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Graph-transformation verification using monadic second-order logic

2011
*
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming - PPDP '11
*

We tackle the problem by first reformulating the semantics of UnCAL into

doi:10.1145/2003476.2003482
dblp:conf/ppdp/InabaHHKN11
fatcat:p5sehv2ycnfazp24dxxz4w3sxm
*monadic**second*-*order**logic*(MSO). ... This paper presents a new approach to solving the problem of*verification*of*graph**transformation*, by proposing a new static*verification*algorithm for the Core UnCAL, the query algebra for*graph*-structured ...*GRAPH*SCHEMA IN MSO We employ powerful*monadic**second*-*order**logic*(MSO) to describe a*graph*schema which specifies structural constrains of*graphs*. ...##
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Semantical Evaluations as Monadic Second-Order Compatible Structure Transformations
[chapter]

2002
*
Lecture Notes in Computer Science
*

A

doi:10.1007/3-540-45931-6_1
fatcat:fwtgkhd46bcctobt34roiou6ou
*transformation*of structures τ is*monadic**second*-*order*compatible (MS-compatible) if every*monadic**second*-*order*property P can be effectively rewritten into a*monadic**second*-*order*property Q such that ... We will review*Monadic**Second*-*order*definable transductions (MS-transductions): they are MS-compatible*transformations*of a particular form, i.e., defined by*monadic**second*-*order*(MS) formulas. ... Overview of the Lecture Our working*logical*language is*Monadic**Second*-*Order**Logic*, i.e., the extension of First-*Order**Logic*with variables denoting sets of elements of the considered structures. ...##
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Verifying a Behavioural Logic for Graph Transformation Systems

2004
*
Electronical Notes in Theoretical Computer Science
*

The properties can be expressed in a temporal

doi:10.1016/j.entcs.2004.08.018
fatcat:q25djbt4ozfpjgj4ac7svx3zwa
*logic*which is basically a µ-calculus where the state predicates are formulae of a*monadic**second**order**logic*, describing*graph*properties. ... We propose a framework for the*verification*of behavioural properties of systems modelled as*graph**transformation*systems. ... In the rest of the paper, after introducing the class of*graph**transformation*systems handled by our approach, we will present the*monadic**second*-*order**logic*L2 of*graph*formulae, and the temporal*logic*...##
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Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects
[chapter]

2008
*
Lecture Notes in Computer Science
*

Hierarchical decompositions yielding the notions of tree-width and clique-width, expressed by terms written with appropriate

doi:10.1007/978-3-540-70575-8_1
fatcat:ftpcqszcb5fs5nswbqnbnmy5ja
*graph*operations and associated with*Monadic**Second*-*order**Logic*are important ...*Graph*structure is a flexible concept covering many different types of*graph*properties. ... Walukiewicz for many*useful*comments on a first draft of this overview. The first 11 references are books and survey articles. ...##
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Verification of Pointers

1994
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DAIMI Report Series
*

Such properties seemed to have called for a full Hoare

doi:10.7146/dpb.v23i470.6943
fatcat:i34abcwqwvhltn3fuvkck5cizm
*logic*beyond the reach of type checking and decidability.</p><p> </p><p>Our work is based on*monadic**second*-*order**logic*. ... Thus*verification*boils down to calculations on finite-state automata. ... Our Approach We*use**monadic**second*-*order**logic*on trees to specify the stores. ...##
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Mosel: A flexible toolset for monadic second-order logic
[chapter]

1997
*
Lecture Notes in Computer Science
*

MOSEL is a new tool-set for the analysis and

doi:10.1007/bfb0035388
fatcat:negr5oz64vfkdknlmxdk7mzktm
*verification*in*Monadic**Second*-*order*kogic. ... At the moment we have implemented in MOSEL a semantic decision procedure for*monadic**second*-*order**logic*over finite strings and a set of interface modules. ... In this paper we present MOSEL, a new system for the automatic analysis and*verification*in*Monadic**Second*-*order*[ogic. ...##
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Decidable logics combining heap structures and data

2011
*
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '11
*

relations over trees, and are of the form ∃ x∀ yϕ( x, y), where ϕ is a

doi:10.1145/1926385.1926455
dblp:conf/popl/MadhusudanPQ11
fatcat:42slcx4kh5b7fabsayvkffxk3e
*monadic**second*-*order**logic*(MSO) formula with additional quantification that combines structural constraints as well as data-constraints ... We define a new*logic*, STRAND, that allows reasoning with heapmanipulating programs*using*deductive*verification*and SMT solvers. ... This phase is effected by*using*MONA [13] , a*monadic**second*-*order**logic*solver over (strings and) trees. ...##
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Decidable logics combining heap structures and data

2011
*
SIGPLAN notices
*

relations over trees, and are of the form ∃ x∀ yϕ( x, y), where ϕ is a

doi:10.1145/1925844.1926455
fatcat:ejzbctzpafhoxemin6wstjkr5a
*monadic**second*-*order**logic*(MSO) formula with additional quantification that combines structural constraints as well as data-constraints ... We define a new*logic*, STRAND, that allows reasoning with heapmanipulating programs*using*deductive*verification*and SMT solvers. ... This phase is effected by*using*MONA [13] , a*monadic**second*-*order**logic*solver over (strings and) trees. ...##
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Specification and Verification of Modal Properties for Structured Systems
[chapter]

2012
*
Lecture Notes in Computer Science
*

We consider visual specification formalisms like

doi:10.1007/978-3-642-33654-6_31
fatcat:jdv3e4aqajafvkt52zy3ibzpai
*graph**transformation*systems (GTS) where program states are modelled as*graphs*, and the program behaviour is specified by*graph**transformation*rules. ... System specification formalisms should come with suitable property specification languages and effective*verification*tools. ... State-of-the-art in GTS*Logics*After the pioneering works on*monadic**second*-*order**logic*(MSO) [7] , various*graph**logics*have been proposed and their connection with topological properties of*graphs*investigated ...##
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A Logic for Analyzing Abstractions of Graph Transformation Systems
[chapter]

2003
*
Lecture Notes in Computer Science
*

In this paper we introduce a

doi:10.1007/3-540-44898-5_14
fatcat:okcaxneuffc53kvq4rbbafm4vm
*monadic**second*-*order**logic*over*graphs*expressive enough to characterise typical*graph*properties, and we show how its formulae can be effectively verified. ... This allows*us*to reuse existing*verification*techniques, originally developed for Petri nets, to model-check the*logic*, suitably enriched with temporal operators. ... A*Second*-*Order**Monadic**Logic*for*Graphs*We introduce the*monadic**second*-*order**logic*L2 for specifying*graph*properties. Quantification is allowed over edges, but not over nodes (as, e.g., in [4] ). ...##
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Dijkstra Monads for All
[article]

2019
*
arXiv
*
pre-print

This paper proposes a general semantic framework for verifying programs with arbitrary

arXiv:1903.01237v4
fatcat:rpvq42xi3ng3hgyhfd4gz6gybe
*monadic*side-effects*using*Dijkstra*monads*, which we define as*monad*-like structures indexed by a specification*monad*... We moreover show that a large variety of specification*monads*can be obtained by applying*monad**transformers*to various base specification*monads*, including predicate*transformers*and Hoare-style pre- ... In*order*to prevent confusion, we*use*the term "Dijkstra*monad*" exclusively for the indexed structure D and the term "specification*monad*" for the index W . ...##
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Automatic verification of pointer programs using monadic second-order logic

1997
*
SIGPLAN notices
*

We present a technique for automatic

doi:10.1145/258916.258936
fatcat:5fjsajngnzaq5c5buf7gq4jmxi
*verification*of pointer programs based on a decision procedure for the*monadic**second*-*order**logic*on finite strings. ... The resulting system can be*used*to verify extensive properties of smaller pointer programs and could be particularly*useful*in a teaching environment. * detex paper.tex | wc | cut -d' ' -f2 = 4821 ...*Using**Monadic**Second*-*Order**Logic*Our implementation is based on the*monadic**second*-*order**logic*on finite strings (M2L), which is an inordinately succinct notation for specifying regular sets [16] . ...##
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Automatic verification of pointer programs using monadic second-order logic

1997
*
Proceedings of the ACM SIGPLAN 1997 conference on Programming language design and implementation - PLDI '97
*

We present a technique for automatic

doi:10.1145/258915.258936
dblp:conf/pldi/JensenJKS97
fatcat:dua6z4pijjblzivat55zpysemy
*verification*of pointer programs based on a decision procedure for the*monadic**second*-*order**logic*on finite strings. ... The resulting system can be*used*to verify extensive properties of smaller pointer programs and could be particularly*useful*in a teaching environment. * detex paper.tex | wc | cut -d' ' -f2 = 4821 ...*Using**Monadic**Second*-*Order**Logic*Our implementation is based on the*monadic**second*-*order**logic*on finite strings (M2L), which is an inordinately succinct notation for specifying regular sets [16] . ...##
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Composition of Path Transductions
[chapter]

2004
*
Lecture Notes in Computer Science
*

They define strict subclasses of

doi:10.1007/978-3-540-30203-2_26
fatcat:rmak6wmv5nfnfprviv6awj7iya
*monadic*transductions and preserve the decidability of*monadic**second**order*theory. ... These*graph**transformations*are based on path substitutions and*graph*products. ... Let G be a*graph*and let H = T 2 (T 1 (G)) hence Acknowledgement I would like to thank the referees (especially one) for their numberous remarks. ...##
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The Pointer Assertion Logic Engine

2000
*
BRICS Report Series
*

We work in the

doi:10.7146/brics.v7i39.20205
fatcat:e3y3m6uwv5futax4nh7nhoufey
*logical*tradition by encoding the programs and partial specifications as formulas in*monadic**second*-*order**logic*. ... Our technique can verify a large class of data structures, namely all those that can be expressed as*graph*types. Earlier versions were restricted to simple<br />special cases such as lists or trees. ... Program Annotations Pointer Assertion*Logic*is a*monadic**second*-*order**logic*on*graph*types. ...
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