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

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

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

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

By considering graphs as logical structures, one...

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

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

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

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

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).