekdii57z4qszoqxu

Efficient Decision Procedures for Model Checking of Linear Time Logic Properties [chapter]

Roderick Bloem, Kavita Ravi, Fabio Somenzi
1999 Lecture Notes in Computer Science  
We propose an algorithm for LTL model checking based on the classification of the automata and on guided symbolic search.  ...  Guided search applies hints to constrain the transition relation during fixpoint computations.  ...  Guided Search for the Computation of Greatest Fixpoints The method presented in [32] applies to the computation of least fixpoints.  ... 
doi:10.1007/3-540-48683-6_21 fatcat:z2kfkg4syrbklb7zn7g2ybgmsy

Formal property verification by abstraction refinement with formal, simulation and hybrid engines

Dong Wang, Pei-Hsin Jiang, James Kukula, Yunshan Zhu, Tony Ma, Robert Damiano
2001 Proceedings of the 38th conference on Design automation - DAC '01  
We present RFN, a formal property verification tool based on abstraction refinement. Abstraction refinement is a strategy for property verification.  ...  Third, RFN avoids the weakness of other abstraction-refinement algorithms ---finding error traces on the original design, by utilizing the error trace of the abstract model to guide sequential ATPG to  ...  First, to prove the property on abstract models containing hundreds of registers, we plan to use the overlapping partition technique from [5] [7] .  ... 
doi:10.1145/378239.378260 dblp:conf/dac/WangHLKZMD01 fatcat:er5dntyrpfgqpef2ifrhepqp3u

Abstract regular (tree) model checking

Ahmed Bouajjani, Peter Habermehl, Adam Rogalewicz, Tomáš Vojnar
2011 International Journal on Software Tools for Technology Transfer (STTT)  
In this work, we describe how various incrementally refinable abstractions on finite (word and tree) automata can be used for this purpose.  ...  Regular model checking is a generic technique for verification of infinite-state and/or parametrised systems which uses finite word automata or finite tree automata to finitely represent potentially infinite  ...  Refining Automata Abstractions We call an automata abstraction function α ′ a refinement of α iff ∀M ∈ M Σ : L(α ′ (M )) ⊆ L(α(M )).  ... 
doi:10.1007/s10009-011-0205-y fatcat:z6on6nl64reybd4rf4rrxxmljy

Space-Time Interpolants [chapter]

Goran Frehse, Mirco Giacobbe, Thomas A. Henzinger
2018 Lecture Notes in Computer Science  
We implement, for the first time, a CEGAR (counterexampleguided abstraction refinement) scheme in combination with a fixpoint detection criterion for PWA systems.  ...  Our approach We view iterative abstraction refinement as critical for soundness and precision management, and fixpoint detection as critical for evaluating unbounded properties.  ...  Acknowledgments We thank Luca Geretti for helping us setting up Ariadne.  ... 
doi:10.1007/978-3-319-96145-3_25 fatcat:3kqrmpawv5bvdbxm4fkd7vnzeu

Relational semantics of linear logic and higher-order model-checking [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
We show how to extend this result to alternating parity automata (APT) by introducing a parametric version of the exponential modality of linear logic, capturing the formal properties of colors (or priorities  ...  tree automata (ATA) of the same signature.  ...  A.2 Alternating parity tree automata From this syntactic interpretation of fixpoints over formulae, we can define a class of automata corresponding to modal µ-calculus, namely alternating parity automata  ... 
arXiv:1501.04789v3 fatcat:4yd3ryhkpzgzfhpy52fctlmglq

McScM: A General Framework for the Verification of Communicating Machines [chapter]

Alexander Heußner, Tristan Le Gall, Grégoire Sutre
2012 Lecture Notes in Computer Science  
Our verification tool implements several modelchecking techniques: CEGAR with different abstraction-refinement methods, abstract interpretation, abstract regular model checking, and lazy abstraction.  ...  implement new ideas on a high level of abstraction.  ...  of the system by symbolic successor (or predecessor) calculation; we reimplemented the basic idea in our setting; cegar: Counterexample Guided Abstraction Refinement is a semi-algorithmic approach that  ... 
doi:10.1007/978-3-642-28756-5_34 fatcat:n5mqloosaffj5dqnzse6htx7um

Counterexample-Guided Refinement of Template Polyhedra [chapter]

Sergiy Bogomolov, Goran Frehse, Mirco Giacobbe, Thomas A. Henzinger
2017 Lecture Notes in Computer Science  
They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata.  ...  We evaluate our method on several benchmarks, demonstrating also its superior efficiency for the special case of linear hybrid automata.  ...  Science Fund (FWF) under grants S11402-N23 (RiSE/SHiNE) and Z211-N23 (Wittgenstein Award), by the European Commission under grant 643921 (UnCoVerCPS), and by the ARC project DP140104219 (Robust AI Planning for  ... 
doi:10.1007/978-3-662-54577-5_34 fatcat:ps4gevekdreuzoknnsvuox5cxq

Symbolic guided search for CTL model checking

Roderick Bloem, Kavita Ravi, Fabio Somenzi
2000 Proceedings of the 37th conference on Design automation - DAC '00  
We show how to use hints to obtain overapproximations useful for greatest fixpoints, and we present the first results for backward search.  ...  Symbolic Guided Search applies hints to guide the exploration of the state space.  ...  Incremental Fixpoint Update An alternative to using underapproximations for least fixpoints and overapproximations for greatest fixpoints is to use incremental model checking.  ... 
doi:10.1145/337292.337306 dblp:conf/dac/BloemRS00 fatcat:5re4jlsm7zec5fwd3glnb6ibam

Fixed point guided abstraction refinement for alternating automata

Pierre Ganty, Nicolas Maquet, Jean-François Raskin
2010 Theoretical Computer Science  
Those abstract domains and their refinement operators can be used both in forward and backward algorithms for checking emptiness of alternating automata.  ...  This abstract refinement method does not use counter-examples to refine inconclusive abstractions contrary to most of the methods presented and implemented in the literature; see for example [4] .  ...  Acknowledgements The authors would like to thank Gilles Geeraerts for some fruitful discussions on the abstraction scheme. The second author is supported by an FNRS-FRIA grant.  ... 
doi:10.1016/j.tcs.2010.05.037 fatcat:ojvndzw3zbavholhq7zfryptsi

Modal Mu-Calculus [chapter]

Colin Stirling
2001 Texts in Computer Science  
In this section, we outline the historical context for Lµ.  ...  This line of work has, of course, continued and flourished, and today there are highly sophisticated theories for proving properties of programs, with equally sophisticated machine support for these theories  ...  We define alternating parity automata for this purpose following, for example, [40] .  ... 
doi:10.1007/978-1-4757-3550-5_5 fatcat:mfjlygtmd5e6lbmjdhr73oaisa

Automatic Abstraction Using Generalized Model Checking [chapter]

Patrice Godefroid, Radha Jagadeesan
2002 Lecture Notes in Computer Science  
In this paper, we show how generalized model checking can extend existing automatic abstraction techniques (such as predicate abstraction) for model checking concurrent/reactive programs and yield the  ...  We study the cost needed to improve precision by presenting new upper and lower bounds for the complexity of generalized model checking in the size of the abstraction.  ...  Iterative abstraction refinement [1, 9, 13] in the context of predicate abstraction [12] is a process for automatically refining an abstraction that is guided by spurious counter-examples found at  ... 
doi:10.1007/3-540-45657-0_11 fatcat:pq2p3k4hgjcvbef35ziwvs3kta

Weak MSO

Facundo Carreiro, Alessandro Facchini, Yde Venema, Fabio Zanasi
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
Our proof is automata-theoretic in nature; in particular, we introduce a class of automata characterizing the expressive power of WMSO over tree models of arbitrary branching degree.  ...  We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal µ-calculus where the application of the least fixpoint operator µp.ϕ  ...  We say that f is a winning strategy for Π if (i) for each f -guided match, the moves suggested by f are always available to Π and (ii) Π wins each f -guided match of the game.  ... 
doi:10.1145/2603088.2603101 dblp:conf/csl/CarreiroFVZ14 fatcat:samjqdeccfhjhmnatz6vxmq7vm

Some Experience on the Software Engineering of Abstract Interpretation Tools

Bertrand Jeannet
2010 Electronical Notes in Theoretical Computer Science  
solver (Fixpoint), and two different abstract domains.  ...  The expected advantages of such a modular structure is the ability of sharing development efforts between analyzers for different languages, using common solvers and abstract domains.  ...  New input language: the Fixpoint solver fit the need of our three analyzers of Fig. 2 , although they addresses different analysis challenges: partition refinement for tuning the precision/efficiency  ... 
doi:10.1016/j.entcs.2010.09.016 fatcat:hgashqs4nzbfzohpleybbx3gs4

Dynamic Partitioning in Linear Relation Analysis. Application to the Verification of Synchronous Programs

Bertrand Jeannet
2000 BRICS Report Series  
The presented approach is quite general and can be applied to other abstract interpretations.  ...  </p><p>Keywords and Phrases: Abstract Interpretation, Partitioning,<br />Linear Relation Analysis, Reactive Systems, Program Verification</p>  ...  Acknowledgment I thank Nicolas Halbwachs and Pascal Raymond for their valuable advices and for many helpful discussions and suggestions.  ... 
doi:10.7146/brics.v7i38.20204 fatcat:5h227iocabhsdfw5a35ymzdwzy
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