Symbolic Model Generation for Graph Properties

Abstract

Graphs are ubiquitous in Computer Science. For this reason, in many areas, it is very important to have the means to express and reason about graph properties. In particular, we want to be able to check automatically if a given graph property is satisfiable. Actually, in most application scenarios it is desirable to be able to explore graphs satisfying the graph property if they exist or even to get a complete and compact overview of the graphs satisfying the graph property. We show that the tableau-based reasoning method for graph properties as introduced by Lambers and Orejas paves the way for a symbolic model generation algorithm for graph properties. Graph properties are formulated in a dedicated logic making use of graphs and graph morphisms, which is equivalent to first-order logic on graphs as introduced by Courcelle. Our parallelizable algorithm gradually generates a finite set of so-called symbolic models, where each symbolic model describes a set of finite graphs (i.e., finite models) satisfying the graph property. The set of symbolic models jointly describes all finite models for the graph property (complete) and does not describe any finite graph violating the graph property (sound). Moreover, no symbolic model is already covered by another one (compact). Finally, the algorithm is able to generate from each symbolic model a minimal finite model immediately and allows for an exploration of further finite models. The algorithm is implemented in the new tool AutoGraph.

A graph solver for the automated generation of consistent domain-specific models

“…Symbolic Model Generation Technique Certain techniques use abstract (or symbolic) graphs for analysis purposes. A tableaubased reasoning method is proposed for graph properties [72][73][74], which automatically refine solutions based on well-formedness constraints, and handle state space in the form of a resolution tree. As a key difference, our approach refines possible solutions in the form of partial models, while [72,73] resolves the graph constraints to a concrete solution.…”

Analysis of Graph Transformation Systems: Native vs Translation-based Techniques

“…We have found a few experimental comparisons in the literature with respect to following a native versus translation-based approach for solving particular graph transformation analysis problems. In particular, we describe the main findings of such an experimental comparison for model checking graph transformation systems [59], constraint verification applied to pre-and post-condition reasoning [51], constraint verification applied to invariant checking [9], and constraint verification in the sense of satisfiability solving and automated reasoning [65,63].…”

“…There exist a number of example native approaches as well as translation-based approaches to both problems. For example, Pennemann [50] presents a native theorem prover, whereas Schneider et al [63] and Semerth et al [65] present native SAT solvers for graph conditions. Example translation-based approaches [39,28,66] map the SAT solving problem to target domains such as relational logic [35] and constraint logic programming.…”

“…We conclude with describing another experimental comparison to SAT solving [63], again of a native approach implemented in the tool AutoGraph and translation-based approach using Alloy [35] focusing efficiency as well as conciseness of the generated solutions. In particular, the authors write "AutoGraph is capable of obtaining minimal, symbolic models, which allow for a straightforward exploration of further models whereas Alloy generates models for a given scope not necessarily determining minimal models.…”

“…Several approaches to instance generation, including [64,66,63], have been discussed in Section 4.3. In what follows, we consider a few translation-based approaches to instance generation which use existing SAT/SMT solvers.…”