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Ideal Abstractions for Well-Structured Transition Systems [chapter]

Damien Zufferey, Thomas Wies, Thomas A. Henzinger
2012 Lecture Notes in Computer Science  
Many infinite state systems can be seen as well-structured transition systems (WSTS), i.e., systems equipped with a well-quasi-ordering on states that is also a simulation relation.  ...  Our analysis is an abstract interpretation whose abstract domain builds on the ideal completion of the well-quasi-ordered state space, and a widening operator that mimics acceleration and controls the  ...  Conclusion We proposed a novel abstract interpretation framework to compute precise approximations of the covering set of WSTS.  ... 
doi:10.1007/978-3-642-27940-9_29 fatcat:6e7uezo7sjelti2ed2dug47wvi

Well-abstracted transition systems: application to FIFO automata

Alain Finkel, S. Purushothaman Iyer, Grégoire Sutre
2003 Information and Computation  
We propose the use of abstractions as a general framework to design accelerations. We investigate SemiLinear Regular Expressions (SLREs) as symbolic representations for FIFO automata.  ...  In the case of infinite state systems, there has been a great deal of interest in accelerations -a technique for characterizing the result of iterating an execution sequence an arbitrary number of times  ...  version of Well-Abstracted Transition Systems published in CONCURÕ2000 proceedings.  ... 
doi:10.1016/s0890-5401(02)00027-5 fatcat:jdkiefwb4zd3xohy6y7jbgl7rq

Long time correlation and localization transition in quantum double well systems
6pTA-8 二重井戸型ポテンシャル系における長時間相関と局在化転移(その他の量子力学系,領域11)

Ken-ichi Aoki, Atsushi Horikoshi, Kazuhiko Sakakibara
2002 Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu)  
systems Kanmwa Univ. 、 Nare Co皿.  ...  6pTA − 8 二 重 井戸 型 ポ テ ン シ ャ ル 系 に お け る 長 時 間 相 関 と 局 在 化 転 移 金沢 大理 A , 金 沢大 自然 B , 奈 良高 専 c 青 木 健 一A , °堀 越篤 史 E , 榊 原 和 彦 c Leag time cone ] atLoll 邑皿d LocalizatiDn tra "slLion in guantum dDub] e well  ... 
doi:10.11316/jpsgaiyo.57.2.2.0_219_2 fatcat:v23divjq4rdzjkgb7e5w5rd2pu

Infinite-State Liveness-to-Safety via Implicit Abstraction and Well-Founded Relations [chapter]

Jakub Daniel, Alessandro Cimatti, Alberto Griggio, Stefano Tonetta, Sergio Mover
2016 Lecture Notes in Computer Science  
We present a fully-symbolic LTL model checking approach for infinite-state transition systems.  ...  The algorithm iterates by attempting to remove spurious abstract fair loops: either it finds new predicates, to avoid spurious abstract prefixes, or it introduces new well-founded relations, based on the  ...  Once the abstract transition relation is computed, any algorithm for finite-state systems can be applied.  ... 
doi:10.1007/978-3-319-41528-4_15 fatcat:ge3dpqfpdvcx5h66cpfeclrhbu

From Well Structured Transition Systems to Program Verification

Alain Finkel
2020 Electronic Proceedings in Theoretical Computer Science  
Well Structured Transition Systems Well structured transition systems: wqo and monotony An ordered (labeled) transition system is a triple (X , Σ − →, ≤) such that (X , Σ − →) is a (labeled) transition  ...  A short story of well structured transition systems Well structured transition systems (initially called structured transition systems in [10] ) were initially defined and studied as monotone transition  ... 
doi:10.4204/eptcs.320.3 fatcat:ex6susvyvvajjpgy7vqstaoeaq

Terminator: Beyond Safety [chapter]

Byron Cook, Andreas Podelski, Andrey Rybalchenko
2006 Lecture Notes in Computer Science  
., program analysis tools based on predicate abstraction, pushdown model checking and iterative counterexample-guided abstraction refinement, etc.) are restricted to safety properties.  ...  Termination is determined by the well-foundedness of those abstract transitions, and not the absence of loops.  ...  Transition predicate abstraction induces a finite graph where nodes are labeled by abstract transitions.  ... 
doi:10.1007/11817963_37 fatcat:y52cl4ac3nexrioarh5q4u6dgi

Abstraction Refinement for Stability

Parasara Sridhar Duggirala, Sayan Mitra
2011 2011 IEEE/ACM Second International Conference on Cyber-Physical Systems  
Hybrid Systems  Mix of continuous and discrete dynamics  Several modes of operation  System switches modes based on constraints  Trajectories (τ) and Discrete Transitions  Execution sequences -τ 0  ...  Hybrid System A stable set S Blocking Property of Hybrid Step relation H r Well Founded Relations for proving termination Software Verification  ...  R' Hybrid Step Relation -well foundedness  For a state transition system (s,t)  ... 
doi:10.1109/iccps.2011.24 dblp:conf/iccps/DuggiralaM11 fatcat:uqzjk452mvgftlfx7moaf3xqua

Lyapunov abstractions for inevitability of hybrid systems

Parasara Sridhar Duggirala, Sayan Mitra
2012 Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control - HSCC '12  
The algorithm combines (a) Lyapunov function-based relational abstractions for the continuous dynamics with (b) automated construction of well-founded relations for the loops of the hybrid automaton.  ...  The algorithm is implemented in a prototype tool (LySHA ) which is integrated with a Simulink/Stateflow frontend for modeling hybrid systems.  ...  In [23] , transitional abstractions (relational abstractions) were used to prove safety properties of the systems.  ... 
doi:10.1145/2185632.2185652 dblp:conf/hybrid/DuggiralaM12 fatcat:u62y52byy5f6fnqtpq4yuidlee

Guided Invariant Model Checking Based on Abstraction and Symbolic Pattern Databases [chapter]

Kairong Qian, Albert Nymeyer
2004 Lecture Notes in Computer Science  
system.  ...  We implement this approach in NuSMV and evaluate it using 2 well-known circuit benchmarks.  ...  As well, the refinement of an abstract system can be computationally expensive.  ... 
doi:10.1007/978-3-540-24730-2_37 fatcat:ip5kik2kdzaexinrt4shk5clvu

A Verification Toolkit for Numerical Transition Systems [chapter]

Hossein Hojjat, Filip Konečný, Florent Garnier, Radu Iosif, Viktor Kuncak, Philipp Rümmer
2012 Lecture Notes in Computer Science  
The FLATA system is based on precise acceleration of the transition relation, while the ELDARICA system is based on predicate abstraction with interpolation-based counterexample-driven refinement.  ...  This paper presents a publicly available toolkit and a benchmark suite for rigorous verification of Integer Numerical Transition Systems (INTS), which can be viewed as control-flow graphs whose edges are  ...  We have developed a toolkit for producing and manipulating such representations, as well as two very different analyzers that can analyze such transition systems.  ... 
doi:10.1007/978-3-642-32759-9_21 fatcat:pl2w3gucnrgq3mcvaewbpoamem

Generating finite-state abstractions of reactive systems using decision procedures [chapter]

Michael A. Colón, Tomás E. Uribe
1998 Lecture Notes in Computer Science  
The algorithm compositionally abstracts the transitions of the system, relative to a given, fixed set of assertions.  ...  We present an algorithm that uses decision procedures to generate finite-state abstractions of possibly infinite-state systems.  ...  Introduction An attractive method for proving a temporal property ϕ for a reactive system S is to find a simpler abstract system A such that if A satisfies ϕ, then S satisfies ϕ as well.  ... 
doi:10.1007/bfb0028753 fatcat:3ezydqi3vjgynl7s7b4bntohta

Synthia: Verification and Synthesis for Timed Automata [chapter]

Hans-Jörg Peter, Rüdiger Ehlers, Robert Mattmüller
2011 Lecture Notes in Computer Science  
Our experiments show that the analysis of both closed and open systems greatly benefits from identifying large relevant and irrelevant system parts on coarse abstractions early in the solution process.  ...  of binary decision diagrams (BDDs) for the discrete parts of the system description.  ...  Introduction A crucial factor for the acceptance of automatic system analysis techniques is how well they scale when the models become more complex.  ... 
doi:10.1007/978-3-642-22110-1_52 fatcat:v3vmyymgonfpha6hn7dnzdiev4

All for the Price of Few [chapter]

Parosh Aziz Abdulla, Frédéric Haziza, Lukáš Holík
2013 Lecture Notes in Computer Science  
We show that the method is complete for a large class of well quasi-ordered systems including Petri nets.  ...  It relies on an abstraction function that views the system from the perspective of a fixed number of processes.  ...  We have proved that the presented algorithm is complete for a wide class of well quasi-ordered systems.  ... 
doi:10.1007/978-3-642-35873-9_28 fatcat:wx5okrcigzhfvc76x6iosisvmy

Environment Abstraction for Parameterized Verification [chapter]

Edmund Clarke, Muralidhar Talupur, Helmut Veith
2005 Lecture Notes in Computer Science  
transition systems which can be verified by a finite state model checker.  ...  Environment abstraction enriches predicate abstraction by ideas from counter abstraction; it enables us to reduce concurrent parameterized systems with unbounded variables to precise abstract finite state  ...  In our framework, the abstract model does have a transition relation, and we can verify liveness properties as well as safety properties.  ... 
doi:10.1007/11609773_9 fatcat:4ebjs3zw6vf5lfe7qvvemyrgpu

Structural Counter Abstraction [chapter]

Kshitij Bansal, Eric Koskinen, Thomas Wies, Damien Zufferey
2013 Lecture Notes in Computer Science  
Depth-Bounded Systems form an expressive class of well-structured transition systems.  ...  This numerical abstraction can be analyzed with existing termination provers. What makes our approach unique is the way in which it exploits the well-structuredness of the analyzed system.  ...  (Well-Structured) Labeled Transition Systems.  ... 
doi:10.1007/978-3-642-36742-7_5 fatcat:xhaslsqws5dvjnlwb3syfl6ray
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