Methodology for testing and validating knowledge bases

A test and validation toolset developed for artificial intelligence programs is described. The basic premises of this method are: (1) knowledge bases have a strongly declarative character and represent mostly structural information about different domains, (2) the conditions for integrity, consistency, and correctness can be transformed into structural properties of knowledge bases, and (3) structural information and structural properties can be uniformly represented by graphs and checked by graph algorithms. The interactive test and validation environment have been implemented on a SUN workstation

Automated verification of termination certificates

In order to increase user confidence, many automated theorem provers provide certificates that can be independently verified. In this paper, we report on our progress in developing a standalone tool for checking the correctness of certificates for the termination of term rewrite systems, and formally proving its correctness in the proof assistant Coq. To this end, we use the extraction mechanism of Coq and the library on rewriting theory and termination called CoLoR

Computing Persistent Homology within Coq/SSReflect

Persistent homology is one of the most active branches of Computational Algebraic Topology with applications in several contexts such as optical character recognition or analysis of point cloud data. In this paper, we report on the formal development of certified programs to compute persistent Betti numbers, an instrumental tool of persistent homology, using the Coq proof assistant together with the SSReflect extension. To this aim it has been necessary to formalize the underlying mathematical theory of these algorithms. This is another example showing that interactive theorem provers have reached a point where they are mature enough to tackle the formalization of nontrivial mathematical theories

Binary-Compatible Verification of Filesystems with ACL2

Filesystems are an essential component of most computer systems. Work on the verification of filesystem functionality has been focused on constructing new filesystems in a manner which simplifies the process of verifying them against specifications. This leaves open the question of whether filesystems already in use are correct at the binary level. This paper introduces LoFAT, a model of the FAT32 filesystem which efficiently implements a subset of the POSIX filesystem operations, and HiFAT, a more abstract model of FAT32 which is simpler to reason about. LoFAT is proved to be correct in terms of refinement of HiFAT, and made executable by enabling the state of the model to be written to and read from FAT32 disk images. EqFAT, an equivalence relation for disk images, considers whether two disk images contain the same directory tree modulo reordering of files and implementation-level details regarding cluster allocation. A suite of co-simulation tests uses EqFAT to compare the operation of existing FAT32 implementations to LoFAT and check the correctness of existing implementations of FAT32 such as the mtools suite of programs and the Linux FAT32 implementation. All models and proofs are formalized and mechanically verified in ACL2