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Graph-transformation verification using monadic second-order logic

Kazuhiro Inaba, Soichiro Hidaka, Zhenjiang Hu, Hiroyuki Kato, Keisuke Nakano
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 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.  ...

Semantical Evaluations as Monadic Second-Order Compatible Structure Transformations [chapter]

Bruno Courcelle
2002 Lecture Notes in Computer Science
A 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.  ...

Verifying a Behavioural Logic for Graph Transformation Systems

Paolo Baldan, Andrea Corradini, Barbara König, Bernhard König
2004 Electronical Notes in Theoretical Computer Science
The properties can be expressed in a temporal 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  ...

Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects [chapter]

Bruno Courcelle
2008 Lecture Notes in Computer Science
Hierarchical decompositions yielding the notions of tree-width and clique-width, expressed by terms written with appropriate 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.  ...

Verification of Pointers

Nils Klarlund, Michael I. Schwartzbach
1994 DAIMI Report Series
Such properties seemed to have called for a full Hoare 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.  ...

Mosel: A flexible toolset for monadic second-order logic [chapter]

Peter Kelb, Tiziana Margaria, Michael Mendler, Claudia Gsottberger
1997 Lecture Notes in Computer Science
MOSEL is a new tool-set for the analysis and 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.  ...

Decidable logics combining heap structures and data

P. Madhusudan, Gennaro Parlato, Xiaokang Qiu
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 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.  ...

Decidable logics combining heap structures and data

P. Madhusudan, Gennaro Parlato, Xiaokang Qiu
2011 SIGPLAN notices
relations over trees, and are of the form ∃ x∀ yϕ( x, y), where ϕ is a 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.  ...

Specification and Verification of Modal Properties for Structured Systems [chapter]

Andrea Vandin
2012 Lecture Notes in Computer Science
We consider visual specification formalisms like 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  ...

A Logic for Analyzing Abstractions of Graph Transformation Systems [chapter]

Paolo Baldan, Barbara König, Bernhard König
2003 Lecture Notes in Computer Science
In this paper we introduce a 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] ).  ...

Kenji Maillard, Danel Ahman, Robert Atkey, Guido Martinez, Catalin Hritcu, Exequiel Rivas, Éric Tanter
2019 arXiv   pre-print
This paper proposes a general semantic framework for verifying programs with arbitrary 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 .  ...

Automatic verification of pointer programs using monadic second-order logic

Jakob L. Jensen, Michael E. Jørgensen, Michael I. Schwartzbach, Nils Klarlund
1997 SIGPLAN notices
We present a technique for automatic 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] .  ...

Automatic verification of pointer programs using monadic second-order logic

Jakob L. Jensen, Michael E. Jørgensen, Michael I. Schwartzbach, Nils Klarlund
1997 Proceedings of the ACM SIGPLAN 1997 conference on Programming language design and implementation - PLDI '97
We present a technique for automatic 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] .  ...

Composition of Path Transductions [chapter]

Tanguy Urvoy
2004 Lecture Notes in Computer Science
They define strict subclasses of 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.  ...

The Pointer Assertion Logic Engine

Anders Møller, Michael I. Schwartzbach
2000 BRICS Report Series
We work in the 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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