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Graph-Transformation Verification using Monadic Second-Order Logic

by Kazuhiro Inaba, Soichiro Hidaka, Zhenjiang Hu, Hiroyuki Kato , Keisuke Nakano
"... The 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 databases proposed by Bunemann et al. Given a graph transformation annotated with schema infor ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
information, our algorithm statically verifies that any graph satisfying the input schema is converted by the transformation to a graph satisfying the output schema. We tackle the problem by first reformulating the semantics of UnCAL using monadic second-order logic (MSO). The logic-based foundation allows

The monadic second-order logic of graphs I. Recognizable sets of Finite Graphs

by Bruno Courcelle - Information and Computation , 1990
"... The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic second-order theory of a context-free set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins ..."
Abstract - Cited by 301 (17 self) - Add to MetaCart
an investigation of the monadic second-order logic of graphs and of sets of graphs, using techniques from universal algebra, and the theory of formal languages. (By a graph, we mean a finite directed hyperedge-labelled hypergraph, equipped with a sequence of distinguished vertices.) A survey of this research can

Graph-Query Verification using Monadic Second-Order Logic

by K. Inaba, S. Hidaka, Z. Hu, H. Kato, K. Nakano
"... This paper presents a static verification algorithm for a core subset of UnCAL, the query algebra for graph-structured databases proposed by Bunemann et al. Given a query and input/output schemas, our algorithm statically verifies that any graph satisfying the input schema is converted by the query ..."
Abstract - Cited by 5 (1 self) - Add to MetaCart
by the query to a graph satisfying the output schema. The basic idea is to reformulate the semantics of UnCAL using monadic second-order logic (MSO). The logic-based foundation allows to express the schema satisfaction of transformations as the validity of MSO formulas over graph structures. Furthermore

Hardware Verification using Monadic Second-Order Logic

by David A. Basin, Nils Klarlund - IN COMPUTER AIDED VERIFICATION : 7TH INTERNATIONAL CONFERENCE, CAV '95, LNCS 939 , 1995
"... We show how the second-order monadic theory of strings can be used to specify hardware components and their behavior. This logic admits a decision procedure and counter-model generator based on canonical automata for formulas. We have used a system implementing these concepts to verify, or find e ..."
Abstract - Cited by 26 (10 self) - Add to MetaCart
We show how the second-order monadic theory of strings can be used to specify hardware components and their behavior. This logic admits a decision procedure and counter-model generator based on canonical automata for formulas. We have used a system implementing these concepts to verify, or find

The Expression Of Graph Properties And Graph Transformations In Monadic Second-Order Logic

by B. Courcelle , 1997
"... By considering graphs as logical structures, one... ..."
Abstract - Cited by 162 (40 self) - Add to MetaCart
By considering graphs as logical structures, one...

Monadic Second-order Logic for Parameterized Verification

by Jakob Jensen, Jakob Jensen, Michael Jørgensen, Michael Jrgensen, Nils Klarlund, Nils Klarlund - Basic Research in Computer Science , 1994
"... Much work in automatic verification considers families of similar finite-state systems. But an often overlooked property is that sometimes a single finite-state system can be used to describe a parameterized, infinite family of systems. Thus verification of unbounded state spaces can take place ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
Much work in automatic verification considers families of similar finite-state systems. But an often overlooked property is that sometimes a single finite-state system can be used to describe a parameterized, infinite family of systems. Thus verification of unbounded state spaces can take place

Automatic Verification of Pointer Programs using Monadic Second-Order Logic

by Jakob L. Jensen, Michael E. Jørgensen, Michael I. Schwartzbach, Nils Klarlund - In Proc. ACM PLDI, Las Vegas, NV , 1997
"... We present a technique for automatic verification of pointer programs based on a decision procedure for the monadic second-order logic on finite strings. We are concerned with a while-fragment of Pascal, which includes recursively-defined pointer structures but excludes pointer arithmetic. We define ..."
Abstract - Cited by 63 (8 self) - Add to MetaCart
We present a technique for automatic verification of pointer programs based on a decision procedure for the monadic second-order logic on finite strings. We are concerned with a while-fragment of Pascal, which includes recursively-defined pointer structures but excludes pointer arithmetic. We

MONA: Monadic Second-Order Logic in Practice

by Jesper G. Henriksen, Ole J.L. Jensen, Michael E. Jørgensen, Nils Klarlund, Robert Paige, Theis Rauhe, Anders B. Sandholm - IN PRACTICE, IN TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS, FIRST INTERNATIONAL WORKSHOP, TACAS '95, LNCS 1019 , 1995
"... The purpose of this article is to introduce Monadic Second-order Logic as a practical means of specifying regularity. The logic is a highly succinct alternative to the use of regular expressions. We have built a tool MONA, which acts as a decision procedure and as a translator to finite-state au ..."
Abstract - Cited by 149 (20 self) - Add to MetaCart
The purpose of this article is to introduce Monadic Second-order Logic as a practical means of specifying regularity. The logic is a highly succinct alternative to the use of regular expressions. We have built a tool MONA, which acts as a decision procedure and as a translator to finite

Bounded Model Construction for Monadic Second-Order Logics

by Abdelwaheb Ayari, David Basin - In 12th International Conference on Computer-Aided Verification (CAV’00), number 1855 in LNCS , 2000
"... The monadic logics M2L-Str and WS1S have been successfully used for verification, although they are nonelementary decidable. Motivated by ideas from bounded model checking, we investigate procedures for bounded model construction for these logics. The problem is, given a formula and a bound k, does ..."
Abstract - Cited by 37 (2 self) - Add to MetaCart
The monadic logics M2L-Str and WS1S have been successfully used for verification, although they are nonelementary decidable. Motivated by ideas from bounded model checking, we investigate procedures for bounded model construction for these logics. The problem is, given a formula and a bound k, does

Monadic Second-order Logic for Parameterized Verification

by Deepak Ajwani, Khaled Elbassioni, Sathish Govindarajan, Saurabh Ray - in: Proc. 19th Symp. on Parallelism in Algorithms and Architectures (SPAA , 1994
"... Given a set of points P ⊆ R 2, a conflict-free coloring of P is an assignment of colors to points of P, such that each non-empty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest, and is ..."
Abstract - Cited by 22 (0 self) - Add to MetaCart
Given a set of points P ⊆ R 2, a conflict-free coloring of P is an assignment of colors to points of P, such that each non-empty axis-parallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T. This notion has been the subject of recent interest, and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to bases stations (points), such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R 2 can be conflict-free colored with Õ(n.382+ɛ) colors in expected polynomial time, for any arbitrarily small ɛ> 0. This improves upon the previously known bound of O ( p n log log n/log n).
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