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A Relational Shape Abstract Domain [chapter]

Hugo Illous, Matthieu Lemerre, Xavier Rival
2017 Lecture Notes in Computer Science  
On the other hand, designing abstractions for relations over memory states and taking shapes into account is challenging.  ...  Using these connectives, we build an abstract domain and design a static analysis that over-approximates relations over memory states containing inductive structures.  ...  abstract domain.  ... 
doi:10.1007/978-3-319-57288-8_15 fatcat:jxtdsz7d2nbcha4hse4xzub5ky

Modular Construction of Shape-Numeric Analyzers

Bor-Yuh Evan Chang, Xavier Rival
2013 Electronic Proceedings in Theoretical Computer Science  
We set up an abstract interpretation framework that allows us to reason about simultaneous shape-numeric properties by combining shape and numeric abstractions into a modular, expressive abstract domain  ...  To achieve this, we choose a concrete semantics that can be abstracted step-by-step, while preserving a high level of expressiveness.  ...  We would also wish to thank Dave for being a pillar in the static analysis community and supporting the research community with often thankless, behind-the-scenes work.  ... 
doi:10.4204/eptcs.129.11 fatcat:uj6xzhfufbgxbkhrlz4hxcenwi

Learning to Make Analogies by Contrasting Abstract Relational Structure [article]

Felix Hill, Adam Santoro, David G.T. Barrett, Ari S. Morcos and Timothy Lillicrap
2019 arXiv   pre-print
The most robust capacity for analogical reasoning is induced when networks learn analogies by contrasting abstract relational structures in their input domains, a training method that uses only the input  ...  Analogy is particularly challenging for machines because it requires relational structures to be represented such that they can be flexibly applied across diverse domains of experience.  ...  (shape colour) N/A N/A N/A Target Domain (shape colour) ?  ... 
arXiv:1902.00120v1 fatcat:ht2muuoxufgsrcyyeyfq763rvu

2LS: Heap Analysis and Memory Safety [chapter]

Viktor Malík, Peter Schrammel, Tomáš Vojnar
2020 Lecture Notes in Computer Science  
The paper presents the main improvements done in 2LS since 2018, which concern mainly the way 2LS handles dynamically allocated objects and structures as well as combinations of abstract domains.  ...  2LS is a framework for analysis of sequential C programs based on the CPROVER infrastructure and template-based synthesis techniques for checking both safety and termination.  ...  We build on the shape domain presented in 2018 [5] and introduce abstract domain combinations that allow us to analyse both shape and content of dynamic data structures.  ... 
doi:10.1007/978-3-030-45237-7_22 fatcat:trxnjctgyjgbzh3c3ckjzjpbiy

Widening Operators for Weakly-Relational Numeric Abstractions (Extended Abstract) [article]

Roberto Bagnara, Patricia M. Hill, Elena Mazzi, Enea Zaffanella
2004 arXiv   pre-print
We discuss the divergence problems recently identified in some extrapolation operators for weakly-relational numeric domains.  ...  We identify the cause of the divergences and point out that resorting to more concrete, syntactic domains can be avoided by researching suitable algorithms for the elimination of redundant constraints  ...  Other examples of weakly-relational numeric domains include the 'two variables per inequality' abstract domain [20] , the octahedron abstract domain [8] , and the abstract domain of template constraint  ... 
arXiv:cs/0412043v1 fatcat:d4cxzq4x6nacbkxqwzzvxfkreu

From Shape Analysis to Termination Analysis in Linear Time [chapter]

Roman Manevich, Boris Dogadov, Noam Rinetzky
2016 Lecture Notes in Computer Science  
Our algorithm can be used as a post-processing phase of any shape analysis satisfying some natural properties.  ...  The algorithm proves the existence of the well-founded relation over states by showing that in every loop iteration at least one object (which was allocated before entering the loop) moves to a strictly  ...  Let (S, γ) be a shape domain. An abstract transition relation τ ⊆ S × S is a binary relation over abstract states.  ... 
doi:10.1007/978-3-319-41528-4_23 fatcat:hhr5skypnnabhkutmxoxbnpkxi

2LS: Heap Analysis and Memory Safety (Competition Contribution) [article]

Viktor Malik, Martin Hruska, Peter Schrammel, Tomas Vojnar
2020 arXiv   pre-print
2LS is a framework for analysis of sequential C programs that can verify and refute program assertions and termination.  ...  The main improvements in this year's version are the ability of 2LS to analyse programs requiring combined reasoning about shape and content of dynamic data structures, and an instrumentation for memory  ...  We build on the shape domain presented last year [5] and introduce abstract domain combinations that allow us to analyse both shape and content of dynamic data structures.  ... 
arXiv:1903.00712v2 fatcat:dy3qn7vwuvgkvjxk2kqzxin3za

Towards Abstraction-Based Verification of Shape Calculus

F. Buti, M. Callisto De Donato, F. Corradini, M.R. Di Berardini, E. Merelli, L. Tesei
2012 Electronical Notes in Theoretical Computer Science  
Other possible abstract domains for the verification of more expressive properties are also discussed.  ...  The Shape Calculus is a bio-inspired timed and spatial calculus for describing 3D geometrical shapes moving in a space.  ...  Definition 3 . 2 ( 32 Abstract Domain) The abstract domain is denoted A and it is the complete lattice (℘(3DP ), ⊆, ∪, ∩, {}, 3DP ).  ... 
doi:10.1016/j.entcs.2012.05.013 fatcat:vt3hyd5kdbh7fgreoocqulsraq

What Programs Want: Automatic Inference of Input Data Specifications [article]

Caterina Urban
2020 arXiv   pre-print
The choice of these abstract domain is a parameter of the analysis. We describe various instances built from existing abstract domains.  ...  In this paper, we propose a static shape analysis framework for input data of data-processing programs.  ...  Non-Relational Constraining Abstract Domains In the following, we present a few instances of non-relational constraining domains. These domains abstract each program variable independently.  ... 
arXiv:2007.10688v1 fatcat:2tcqlg5qnfhsbbohkqd3ygllbu

Lattice Automata: A Representation for Languages on Infinite Alphabets, and Some Applications to Verification [chapter]

Tristan Le Gall, Bertrand Jeannet
2007 Lecture Notes in Computer Science  
This paper proposes a new abstract domain for languages on infinite alphabets, which acts as a functor taking an abstract domain for a concrete alphabet and lift it to an abstract domain for words on this  ...  We define a normal form, standard language operations and a widening operator for these automata.  ...  The resulting abstract domain allows to lift any atomic abstract domain A for ℘(S) to an abstract domain Reg(A) for ℘(S * ).  ... 
doi:10.1007/978-3-540-74061-2_4 fatcat:x3aeq7y775avzc3zjiol3jgkwe

Relational inductive shape analysis

Bor-Yuh Evan Chang, Xavier Rival
2008 Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '08  
Around this domain, we build a shape analysis whose interesting components include a pre-analysis on the user-supplied specifications that guides the abstract interpretation and a widening operator over  ...  In this paper, we identify issues inherent to analyzing relational structures and design an abstract domain that is parameterized both by an abstract domain for pure data properties and by user-supplied  ...  We extend our earlier work to the relational case and make the following contributions: • We propose a parametric abstract domain for relational inductive shape analysis.  ... 
doi:10.1145/1328438.1328469 dblp:conf/popl/ChangR08 fatcat:yacuthnavzez5diyfbwlmhbmdq

Relational inductive shape analysis

Bor-Yuh Evan Chang, Xavier Rival
2008 SIGPLAN notices  
Around this domain, we build a shape analysis whose interesting components include a pre-analysis on the user-supplied specifications that guides the abstract interpretation and a widening operator over  ...  In this paper, we identify issues inherent to analyzing relational structures and design an abstract domain that is parameterized both by an abstract domain for pure data properties and by user-supplied  ...  We extend our earlier work to the relational case and make the following contributions: • We propose a parametric abstract domain for relational inductive shape analysis.  ... 
doi:10.1145/1328897.1328469 fatcat:pqnkzy6y6rbndccq3js3acxg4i

Hierarchical Shape Abstraction of Dynamic Structures in Static Blocks [chapter]

Pascal Sotin, Xavier Rival
2012 Lecture Notes in Computer Science  
It combines several instances of simple shape abstract domains, dedicated to the representation of elementary shape properties, and also embeds a numerical abstract domain.  ...  We propose a hierarchical shape abstract domain, so as to infer structural invariants of dynamic structures such as lists living inside static structures, such as arrays.  ...  It was implemented as a functor, which lifts a shape abstract domain into a value abstract domain, which can in turn be fed into the shape abstract domain functor.  ... 
doi:10.1007/978-3-642-35182-2_10 fatcat:btyhveet2rbyniq47dn7tzm4pu

On Verifying Complex Properties using Symbolic Shape Analysis [article]

Thomas Wies, Viktor Kuncak, Karen Zee, Andreas Podelski, Martin Rinard
2006 arXiv   pre-print
We describe Bohne, a new analysis for verifying data structures.  ...  This architecture shows that synthesized loop invariants can serve as a useful communication mechanism between different decision procedures.  ...  Symbolic Shape Analysis Following the framework of abstract interpretation [7] , a static analysis is defined by lattice-theoretic domains and by fixpoint iteration over the domains.  ... 
arXiv:cs/0609104v1 fatcat:fvo3jony5ja23fecutl6s5otzu

Reduced Product Combination of Abstract Domains for Shapes [chapter]

Antoine Toubhans, Bor-Yuh Evan Chang, Xavier Rival
2013 Lecture Notes in Computer Science  
In this paper, we lift this idea to abstract domains for shape analyses, introducing a domain combination operator for memory abstractions.  ...  As an example, we present simultaneous separating shape graphs, a product construction that combines instances of separation logic-based shape domains.  ...  Fig. 1 . 1 A complex tree structure Fig. 3 . 3 A shape abstract domain based on exact separating shape graphs. Fig. 4 . 4 A shape abstract domain based on points-to graphs.  ... 
doi:10.1007/978-3-642-35873-9_23 fatcat:52fwich2uvh3pisfd42cytdney
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