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Constraint-Based Abstract Semantics for Temporal Logic: A Direct Approach to Design and Implementation [chapter]

Gourinath Banda, John P. Gallagher
2010 Lecture Notes in Computer Science  
Then we show that this leads directly to an effective implementation of an abstract model checking algorithm for CTL using abstract domains based on linear constraints.  ...  The abstract semantic function is constructed directly from the standard concrete semantics together with a Galois connection between the concrete state-space and an abstract domain.  ...  We gratefully acknowledge discussions with Dennis Dams, César Sánchez, Kim Guldstrand Larsen and suggestions by the LPAR-16 referees.  ... 
doi:10.1007/978-3-642-17511-4_3 fatcat:fqim7etzrnaf7gbljd2x7quobe

Abstraction, Up-To Techniques and Games for Systems of Fixpoint Equations

Paolo Baldan, Barbara König, Tommaso Padoan, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
The game view opens the way for the development of local algorithms for characterising the solution of such equation systems and we explore some special cases.  ...  In this paper we develop a theory of approximation for systems of fixpoint equations in the style of abstract interpretation: a system over some concrete domain is abstracted to a system in a suitable  ...  ., f (x) = f * (x) c for some c ∈ L and f * , f * : L → L a Galois connection.  ... 
doi:10.4230/lipics.concur.2020.25 dblp:conf/concur/Baldan0P20 fatcat:ntk5jqiye5buxfc6gs22phblny

Data flow analysis is model checking of abstract interpretations

David A. Schmidt
1998 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '98  
In particular, the classic %ow equations for bit-vector-based d-Jo. s reformat trivially into modal mu-Cal&us formulas., A surprising consequence is that two of the classical d&a. s are exposed as unsound  ...  Kozen's modal mu-calculus to express trace properties, we express in simplest possible terms that a d&a. is a model check of a program's a.i. trace.  ...  calculus formula, not just a bit-vector-based one.  ... 
doi:10.1145/268946.268950 dblp:conf/popl/Schmidt98 fatcat:2muvgfeo6bhvva6gnqkukobs7e

Program Analysis as Model Checking of Abstract Interpretations [chapter]

David Schmidt, Bernhard Steffen
1998 Lecture Notes in Computer Science  
In some places the tools are interchangeable; in others, one tool clearly plays a singular role.  ...  To understand the connections between flow analysis and model checking, a third component, abstraction, more precisely, abstract interpretation, must be used.  ...  Acknowledgements We are grateful to Tiziana Margaria for proof reading, to Markus Müller-Olm for his constructive criticism, and to Andreas Holzmann for his support in the type setting.  ... 
doi:10.1007/3-540-49727-7_22 fatcat:ogozwspwqvchdh3tz5olcbkmtq

Calculating Graph Algorithms for Dominance and Shortest Path [chapter]

Ilya Sergey, Jan Midtgaard, Dave Clarke
2012 Lecture Notes in Computer Science  
Both algorithms are calculated directly from the definition of the properties by fixed-point fusion of (1) a least fixed point expressing all finite paths through a directed graph and (2) Galois connections  ...  of abstract interpretation.  ...  Finally, we want to express our gratitude to Shin-Cheng Mu for his dedication to bring out the best of the paper.  ... 
doi:10.1007/978-3-642-31113-0_8 fatcat:muedzvckavcm3c7prbxc7sqjbu

Partial model checking via abstract interpretation

N. De Francesco, G. Lettieri, L. Martini, G. Vaglini
2010 Information Processing Letters  
Nowadays the emphasis in software engineering research is on the evolution of pre-existing sub-systems and component development.  ...  Given P and L, the set of all transition systems that, composed with P and restricted by L, satisfy ϕ, is modeled as the abstract semantics of ϕ, parametric with respect to P and L.  ...  The general problem of formula synthesis has been solved by Andersen in [1] through the partial model checking technique for the full mu-calculus.  ... 
doi:10.1016/j.ipl.2009.10.014 fatcat:emsnlqp2mrhpnnarbayuf57wca

Underapproximating Predicate Transformers [chapter]

David A. Schmidt
2006 Lecture Notes in Computer Science  
We study four such domains -two are based on "set inclusion" approximation, and two are based on "quantification" approximation -and we apply the domains to synthesize the most precise, underapproximating  ...  Because predicate transformers operate on state sets, we define appropriate powerdomains for sound approximation.  ...  The referees gave many useful comments.  ... 
doi:10.1007/11823230_9 fatcat:rqefsrxykzbnhlerovqgrtcfkq

A practical technique for process abstraction [chapter]

Glenn Bruns
1993 Lecture Notes in Computer Science  
The results presented here allow direct simplification of process terms for some important classes of temporal properties.  ...  Most previous work on this problem is based on property-preserving mappings between transition systems.  ...  Acknowledgements I would like to thank Colin Stirling for suggesting this line of research and for many helpful discussions on the subject.  ... 
doi:10.1007/3-540-57208-2_4 fatcat:3dtspjt66bf5lns2rv2zhl4toe

Incompleteness of States w.r.t. Traces in Model Checking [article]

Roberto Giacobazzi, Francesco Ranzato
2005 arXiv   pre-print
This derives from a number of results, one for each incomplete logical/temporal connective of the mu*-calculus, that characterize the structure of models, i.e. transition systems, whose corresponding state-based  ...  The standard state-based semantics of the mu*-calculus is an abstract interpretation of its trace-based semantics, which turns out to be incomplete (i.e., trace-incomplete), even for finite systems.  ...  This work is an extended and revised version of two conference papers [14, 20] and was partially supported by the FIRB Project RBAU018RCZ "Abstract interpretation and model checking for the verification  ... 
arXiv:cs/0404048v2 fatcat:233dclvkizfgzh7cqj5v4mjb24

Closed and Logical Relations for Over- and Under-Approximation of Powersets [chapter]

David A. Schmidt
2004 Lecture Notes in Computer Science  
Almost all Galois-connection-based static analyses are over-approximating: For Galois connection, (P(C), ⊆) α o , γ (A, A ), an abstract value a ∈ A proclaims a property of all the outputs of a program  ...  We redevelop and extend Dams's results on over-and underapproximation with higher-order Galois connections: (1) We show how Galois connections are generated from U-GLB-L-LUBclosed binary relations, and  ...  Tino Cortesi, Patrick Cousot, Dennis Dams, and the referees made useful comments.  ... 
doi:10.1007/978-3-540-27864-1_5 fatcat:rgfw7yztsnczbgsyfiiscki56q


1974 Historia Mathematica  
Based on a doctoral thesis at George Peabody College for Teachers.  ...  (Abstracted by David E Zitarelli) DASTON, Lorraine 1973 Evariste Galois and the Acadgmie des Sciences Synthesis l(2), 11-13 E GALOIS.  ... 
doi:10.1016/0315-0860(74)90196-7 fatcat:vz3xwkbqevg3xni7jbwhyyolby

Programming from Galois Connections [chapter]

Shin-Cheng Mu, José Nuno Oliveira
2011 Lecture Notes in Computer Science  
This applies in particular to specifications written in the form of Galois connections, in which one of the adjoints delivers the optimal solution.  ...  defining a broad class of solutions (the easy part) and the other requesting one particular such solution, optimal in some sense (the hard part).  ...  Special thanks go to Roland Backhouse for spotting the Galois connection of take, which triggered talk [20] and interesting discussions at IFIP WG2.1 thereupon.  ... 
doi:10.1007/978-3-642-21070-9_22 fatcat:tfn6noys65hd5kxgduehjwwikq

Injecting Abstract Interpretations into Linear Cost Models

David Cachera, Arnaud Jobin
2010 Electronic Proceedings in Theoretical Computer Science  
Abstraction has to take two distinct notions of order into account: the order on costs and the order on states.  ...  We present a semantics based framework for analysing the quantitative behaviour of programs with regard to resource usage. We start from an operational semantics equipped with costs.  ...  Even if we managed to get residuated pairs for translating Galois connection into a linear model, the correctness of cost computations for a lifted Galois connection is defined only for its linear part  ... 
doi:10.4204/eptcs.28.5 fatcat:epfvpgtmy5getoi64efbfhtqya

Programming from Galois connections

Shin-Cheng Mu, José Nuno Oliveira
2012 The Journal of Logic and Algebraic Programming  
This applies in particular to specifications written in the form of Galois connections, in which one of the adjoints delivers the optimal solution.  ...  defining a broad class of solutions (the easy part) and the other requesting one particular such solution, optimal in some sense (the hard part).  ...  Special thanks go to Roland Backhouse for spotting the Galois connection of take, which triggered talk [20] and interesting discussions at IFIP WG2.1 thereupon.  ... 
doi:10.1016/j.jlap.2012.05.003 fatcat:eekpaf2tpjgwjlrkg5civnjmfy

Contracts in CML [chapter]

Jim Woodcock, Ana Cavalcanti, John Fitzgerald, Simon Foster, Peter Gorm Larsen
2014 Lecture Notes in Computer Science  
The semantics of CML directly supports the use of these contracts for all language constructs, including the use of communication channels, parallel processes, and processes that run forever.  ...  We describe the COMPASS Modelling Language (CML), which is used to model large-scale Systems of Systems and the contracts that bind them together.  ...  One purpose of a Galois connection is to embed one theory within another, and this is what gives the compositional avour of UTP and CML, since Galois connections compose to form other Galois connections  ... 
doi:10.1007/978-3-662-45231-8_5 fatcat:a7rqhg5jonesnhghaltkmgfxhq
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